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Diffstat (limited to 'modules/polynomials/help')
150 files changed, 11792 insertions, 0 deletions
diff --git a/modules/polynomials/help/en_US/addchapter.sce b/modules/polynomials/help/en_US/addchapter.sce new file mode 100755 index 000000000..97bf13cc2 --- /dev/null +++ b/modules/polynomials/help/en_US/addchapter.sce @@ -0,0 +1,11 @@ +// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) 2009 - DIGITEO +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +add_help_chapter("Polynomials",SCI+"/modules/polynomials/help/en_US",%T); + diff --git a/modules/polynomials/help/en_US/bezout.xml b/modules/polynomials/help/en_US/bezout.xml new file mode 100755 index 000000000..6e01106c9 --- /dev/null +++ b/modules/polynomials/help/en_US/bezout.xml @@ -0,0 +1,121 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Serge STEER + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="bezout"> + <refnamediv> + <refname>bezout</refname> + <refpurpose>Bezout equation for polynomials or integers</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[thegcd,U]=bezout(p1,p2)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>p1, p2</term> + <listitem> + <para>two real polynomials or two integer scalars (type equal to 1, 2 or 8)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>thegcd</term> + <listitem> + <para> + scalar of the same type as <literal>p1</literal> and <literal>p2</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para> + <literal>2x2</literal> matrix of the same type as <literal>p1</literal> and <literal>p2</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[thegcd, U] = bezout(p1, p2)</literal> computes the GCD <literal>thegcd</literal> of <literal>p1</literal> and <literal>p2</literal>, and in addition a (2x2) + unimodular matrix <literal>U</literal> such that: + </para> + <para> + <literal>[p1 p2]*U = [thegcd 0]</literal> + </para> + <para> + The lcm of <literal>p1</literal> and <literal>p2</literal> is given by: + </para> + <para> + <literal>p1*U(1,2)</literal> (or <literal>-p2*U(2,2)</literal>) + </para> + <para> + If <literal>p1</literal> or <literal>p2</literal> are given as doubles (type 1), then they are treated as + null degree polynomials. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +// Polynomial case +x = poly(0, 'x'); +p1 = (x+1)*(x-3)^5; +p2 = (x-2)*(x-3)^3; +[thegcd,U] = bezout(p1, p2) +det(U) +clean([p1 p2]*U) +thelcm = p1*U(1,2) +lcm([p1 p2]) + +// Double case +i1 = 2*3^5; +i2 = 2^3*3^2; +[thegcd,U] = bezout(i1, i2) +V = [2^2*3^5 2^3*3^2 2^2*3^4*5]; +[thegcd,U] = gcd(V) +V*U +lcm(V) + +// Integer case +i1 = int32(2*3^5); +i2 = int32(2^3*3^2); +[thegcd,U] = bezout(i1, i2) +V = int32([2^2*3^5 2^3*3^2 2^2*3^4*5]); +[thegcd,U] = gcd(V) +V*U +lcm(V) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="roots">roots</link> + </member> + <member> + <link linkend="simp">simp</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + <member> + <link linkend="lcm">lcm</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/chepol.xml b/modules/polynomials/help/en_US/chepol.xml new file mode 100755 index 000000000..e7cec8330 --- /dev/null +++ b/modules/polynomials/help/en_US/chepol.xml @@ -0,0 +1,50 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="chepol"> + <refnamediv> + <refname>chepol</refname> + <refpurpose>Chebychev polynomial</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Tn]=chepol(n,var)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>n</term> + <listitem> + <para>integer : polynomial order</para> + </listitem> + </varlistentry> + <varlistentry> + <term>var</term> + <listitem> + <para>string : polynomial variable</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Tn</term> + <listitem> + <para> + polynomial in the variable <literal>var</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Recursive implementation of Chebychev polynomial. + <literal>Tn=2*poly(0,var)*chepol(n-1,var)-chepol(n-2,var)</literal> with + <literal>T0=1</literal> and <literal>T1=poly(0,var)</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +chepol(4,'x') + ]]></programlisting> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/cmndred.xml b/modules/polynomials/help/en_US/cmndred.xml new file mode 100755 index 000000000..2d1bd7123 --- /dev/null +++ b/modules/polynomials/help/en_US/cmndred.xml @@ -0,0 +1,58 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="cmndred"> + <refnamediv> + <refname>cmndred</refname> + <refpurpose>common denominator form</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[n,d]=cmndred(num,den)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>num, den</term> + <listitem> + <para>two polynomial matrices of same dimensions</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[n,d]=cmndred(num,den)</literal> computes a polynomial matrix + <literal>n</literal> and a common denominator polynomial <literal>d</literal> + such that: + </para> + <para> + <literal>n/d=num./den</literal> + </para> + <para> + The rational matrix defined by <literal>num./den</literal> is <literal>n/d</literal> + </para> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="simp">simp</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/coeff.xml b/modules/polynomials/help/en_US/coeff.xml new file mode 100755 index 000000000..ec158dc23 --- /dev/null +++ b/modules/polynomials/help/en_US/coeff.xml @@ -0,0 +1,90 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Serge STEER + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="coeff"> + <refnamediv> + <refname>coeff</refname> + <refpurpose>coefficients of matrix polynomial</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[C]=coeff(Mp [,v])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>Mp</term> + <listitem> + <para>polynomial matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>v</term> + <listitem> + <para>integer (row or column) vector of selected degrees</para> + </listitem> + </varlistentry> + <varlistentry> + <term>C</term> + <listitem> + <para>big matrix of the coefficients</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>C=coeff(Mp)</literal> + returns in a big matrix <literal>C</literal> the coefficients of the + polynomial matrix <literal>Mp</literal> . <literal>C</literal> is partitioned + as <literal>C=[C0,C1,...,Ck]</literal> + where the <literal>Ci</literal> are arranged in increasing order + <literal>k = max(degree(Mp))</literal> + </para> + <para> + <literal>C=coeff(Mp,v)</literal> returns the matrix of coefficients with + degree in <literal>v</literal> . (<literal>v</literal> is a row or column vector). + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +w=s*rand(10,10); +determ(w) +coeff(w,1) + +r = poly([0 -1+%i -1-%i],'s',"roots"); +coeff(r) + +r = poly([-1-%i -1+2*%i 0],'s',"roots"); +coeff(r) + + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="degree">degree</link> + </member> + <member> + <link linkend="inv_coeff">inv_coeff</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/coffg.xml b/modules/polynomials/help/en_US/coffg.xml new file mode 100755 index 000000000..248e00e28 --- /dev/null +++ b/modules/polynomials/help/en_US/coffg.xml @@ -0,0 +1,78 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Francois DELBECQUE + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="coffg"> + <refnamediv> + <refname>coffg</refname> + <refpurpose>inverse of polynomial matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Ns,d]=coffg(Fs)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>Fs</term> + <listitem> + <para>square polynomial matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>coffg</literal> computes <literal>Fs^-1</literal> where <literal>Fs</literal> is a polynomial + matrix by co-factors method. + </para> + <para> + <literal>Fs</literal> inverse = <literal>Ns/d</literal> + </para> + <para> + <literal>d</literal> = common denominator; <literal>Ns</literal> = numerator (a polynomial matrix) + </para> + <para> + (For large matrices,be patient...results are generally reliable) + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s') +a=[ s, s^2+1; s s^2-1]; +[a1,d]=coffg(a); +(a1/d)-inv(a) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="determ">determ</link> + </member> + <member> + <link linkend="detr">detr</link> + </member> + <member> + <link linkend="invr">invr</link> + </member> + <member> + <link linkend="penlaur">penlaur</link> + </member> + <member> + <link linkend="glever">glever</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/colcompr.xml b/modules/polynomials/help/en_US/colcompr.xml new file mode 100755 index 000000000..937e2ff72 --- /dev/null +++ b/modules/polynomials/help/en_US/colcompr.xml @@ -0,0 +1,78 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="colcompr"> + <refnamediv> + <refname>colcompr</refname> + <refpurpose>column compression of polynomial matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Y,rk,ac]=colcompr(A);</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>polynomial matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Y</term> + <listitem> + <para>square polynomial matrix (right unimodular basis)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + normal rank of <literal>A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ac</term> + <listitem> + <para> + <literal>Ac=A*Y</literal>, polynomial matrix + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + column compression of polynomial matrix <literal>A</literal> (compression to the left) + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +p=[s;s*(s+1)^2;2*s^2+s^3]; +[Y,rk,ac]=colcompr(p*p'); +p*p'*Y + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="rowcompr">rowcompr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/degree.xml b/modules/polynomials/help/en_US/degree.xml new file mode 100755 index 000000000..014888c59 --- /dev/null +++ b/modules/polynomials/help/en_US/degree.xml @@ -0,0 +1,71 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="degree"> + <refnamediv> + <refname>degree</refname> + <refpurpose>degree of polynomial matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[D]=degree(M)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>M</term> + <listitem> + <para>polynomial matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>D</term> + <listitem> + <para>integer matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + returns the matrix of highest degrees of <literal>M</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +v=[-2-5*%s+%s^2;-6+11*%s-6*%s^2+%s^3]; +degree(v) // should return 2 and 3 + +s=poly(0,"s"); +p=1+s+2*s^42; +degree(p) // should return 42 + ]]></programlisting> + </refsection> + + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="coeff">coeff</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/denom.xml b/modules/polynomials/help/en_US/denom.xml new file mode 100755 index 000000000..e90cee2f6 --- /dev/null +++ b/modules/polynomials/help/en_US/denom.xml @@ -0,0 +1,73 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="denom"> + <refnamediv> + <refname>denom</refname> + <refpurpose>denominator</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>den=denom(r)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>r</term> + <listitem> + <para>rational or polynomial or constant matrix.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>den</term> + <listitem> + <para>polynomial matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>den=denom(r)</literal> returns the denominator of a rational matrix. + </para> + <para> + Since rationals are internally represented as + <literal>r=list(['r','num','den','dt'],num,den,[])</literal>, + <literal>denom(r</literal>) is the same as <literal>r(3)</literal>, + <literal>r('den')</literal> or <literal>r.den</literal> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +h=(1+2*%s)/poly(1:4,'s','c'); +denom(h) +numer(h) + +s=poly(0,"s"); +p=1+s+2*s^2; +denom(p) // Should return 1 +numer(p) + ]]></programlisting> + </refsection> + + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="numer">numer</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/derivat.xml b/modules/polynomials/help/en_US/derivat.xml new file mode 100755 index 000000000..862827aa5 --- /dev/null +++ b/modules/polynomials/help/en_US/derivat.xml @@ -0,0 +1,72 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="derivat"> + <refnamediv> + <refname>derivat</refname> + <refpurpose>Rational matrix derivative</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>pd=derivat(p)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>polynomial or rational matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + The derivat() function works with expressions like + <latex>p(z) = \sum \limits_{i = -\infty}^{\infty} A_{i} z^{i}</latex> + which consists of functions of linear combinations with integer exponents of one variable (in the example denoted by z). + </para> + <para> + The function derivat() implements the analytical derivation of p(z), giving the following result. + <latex>\dfrac{d(p(z))}{d z} = \sum \limits_{i = -\infty}^{\infty} i A_{i} z^{i - 1}</latex> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +derivat(1/s) // -1/s^2; + ]]></programlisting> + <programlisting role="example"><![CDATA[ +p1 = poly([1 -2 1], 'x', 'coeff') +derivat(p1) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +p2 = poly([1 -4 2], 'y', 'coeff') +derivat(p2) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +p3 = poly(ones(1, 10), 'z', 'coeff') +derivat(p3) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +p4 = poly([-1 1], 't', 'roots') +derivat(p4) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +s = %s; p5 = s^{-1} + 2 + 3*s +derivat(p5) + ]]></programlisting> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/determ.xml b/modules/polynomials/help/en_US/determ.xml new file mode 100755 index 000000000..88322216a --- /dev/null +++ b/modules/polynomials/help/en_US/determ.xml @@ -0,0 +1,81 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Francois DELBECQUE + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="determ"> + <refnamediv> + <refname>determ</refname> + <refpurpose>determinant of polynomial matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>res=determ(W [,k])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>W</term> + <listitem> + <para>real square polynomial matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>k</term> + <listitem> + <para>integer (upper bound for the degree of the determinant of W)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + returns the determinant of a real polynomial matrix + (computation made by FFT if W size is greater than 2*2). + </para> + <para> + <literal>res=determ(W [,k])</literal><literal>k</literal> is an integer larger than the actual degree of the determinant + of <literal>W</literal>. + </para> + <para> + The default value of <literal>k</literal> is the smallest power of 2 which is larger + than <literal>n*max(degree(W))</literal>. + </para> + <para> + Method (Only if W size is greater than 2*2) : evaluate the determinant of <literal>W</literal> for the Fourier frequencies + and apply inverse FFT to the coefficients of the determinant. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +w=s*rand(10,10); +determ(w) +det(coeff(w,1))*s^10 + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="det">det</link> + </member> + <member> + <link linkend="detr">detr</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/detr.xml b/modules/polynomials/help/en_US/detr.xml new file mode 100755 index 000000000..2d34f2f9d --- /dev/null +++ b/modules/polynomials/help/en_US/detr.xml @@ -0,0 +1,74 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="detr"> + <refnamediv> + <refname>detr</refname> + <refpurpose>polynomial determinant</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>d=detr(h)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>h</term> + <listitem> + <para>double or polynomial or rational square matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>d=detr(h)</literal> returns the determinant <literal>d</literal> of the double + or polynomial or rational function matrix <literal>h</literal>. + Based on Leverrier's algorithm. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"> + <![CDATA[ +// Matrix of doubles +A = rand(5,5); +detr(A) + +A = A+%i; +detr(A) + +// Matrix of polynomials +x = poly(0, 'x') +A = [1+x 2 5; 3 4-x 3+x; x^2 1 x]; +detr(A) + +// Matrix of rationals +A = [1/x 2 3; 3 4/x 3/x; 1/x^2 1 1/x]; +detr(A) + ]]> + </programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="det">det</link> + </member> + <member> + <link linkend="determ">determ</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/diophant.xml b/modules/polynomials/help/en_US/diophant.xml new file mode 100755 index 000000000..821a0661f --- /dev/null +++ b/modules/polynomials/help/en_US/diophant.xml @@ -0,0 +1,72 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="diophant"> + <refnamediv> + <refname>diophant</refname> + <refpurpose>diophantine (Bezout) equation</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[x,err]=diophant(p1p2,b)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>p1p2</term> + <listitem> + <para> + polynomial vector <literal>p1p2 = [p1 p2]</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>b</term> + <listitem> + <para>polynomial</para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para>polynomial vector [x1; x2]</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>diophant</literal> solves the bezout equation: + </para> + <para> + <literal>p1*x1+p2*x2=b</literal> with <literal>p1p2</literal> a polynomial vector. + If the equation is not solvable, <literal>err = ||p1*x1 + p2*x2 - b|| / ||b||</literal> + </para> + <para> + else <literal>err = 0</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s = poly(0, 's'); +p1 = (s+3)^2; +p2 = (1+s); +x1 = s; +x2 = (2+s); +[x,err] = diophant([p1 p2], p1*x1 + p2*x2); +p1*x1 + p2*x2 - p1*x(1) - p2*x(2) + ]]></programlisting> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/factors.xml b/modules/polynomials/help/en_US/factors.xml new file mode 100755 index 000000000..80f97dfb0 --- /dev/null +++ b/modules/polynomials/help/en_US/factors.xml @@ -0,0 +1,126 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="factors"> + <refnamediv> + <refname>factors</refname> + <refpurpose>numeric real factorization</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[lnum,g]=factors(pol [,'flag']) + [lnum,lden,g]=factors(rat [,'flag']) + rat=factors(rat,'flag') + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>pol</term> + <listitem> + <para>real polynomial</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rat</term> + <listitem> + <para> + real rational polynomial (<literal>rat=pol1/pol2</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>lnum</term> + <listitem> + <para>list of polynomials (of degrees 1 or 2)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>lden</term> + <listitem> + <para>list of polynomials (of degrees 1 or 2)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>g</term> + <listitem> + <para>real number</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + character string <literal>'c'</literal> or <literal>'d'</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + returns the factors of polynomial <literal>pol</literal> in the list <literal>lnum</literal> + and the "gain" g. + </para> + <para> + One has pol= g times product of entries of the list <literal>lnum</literal> + (if <literal>flag</literal> is not given). If <literal>flag='c'</literal> is given, then + one has <literal>|pol(i omega)|</literal> = <literal>|g*prod(lnum_j(i omega)|</literal>. + If <literal>flag='d'</literal> is given, then + one has <literal>|pol(exp(i omega))|</literal> = <literal>|g*prod(lnum_i(exp(i omega))|</literal>. + If argument of <literal>factors</literal> is a 1x1 rational <literal>rat=pol1/pol2</literal>, + the factors of the numerator <literal>pol1</literal> and the denominator <literal>pol2</literal> + are returned in the lists <literal>lnum</literal> and <literal>lden</literal> respectively. + </para> + <para> + The "gain" is returned as <literal>g</literal>,i.e. one has: + rat= g times (product entries in lnum) / (product entries in lden). + </para> + <para> + If <literal>flag</literal> is <literal>'c'</literal> (resp. <literal>'d'</literal>), the roots of <literal>pol</literal> + are refected wrt the imaginary axis (resp. the unit circle), i.e. + the factors in <literal>lnum</literal> are stable polynomials. + </para> + <para> + Same thing if <literal>factors</literal> is invoked with a rational arguments: + the entries in <literal>lnum</literal> and <literal>lden</literal> are stable polynomials if + <literal>flag</literal> is given. <literal>R2=factors(R1,'c')</literal> or <literal>R2=factors(R1,'d')</literal> + with <literal>R1</literal> a rational function or SISO <literal>syslin</literal> list then the + output <literal>R2</literal> is a transfer with stable numerator and denominator and + with same magnitude as <literal>R1</literal> along the imaginary axis (<literal>'c'</literal>) + or unit circle (<literal>'d'</literal>). + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +n=poly([0.2,2,5],'z'); +d=poly([0.1,0.3,7],'z'); +R=syslin('d',n,d); +R1=factors(R,'d') +roots(R1('num')) +roots(R1('den')) +w=exp(2*%i*%pi*[0:0.1:1]); +norm(abs(horner(R1,w))-abs(horner(R,w))) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="simp">simp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/hermit.xml b/modules/polynomials/help/en_US/hermit.xml new file mode 100755 index 000000000..4b8b4f695 --- /dev/null +++ b/modules/polynomials/help/en_US/hermit.xml @@ -0,0 +1,80 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="hermit"> + <refnamediv> + <refname>hermit</refname> + <refpurpose>Hermite form</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Ar,U]=hermit(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>polynomial matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ar</term> + <listitem> + <para>triangular polynomial matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>unimodolar polynomial matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Hermite form: <literal>U</literal> is an unimodular matrix such that <literal>A*U</literal> is + in Hermite triangular form: + </para> + <para> + The output variable is <literal>Ar=A*U</literal>. + </para> + <para> + <warning> + Warning: Experimental version + </warning> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +p=[s, s*(s+1)^2, 2*s^2+s^3]; +[Ar,U]=hermit(p'*p); +clean(p'*p*U), det(U) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="hrmt">hrmt</link> + </member> + <member> + <link linkend="htrianr">htrianr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/horner.xml b/modules/polynomials/help/en_US/horner.xml new file mode 100755 index 000000000..d3b7d471b --- /dev/null +++ b/modules/polynomials/help/en_US/horner.xml @@ -0,0 +1,94 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="horner"> + <refnamediv> + <refname>horner</refname> + <refpurpose>polynomial/rational evaluation</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>horner(P,x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>P</term> + <listitem> + <para>polynomial or rational matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para> array of numbers or polynomials or rationals</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + evaluates the polynomial or rational + matrix <literal>P = P(s)</literal> when the variable <literal>s</literal> of the + polynomial is replaced by <literal>x</literal>: + </para> + <para> + <literal>horner(P,x)</literal>=<literal>P(x)</literal> + </para> + <para> + Example (Bilinear transform): Assume <literal>P = P(s)</literal> is + a rational matrix then the rational matrix + <literal>P((1+s)/(1-s))</literal> is obtained by <literal>horner(P,(1+s)/(1-s))</literal>. + </para> + <para> + To evaluate a rational matrix at given frequencies use + preferably the <literal>freq</literal> primitive. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +//evaluation of a polynomial for a vector of numbers +P=poly(1:3,'x') +horner(P,[1 2 5]) +horner(P,[1 2 5]+%i) + +//evaluation of a rational +s=poly(0,'s');M=[s,1/s]; +horner(M,1) +horner(M,%i) +horner(M,1/s) + +//evaluation of a polynomial for a matrix of numbers +X= [1 2;3 4] +p=poly(1:3,'x','c') +m=horner(p, X) +1*X.^0+2*X.^1+3*X.^2 + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="freq">freq</link> + </member> + <member> + <link linkend="repfreq">repfreq</link> + </member> + <member> + <link linkend="evstr">evstr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/hrmt.xml b/modules/polynomials/help/en_US/hrmt.xml new file mode 100755 index 000000000..2882df4d8 --- /dev/null +++ b/modules/polynomials/help/en_US/hrmt.xml @@ -0,0 +1,74 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="hrmt"> + <refnamediv> + <refname>hrmt</refname> + <refpurpose>gcd of polynomials</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[pg,U]=hrmt(v)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>v</term> + <listitem> + <para> + row of polynomials i.e. <literal>1</literal>x<literal>k</literal> polynomial matrix + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>pg</term> + <listitem> + <para>polynomial</para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>unimodular matrix polynomial</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[pg,U]=hrmt(v)</literal> returns a unimodular matrix <literal>U</literal> and <literal>pg</literal> = gcd of row of + polynomials <literal>v</literal> such that <literal>v*U = [pg,0]</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +x=poly(0,'x'); +v=[x*(x+1),x^2*(x+1),(x-2)*(x+1),(3*x^2+2)*(x+1)]; +[pg,U]=hrmt(v);U=clean(U) +det(U) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="gcd">gcd</link> + </member> + <member> + <link linkend="htrianr">htrianr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/htrianr.xml b/modules/polynomials/help/en_US/htrianr.xml new file mode 100755 index 000000000..bdb6383cb --- /dev/null +++ b/modules/polynomials/help/en_US/htrianr.xml @@ -0,0 +1,91 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="htrianr"> + <refnamediv> + <refname>htrianr</refname> + <refpurpose>triangularization of polynomial matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Ar,U,rk]=htrianr(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>polynomial matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ar</term> + <listitem> + <para>polynomial matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>unimodular polynomial matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + integer, normal rank of <literal>A</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + triangularization of polynomial matrix <literal>A</literal>. + </para> + <para> + <literal>A</literal> is <literal>[m,n]</literal> , <literal>m <= n</literal>. + </para> + <para> + <literal>Ar=A*U</literal> + </para> + <para> + <warning> + Warning: there is an elimination of "small" terms (see function code). + </warning> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +x=poly(0,'x'); +M=[x;x^2;2+x^3]*[1,x-2,x^4]; +[Mu,U,rk]=htrianr(M) +det(U) +M*U(:,1:2) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="hrmt">hrmt</link> + </member> + <member> + <link linkend="colcompr">colcompr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/inv_coeff.xml b/modules/polynomials/help/en_US/inv_coeff.xml new file mode 100755 index 000000000..d5c98a112 --- /dev/null +++ b/modules/polynomials/help/en_US/inv_coeff.xml @@ -0,0 +1,72 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="inv_coeff"> + <refnamediv> + <refname>inv_coeff</refname> + <refpurpose>build a polynomial matrix from its coefficients</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[P]=inv_coeff(C,[,d,[name])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>C</term> + <listitem> + <para>a big matrix of the coefficients</para> + </listitem> + </varlistentry> + <varlistentry> + <term>d</term> + <listitem> + <para> + a polynomial matrix degree. The optional parameter with default value <literal>d=-1+size(C,'c')/size(C,'r')</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>name</term> + <listitem> + <para> + a string giving the polynomial variable name (default value <literal>'x'</literal>). + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>P=inv_coeff(Mp,k)</literal>, when <literal>k</literal> is compatible with <literal>Mp</literal> + size, returns a polynomial matrix of degree <literal>k</literal>. <literal>C=[C0,C1,...,Ck]</literal> and + <literal>P= C0 + C1*x +... +Ck*x^k</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +A=int(10*rand(2,6)) +// Building a degree 1 polynomial matrix +P=inv_coeff(A,1) +norm(coeff(P)-A) +// Using default value for degree +P1=inv_coeff(A) +norm(coeff(P1)-A) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="degree">degree</link> + </member> + <member> + <link linkend="coeff">coeff</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/invr.xml b/modules/polynomials/help/en_US/invr.xml new file mode 100755 index 000000000..bf57d29c1 --- /dev/null +++ b/modules/polynomials/help/en_US/invr.xml @@ -0,0 +1,69 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="invr"> + <refnamediv> + <refname>invr</refname> + <refpurpose>inversion of (rational) matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>F = invr(H)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>H</term> + <listitem> + <para>polynomial or rational matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>F</term> + <listitem> + <para>polynomial or rational matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + If <literal>H</literal> is a polynomial or rational function matrix, <literal>invr</literal> + computes <literal>H^(-1)</literal> using Leverrier's algorithm (see function code) + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s') +H=[s,s*s+2;1-s,1+s]; invr(H) +[Num,den]=coffg(H);Num/den +H=[1/s,(s+1);1/(s+2),(s+3)/s];invr(H) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="glever">glever</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + <member> + <link linkend="inv">inv</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/lcmdiag.xml b/modules/polynomials/help/en_US/lcmdiag.xml new file mode 100755 index 000000000..320272633 --- /dev/null +++ b/modules/polynomials/help/en_US/lcmdiag.xml @@ -0,0 +1,90 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="lcmdiag"> + <refnamediv> + <refname>lcmdiag</refname> + <refpurpose>least common multiple diagonal factorization</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[N,D]=lcmdiag(H) + [N,D]=lcmdiag(H,flag) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>H</term> + <listitem> + <para>rational matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>N</term> + <listitem> + <para>polynomial matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>D</term> + <listitem> + <para>diagonal polynomial matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + character string: <literal>'row'</literal> or <literal>'col'</literal> (default) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[N,D]=lcmdiag(H,'row')</literal> computes a factorization <literal>D*H=N</literal>, + i.e. <literal>H=D^(-1)*N</literal> where D is a diagonal matrix with D(k,k)=lcm of + kth row of H('den'). + </para> + <para> + <literal>[N,D]=lcmdiag(H)</literal> or <literal>[N,D]=lcmdiag(H,'col)</literal> returns + <literal>H=N*D^(-1)</literal> with diagonal D and D(k,k)=lcm of kth col of H('den') + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +H=[1/s,(s+2)/s/(s+1)^2;1/(s^2*(s+2)),2/(s+2)]; +[N,D]=lcmdiag(H); +N/D-H + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="lcm">lcm</link> + </member> + <member> + <link linkend="gcd">gcd</link> + </member> + <member> + <link linkend="bezout">bezout</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/ldiv.xml b/modules/polynomials/help/en_US/ldiv.xml new file mode 100755 index 000000000..fbad2be45 --- /dev/null +++ b/modules/polynomials/help/en_US/ldiv.xml @@ -0,0 +1,77 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="ldiv"> + <refnamediv> + <refname>ldiv</refname> + <refpurpose>polynomial matrix long division</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[x]=ldiv(n,d,k)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>n,d</term> + <listitem> + <para>two real polynomial matrices</para> + </listitem> + </varlistentry> + <varlistentry> + <term>k</term> + <listitem> + <para>integer</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>x=ldiv(n,d,k)</literal> gives the <literal>k</literal> first coefficients of the long + division of <literal>n</literal> by <literal>d</literal> i.e. the Taylor expansion of the rational + matrix <literal>[nij(z)/dij(z)]</literal> near infinity. + </para> + <para> + Coefficients of expansion of <literal>nij/dij</literal> are stored in + <literal>x((i-1)*n+k,j) k=1:n</literal> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +wss=ssrand(1,1,3);[a,b,c,d]=abcd(wss); +wtf=ss2tf(wss); +x1=ldiv(numer(wtf),denom(wtf),5) +x2=[c*b;c*a*b;c*a^2*b;c*a^3*b;c*a^4*b] +wssbis=markp2ss(x1',5,1,1); +wtfbis=clean(ss2tf(wssbis)) +x3=ldiv(numer(wtfbis),denom(wtfbis),5) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="arl2">arl2</link> + </member> + <member> + <link linkend="markp2ss">markp2ss</link> + </member> + <member> + <link linkend="pdiv">pdiv</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/numer.xml b/modules/polynomials/help/en_US/numer.xml new file mode 100755 index 000000000..06ac349d4 --- /dev/null +++ b/modules/polynomials/help/en_US/numer.xml @@ -0,0 +1,68 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="numer"> + <refnamediv> + <refname>numer</refname> + <refpurpose>numerator</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>num=numer(R)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>R</term> + <listitem> + <para>rational or polynomial or constant matrix.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>num</term> + <listitem> + <para>polynomial matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Utility fonction. <literal>num=numer(R)</literal> returns the numerator <literal>num</literal> of a rational + function matrix <literal>R</literal> (<literal>R</literal> may be also a constant or polynomial matrix). + <literal>numer(R)</literal> is equivalent to <literal>R(2)</literal>, <literal>R('num')</literal> or <literal>R.num</literal> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +h=(1+2*%s)/poly(1:4,'s','c'); +denom(h) +numer(h) + +s=poly(0,"s"); +p=1+s+2*s^2; +denom(p) // Should return 1 +numer(p) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="denom">denom</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/pdiv.xml b/modules/polynomials/help/en_US/pdiv.xml new file mode 100755 index 000000000..d8e07f2c1 --- /dev/null +++ b/modules/polynomials/help/en_US/pdiv.xml @@ -0,0 +1,79 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="pdiv"> + <refnamediv> + <refname>pdiv</refname> + <refpurpose>polynomial division</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[R,Q]=pdiv(P1,P2) + [Q]=pdiv(P1,P2) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>P1</term> + <listitem> + <para>polynomial matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>P2</term> + <listitem> + <para>polynomial or polynomial matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>R,Q</term> + <listitem> + <para>two polynomial matrices</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Element-wise euclidan division of the polynomial matrix <literal>P1</literal> + by the polynomial <literal>P2</literal> or by the polynomial matrix <literal>P2</literal>. + <literal>Rij</literal> is the matrix of remainders, <literal>Qij</literal> is the matrix + of quotients and <literal>P1ij = Qij*P2 + Rij</literal> or <literal>P1ij = Qij*P2ij + Rij</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +x=poly(0,'x'); +p1=(1+x^2)*(1-x);p2=1-x; +[r,q]=pdiv(p1,p2) +p2*q-p1 +p2=1+x; +[r,q]=pdiv(p1,p2) +p2*q+r-p1 + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="ldiv">ldiv</link> + </member> + <member> + <link linkend="gcd">gcd</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/pol2str.xml b/modules/polynomials/help/en_US/pol2str.xml new file mode 100755 index 000000000..79878bfbe --- /dev/null +++ b/modules/polynomials/help/en_US/pol2str.xml @@ -0,0 +1,88 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * Copyright (C) 2013 - Samuel GOUGEON : upgrade for 5.5.0 + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="pol2str"> + <refnamediv> + <refname>pol2str</refname> + <refpurpose>polynomial to string conversion</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>strs = pol2str(p)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>matrix or hypermatrix of polynomials with real or complex coefficients</para> + </listitem> + </varlistentry> + <varlistentry> + <term>strs</term> + <listitem> + <para>matrix or hypermatrix of strings</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + converts polynomial to character string (utility function). + </para> + <para> + <note> + The output format of coefficients is set through <link linkend="format">format(..)</link>. + </note> + </para> + </refsection> + + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +pol2str(%z) + +p = poly ([1, 2, 3], "x","coeff"); +pol2str(p) + +p = (1+%i+%z)^(1:4) +pol2str(p) + ]]></programlisting> + </refsection> + + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="string">string</link> + </member> + <member> + <link linkend="prettyprint">prettyprint</link> + </member> + <member> + <link linkend="sci2exp">sci2exp</link> + </member> + </simplelist> + </refsection> + <refsection role="history tag"> + <title>History</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revdescription>pol2str() extended to polynomials with complex coefficients and to hypermatrix. Array processing vectorized.</revdescription> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/polfact.xml b/modules/polynomials/help/en_US/polfact.xml new file mode 100755 index 000000000..6b152b9d1 --- /dev/null +++ b/modules/polynomials/help/en_US/polfact.xml @@ -0,0 +1,88 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Serge STEER + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="polfact"> + <refnamediv> + <refname>polfact</refname> + <refpurpose>minimal factors</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[f]=polfact(p)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>polynomial</para> + </listitem> + </varlistentry> + <varlistentry> + <term>f</term> + <listitem> + <para> + vector <literal>[f0 f1 ... fn]</literal> such that <literal>p=prod(f)</literal> + </para> + <variablelist> + <varlistentry> + <term>f0</term> + <listitem> + <para>constant</para> + </listitem> + </varlistentry> + <varlistentry> + <term>fi</term> + <listitem> + <para>polynomial</para> + </listitem> + </varlistentry> + </variablelist> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>f=polfact(p)</literal> returns the minimal factors of p i.e. <literal>f=[f0 f1 ... fn]</literal> such + that <literal>p=prod(f)</literal> + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +x = poly(0,"x") +polfact(x^2-1) + +polfact(x^7-1) + + + ]]></programlisting> + </refsection> + + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="lcm">lcm</link> + </member> + <member> + <link linkend="cmndred">cmndred</link> + </member> + <member> + <link linkend="factors">factors</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/poly.xml b/modules/polynomials/help/en_US/poly.xml new file mode 100755 index 000000000..5f70c732c --- /dev/null +++ b/modules/polynomials/help/en_US/poly.xml @@ -0,0 +1,136 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="poly"> + <refnamediv> + <refname>poly</refname> + <refpurpose>polynomial definition</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>p = poly(a, vname, ["flag"])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>a</term> + <listitem> + <para>a matrix or real number</para> + </listitem> + </varlistentry> + <varlistentry> + <term>vname</term> + <listitem> + <para>a string, the symbolic variable name. The string must be 4 characters max. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>"flag"</term> + <listitem> + <para> + string (<literal>"roots"</literal>, <literal>"coeff"</literal>), + default value is <literal>"roots"</literal>. + </para> + <para> + Shortcuts can be also used: <literal>"r"</literal> for <literal>"roots"</literal> and <literal>"c"</literal> for <literal>"coeff"</literal>. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <variablelist> + <varlistentry> + <term> + If <literal>a</literal> is a matrix, + </term> + <listitem> + <para> + <varname>p</varname> is the characteristic + polynomial i.e. <code>determinant(x*eye()-a)</code>, <literal>x</literal> being + the symbolic variable. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term> + If <literal>v</literal> is a vector, + </term> + <listitem> + <itemizedlist> + <listitem> + <para> + <code>poly(v,"x",["roots"])</code> is the polynomial + with <literal>roots</literal> the entries of <varname>v</varname> and + <literal>"x"</literal> as formal variable. (In this case, + <function>roots</function> and <function>poly</function> are inverse functions). + <note> + Note that Infinite roots gives zero highest degree coefficients. + </note> + </para> + </listitem> + <listitem> + <para> + <code>poly(v,"x","coeff")</code> creates the + polynomial with symbol <literal>"x"</literal> and with coefficients + the entries of <varname>v</varname> (<code>v(1)</code> is the constant term + of the polynomial). (Here <function>poly</function> and <function>coeff</function> are inverse functions). + </para> + </listitem> + </itemizedlist> + </listitem> + </varlistentry> + </variablelist> + <para> + <code>s=poly(0,"s")</code> is the seed for defining + polynomials with symbol <literal>"s"</literal>. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,"s"); +p=1+s+2*s^2 +A=rand(2,2); +poly(A,"x") +//rational fractions +h=(1+2*%s)/poly(1:4,'s','coeff') + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="coeff">coeff</link> + </member> + <member> + <link linkend="roots">roots</link> + </member> + <member> + <link linkend="varn">varn</link> + </member> + <member> + <link linkend="horner">horner</link> + </member> + <member> + <link linkend="derivat">derivat</link> + </member> + <member> + <link linkend="matrices">matrices</link> + </member> + <member> + <link linkend="rational">rational</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>History</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>The only values allowed for the third argument are "roots", "coeff", "c" and "r".</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/rational.xml b/modules/polynomials/help/en_US/rational.xml new file mode 100755 index 000000000..fa20b3f49 --- /dev/null +++ b/modules/polynomials/help/en_US/rational.xml @@ -0,0 +1,48 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="rational"> + <refnamediv> + <refname>rational</refname> + <refpurpose>Scilab objects, rational in Scilab</refpurpose> + </refnamediv> + <refsection> + <title>Description</title> + <para> + A rational <literal>r</literal> is a quotient of two polynomials <literal>r=num/den</literal>. + The internal representation of a rational is a list. + <literal>r=tlist(['r','num','den','dt'],num,den,[])</literal> is the same as <literal>r=num/den</literal>. + A rational matrix can be defined with the usual syntax + e.g. <literal>[r11,r12;r21,r22]</literal> is a 2x2 matrix where <literal>rij</literal> are + 1x1 rationals. + A rational matrix can also be defined as above as a list + <literal>rlist(num,den,[])</literal> with <literal>num</literal> and <literal>den</literal> polynomial matrices. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +W=[1/s,1/(s+1)] +W'*W +Num=[s,s+2;1,s];Den=[s*s,s;s,s*s]; +rlist(Num,Den,[]) +H=Num./Den +syslin('c',Num,Den) +syslin('c',H) +[Num1,Den1]=simp(Num,Den) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="syslin">syslin</link> + </member> + <member> + <link linkend="simp">simp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/residu.xml b/modules/polynomials/help/en_US/residu.xml new file mode 100755 index 000000000..fef55e15d --- /dev/null +++ b/modules/polynomials/help/en_US/residu.xml @@ -0,0 +1,84 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Francois DELBECQUE + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="residu"> + <refnamediv> + <refname>residu</refname> + <refpurpose>residue</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[V]=residu(P,Q1,Q2)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>P, Q1, Q2</term> + <listitem> + <para>polynomials or matrix polynomials with real or complex coefficients.</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>V=residu(P,Q1,Q2)</literal> returns the matrix <literal>V</literal> + such that <literal>V(i,j)</literal> is the sum of the residues of the + rational fraction <literal>P(i,j)/(Q1(i,j)*Q2(i,j))</literal> calculated + at the zeros of <literal>Q1(i,j)</literal>. + </para> + <para> + <literal>Q1(i,j)</literal> and <literal>Q2(i,j)</literal> must not have any common root. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +H=[s/(s+1)^2,1/(s+2)];N=numer(H);D=denom(H); +w=residu(N.*horner(N,-s),D,horner(D,-s)); //N(s) N(-s) / D(s) D(-s) +sqrt(sum(w)) //This is H2 norm +h2norm(tf2ss(H)) + +p=(s-1)*(s+1)*(s+2)*(s+10);a=(s-5)*(s-1)*(s*s)*((s+1/2)**2); +b=(s-3)*(s+2/5)*(s+3); +residu(p,a,b)+531863/4410 //Exact +z=poly(0,'z');a=z^3+0.7*z^2+0.5*z-0.3;b=z^3+0.3*z^2+0.2*z+0.1; +atild=gtild(a,'d');btild=gtild(b,'d'); +residu(b*btild,z*a,atild)-2.9488038 //Exact +a=a+0*%i;b=b+0*%i; +real(residu(b*btild,z*a,atild)-2.9488038) //Complex case + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="pfss">pfss</link> + </member> + <member> + <link linkend="bdiag">bdiag</link> + </member> + <member> + <link linkend="roots">roots</link> + </member> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="gtild">gtild</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/roots.xml b/modules/polynomials/help/en_US/roots.xml new file mode 100755 index 000000000..20d034a79 --- /dev/null +++ b/modules/polynomials/help/en_US/roots.xml @@ -0,0 +1,178 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * Copyright (C) 2011 - DIGITEO - Michael Baudin + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="roots" xml:lang="en"> + <refnamediv> + <refname>roots</refname> + <refpurpose>roots of polynomials</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis> + x=roots(p) + x=roots(p,algo) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para> + a polynomial with real or complex coefficients, or + a m-by-1 or 1-by-m matrix of doubles, the polynomial coefficients in decreasing degree order. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>algo</term> + <listitem> + <para> + a string, the algorithm to be used (default algo="e"). + If algo="e", then the eigenvalues of the companion matrix are returned. + If algo="f", then the Jenkins-Traub method is used (if the polynomial is real and + has degree lower than 100). + If algo="f" and the polynomial is complex, then an error is generated. + If algo="f" and the polynomial has degree greater than 100, then an error is generated. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + This function returns in the complex vector + <literal>x</literal> the roots of the polynomial <literal>p</literal>. + </para> + <para> + The "e" option corresponds to method based on the eigenvalues of the + companion matrix. + </para> + <para> + The "f" option corresponds to the fast RPOLY algorithm, based on + Jenkins-Traub method. + </para> + <para> + For real polynomials of degree <=100, users may consider the "f" option, + which might be faster in some cases. + On the other hand, some specific polynomials are known to be able to + make this option to fail. + For instance, <literal>p=poly([1.e300,1.e0,1.e-300],'x');</literal> + provokes infinite looping of <literal>roots(p,"f")</literal> + </para> + </refsection> + <refsection> + <title>Examples</title> + <para> + In the following examples, we compute roots of polynomials. + </para> + <programlisting role="example"><![CDATA[ +// Roots given a real polynomial +p = poly([1 2 3],"x") +roots(p) +// Roots, given the real coefficients +p = [3 2 1] +roots(p) +// The roots of a complex polynomial +p=poly([0,10,1+%i,1-%i],'x'); +roots(p) +// The roots of the polynomial of a matrix +A=rand(3,3); +p = poly(A,'x') +roots(p) +spec(A) + ]]></programlisting> + <para> + The polynomial representation can have a significant + impact on the roots. + In the following example, suggested by Wilkinson in the 60s and presented by Moler, + we consider a diagonal matrix with diagonal entries equal to 1, 2, ..., 20. + The eigenvalues are obviously equal to 1, 2, ..., 20. + If we compute the associated characteristic polynomial and compute its roots, + we can see that the eigenvalues are significantly different from the expected + ones. + This implies that just representing the coefficients as IEEE doubles changes the + roots. + </para> + <programlisting role="example"><![CDATA[ +A = diag(1:20); +p = poly(A,'x') +roots(p) + ]]></programlisting> + <para> + The "f" option produces an error if the polynomial is complex or + if the degree is greater than 100. + </para> + <programlisting role="example"><![CDATA[ + // The following case produces an error. + p = %i+%s; + roots(p,"f") + // The following case produces an error. + p = ones(101,1); + roots(p,"f") + ]]></programlisting> + <para> + The following script is a simple way of checking that the companion matrix gives the same result as the "e" option. + It explicitly uses the companion matrix to compute the roots. + There is a small step to reverse the coefficients of the polynomial ; + indeed, "roots" expects the coefficients in decreasing degree order, + while "poly" expects the coefficients in increasing degree order. + </para> + <programlisting role="example"><![CDATA[ +v= [1.12119799 0 3.512D+13 32 3.275D+27 0 1.117D+41 4.952D+27 1.722D+54 0 1.224D+67 0 3.262D+79 ]; +r1 = roots(v,"e"); // With "e" option +dv = size(v,"*"); +p = poly(v(dv:-1:1),"x","coeff"); // Reversing v's coefficients +A = companion(p); +r2 = spec(A); // With the companion matrix +max(abs(r1-r2)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="spec">spec</link> + </member> + <member> + <link linkend="companion">companion</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>References</title> + <para> + The RPOLY algorithm is described in "Algorithm 493: Zeros of a Real + Polynomial", ACM TOMS Volume 1, Issue 2 (June 1975), pp. 178-189 + </para> + <para>Jenkins, M. A. and Traub, J. F. (1970), A Three-Stage Algorithm for + Real Polynomials Using Quadratic Iteration, SIAM J. Numer. Anal., 7(1970), 545-566. + </para> + <para>Jenkins, M. A. and Traub, J. F. (1970), Principles for Testing Polynomial Zerofinding Programs. + ACM TOMS 1, 1 (March 1975), pp. 26-34 + </para> + </refsection> + <refsection> + <title>Used Functions</title> + <para>The rpoly.f source codes can be found in the directory + SCI/modules/polynomials/src/fortran of a Scilab source distribution. In the case where the + companion matrix is used, the eigenvalue computation is perfomed using + DGEEV and ZGEEV LAPACK codes. + </para> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/rowcompr.xml b/modules/polynomials/help/en_US/rowcompr.xml new file mode 100755 index 000000000..06f19379a --- /dev/null +++ b/modules/polynomials/help/en_US/rowcompr.xml @@ -0,0 +1,78 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="rowcompr"> + <refnamediv> + <refname>rowcompr</refname> + <refpurpose>row compression of polynomial matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[X,rk,Ac]=rowcompr(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>polynomial matrix</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Y</term> + <listitem> + <para>square polynomial matrix (left unimodular basis)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + normal rank of <literal>A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ac</term> + <listitem> + <para> + <literal>Ac=X*A</literal>, polynomial matrix + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + row compression of polynomial matrix <literal>A</literal>. + </para> + <para> + <literal>X</literal> is a left polynomial unimodular basis which row compressed + thee rows of <literal>A</literal>. <literal>rk</literal> is the normal rank of A. + </para> + <para> + <warning> + Warning: elimination of "small" terms (use with care!). + </warning> + </para> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="colcompr">colcompr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/sfact.xml b/modules/polynomials/help/en_US/sfact.xml new file mode 100755 index 000000000..2902e79e8 --- /dev/null +++ b/modules/polynomials/help/en_US/sfact.xml @@ -0,0 +1,94 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="sfact"> + <refnamediv> + <refname>sfact</refname> + <refpurpose>discrete time spectral factorization</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>F=sfact(P)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>P</term> + <listitem> + <para>real polynomial matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Finds <literal>F</literal>, a spectral factor of + <literal>P</literal>. <literal>P</literal> is a polynomial matrix such that + each root of <literal>P</literal> has a mirror image w.r.t the unit + circle. Problem is singular if a root is on the unit circle. + </para> + <para> + <literal>sfact(P)</literal> returns a polynomial matrix + <literal>F(z)</literal> which is antistable and such that + </para> + <para> + <literal>P = F(z)* F(1/z) *z^n</literal> + </para> + <para> + For scalar polynomials a specific algorithm is implemented. + Algorithms are adapted from Kucera's book. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +//Simple polynomial example +z=poly(0,'z'); +p=(z-1/2)*(2-z) +w=sfact(p); +w*numer(horner(w,1/z)) + +//matrix example +F1=[z-1/2,z+1/2,z^2+2;1,z,-z;z^3+2*z,z,1/2-z]; +P=F1*gtild(F1,'d'); //P is symmetric +F=sfact(P) +roots(det(P)) +roots(det(gtild(F,'d'))) //The stable roots +roots(det(F)) //The antistable roots +clean(P-F*gtild(F,'d')) + +//Example of continuous time use +s=poly(0,'s'); +p=-3*(s+(1+%i))*(s+(1-%i))*(s+0.5)*(s-0.5)*(s-(1+%i))*(s-(1-%i));p=real(p); +//p(s) = polynomial in s^2 , looks for stable f such that p=f(s)*f(-s) +w=horner(p,(1-s)/(1+s)); // bilinear transform w=p((1-s)/(1+s)) +wn=numer(w); //take the numerator +fn=sfact(wn);f=numer(horner(fn,(1-s)/(s+1))); //Factor and back transform +f=f/sqrt(horner(f*gtild(f,'c'),0));f=f*sqrt(horner(p,0)); //normalization +roots(f) //f is stable +clean(f*gtild(f,'c')-p) //f(s)*f(-s) is p(s) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="gtild">gtild</link> + </member> + <member> + <link linkend="fspecg">fspecg</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/simp.xml b/modules/polynomials/help/en_US/simp.xml new file mode 100755 index 000000000..5d16c2790 --- /dev/null +++ b/modules/polynomials/help/en_US/simp.xml @@ -0,0 +1,110 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="simp"> + <refnamediv> + <refname>simp</refname> + <refpurpose>rational simplification</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[N1,D1]=simp(N,D) + H1=simp(H) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>N,D</term> + <listitem> + <para>real polynomials or real matrix polynomials</para> + </listitem> + </varlistentry> + <varlistentry> + <term>H</term> + <listitem> + <para> + rational matrix (i.e matrix with entries <literal>n/d</literal> ,<literal>n</literal> and <literal>d</literal> real polynomials) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[n1,d1]=simp(n,d)</literal> calculates two polynomials <literal>n1</literal> and <literal>d1</literal> + such that <literal>n1/d1 = n/d</literal>. + </para> + <para> + If <literal>N</literal> and <literal>D</literal> are polynomial matrices the calculation + is performed element-wise. + </para> + <para> + <literal>H1=simp(H)</literal> is also valid (each entry of <literal>H</literal> is + simplified in <literal>H1</literal>). + </para> + <para> + <warning> + Caution: + </warning> + </para> + <para> + -no threshold is given i.e. <literal>simp</literal> cannot forces a + simplification. + </para> + <para> + -For linear dynamic systems which include integrator(s) simplification + changes the static gain. (<literal>H(0)</literal> for continuous systems or <literal>H(1)</literal> for + discrete systems) + </para> + <para> + -for complex data, <literal>simp</literal> returns its input(s). + </para> + <para> + -rational simplification is called after nearly each operations on + rationals. It is possible to toggle simplification on or off using + <literal>simp_mode</literal> function. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +[n,d]=simp((s+1)*(s+2),(s+1)*(s-2)) + +simp_mode(%F);hns=s/s +simp_mode(%T);hns=s/s + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="roots">roots</link> + </member> + <member> + <link linkend="trfmod">trfmod</link> + </member> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + <member> + <link linkend="simp_mode">simp_mode</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/simp_mode.xml b/modules/polynomials/help/en_US/simp_mode.xml new file mode 100755 index 000000000..74c8af548 --- /dev/null +++ b/modules/polynomials/help/en_US/simp_mode.xml @@ -0,0 +1,71 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="simp_mode"> + <refnamediv> + <refname>simp_mode</refname> + <refpurpose>toggle rational simplification</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>mod=simp_mode() + simp_mode(mod) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>mod</term> + <listitem> + <para>a boolean</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + rational simplification is called after nearly each operations on + rationals. It is possible to toggle simplification on or off using + <literal>simp_mode</literal> function. + </para> + <para> + <literal>simp_mode(%t)</literal> set rational simplification mode on + </para> + <para> + <literal>simp_mode(%f)</literal> set rational simplification mode off + </para> + <para> + <literal>mod=simp_mode()</literal> returns in mod the current rational + simplification mode + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +mod=simp_mode() +simp_mode(%f);hns=s/s +simp_mode(%t);hns=s/s +simp_mode(mod); + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="simp">simp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/sylm.xml b/modules/polynomials/help/en_US/sylm.xml new file mode 100755 index 000000000..26b7d8425 --- /dev/null +++ b/modules/polynomials/help/en_US/sylm.xml @@ -0,0 +1,78 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="sylm"> + <refnamediv> + <refname>sylm</refname> + <refpurpose>Sylvester matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[S]=sylm(a,b)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>a,b</term> + <listitem> + <para>two polynomials</para> + </listitem> + </varlistentry> + <varlistentry> + <term>S</term> + <listitem> + <para>matrix</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>sylm(a,b)</literal> gives the Sylvester matrix associated to polynomials + <literal>a</literal> and <literal>b</literal>, i.e. the matrix <literal>S</literal> such that: + </para> + <para> + <literal>coeff( a*x + b*y )' = S * [coeff(x)';coeff(y)']</literal>. + </para> + <para> + Dimension of <literal>S</literal> is equal to <literal>degree(a)+degree(b)</literal>. + </para> + <para> + If <literal>a</literal> and <literal>b</literal> are coprime polynomials then + </para> + <para> + <literal>rank(sylm(a,b))=degree(a)+degree(b))</literal> and the instructions + </para> + <programlisting role="no-scilab-exec"><![CDATA[ +u = sylm(a,b) \ eye(na+nb,1) +x = poly(u(1:nb),'z','coeff') +y = poly(u(nb+1:na+nb),'z','coeff') + ]]></programlisting> + <para> + compute Bezout factors <literal>x</literal> and <literal>y</literal> of minimal degree + such that <literal>a*x+b*y = 1</literal> + </para> + </refsection> + + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +x = poly(0,"x") +y = poly ([1, 2, 3], "x","coeff"); +sylm(x,y) + + ]]></programlisting> + </refsection> + +</refentry> diff --git a/modules/polynomials/help/en_US/systmat.xml b/modules/polynomials/help/en_US/systmat.xml new file mode 100755 index 000000000..0b15e073d --- /dev/null +++ b/modules/polynomials/help/en_US/systmat.xml @@ -0,0 +1,73 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="systmat"> + <refnamediv> + <refname>systmat</refname> + <refpurpose>system matrix</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[Sm]=systmat(Sl);</synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>Sl</term> + <listitem> + <para> + linear system (<literal>syslin</literal> list) or descriptor system + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Sm</term> + <listitem> + <para>matrix pencil</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + System matrix of the linear system <literal>Sl</literal> (<literal>syslin</literal> list) + in state-space form (utility function). + </para> + <programlisting role=""><![CDATA[ +Sm = [-sI + A B; + [ C D] + ]]></programlisting> + <para> + For a descriptor system (<literal>Sl=list('des',A,B,C,D,E)</literal>), <literal>systmat</literal> returns: + </para> + <programlisting role=""><![CDATA[ +Sm = [-sE + A B; + [ C D] + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="ss2des">ss2des</link> + </member> + <member> + <link linkend="sm2des">sm2des</link> + </member> + <member> + <link linkend="sm2ss">sm2ss</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/en_US/varn.xml b/modules/polynomials/help/en_US/varn.xml new file mode 100755 index 000000000..d1423ff23 --- /dev/null +++ b/modules/polynomials/help/en_US/varn.xml @@ -0,0 +1,92 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="varn"> + <refnamediv> + <refname>varn</refname> + <refpurpose>symbolic variable of a polynomial or a rational</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[symb]=varn(p) + [pm]=varn(p,varname) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Arguments</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>matrix of polynomials or of rationals</para> + </listitem> + </varlistentry> + <varlistentry> + <term>symb</term> + <listitem> + <para>character string: name of the variable</para> + </listitem> + </varlistentry> + <varlistentry> + <term>varname</term> + <listitem> + <para> + character string: the new name of the variable of <literal>p</literal>, set for <literal>pm</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>pm</term> + <listitem> + <para>matrix of polynomials or of rationals</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>symb=varn(p)</literal> returns in <literal>symb</literal> the symbolic variable of the polynomial <literal>p</literal> + (i.e. <literal>varn(poly(0,'x'))</literal> is <literal>'x'</literal>). + </para> + <para> + <literal>varn(p,'s')</literal> returns a polynomial matrix with same coefficients + as <literal>p</literal> but with <literal>'s'</literal> as symbolic variable (change of variable name). + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +s = poly(0,'s'); p = [s^2+1,s]; +varn(p) +varn(p,'x') + +f = %z / (%z-1); f = [f f^2] +varn(f) +varn(f,"x") + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="rlist">rlist</link> + </member> + <member> + <link linkend="horner">horner</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>History</title> + <revhistory> + <revision> + <revnumber>5.5.1</revnumber> + <revdescription> + <para>Extension to rationals</para> + </revdescription> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/addchapter.sce b/modules/polynomials/help/fr_FR/addchapter.sce new file mode 100755 index 000000000..ee2913d43 --- /dev/null +++ b/modules/polynomials/help/fr_FR/addchapter.sce @@ -0,0 +1,11 @@ +// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) 2009 - DIGITEO +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +add_help_chapter("Polynômes",SCI+"/modules/polynomials/help/fr_FR",%T); + diff --git a/modules/polynomials/help/fr_FR/bezout.xml b/modules/polynomials/help/fr_FR/bezout.xml new file mode 100755 index 000000000..5603c0014 --- /dev/null +++ b/modules/polynomials/help/fr_FR/bezout.xml @@ -0,0 +1,95 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="bezout"> + <refnamediv> + <refname>bezout</refname> + <refpurpose>équation de Bezout pour les polynômes </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[pgcd,U]=bezout(p1,p2)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>p1, p2 </term> + <listitem> + <para>deux polynômes réels ou deux entiers (type égal à 1, 2 ou 8) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[thegcd,U]=bezout(p1,p2)</literal> calcule le PGCD <literal>pgcd</literal> de <literal>p1</literal> et <literal>p2</literal> et de plus une matrice + unimodulaire (2x2) <literal>U</literal> telle que : + </para> + <para> + <literal>[p1,p2]*U = [pgcd,0]</literal> + </para> + <para> + Le PPCM de <literal>p1</literal> et <literal>p2</literal> est donné par + </para> + <para> + <literal>p1*U(1,2)</literal> (ou <literal>-p2*U(2,2)</literal>) + </para> + <para> + Si <literal>p1</literal> ou <literal>p2</literal> sont donnés comme des flottants (type 1), alors ils sont traités + comme des polynômes de degré nul. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +// Cas des polynômes +x = poly(0,'x'); +p1 = (x+1)*(x-3)^5; +p2 = (x-2)*(x-3)^3; +[pgcd,U] = bezout(p1,p2) +det(U) +clean([p1,p2]*U) +ppcm = p1*U(1,2) +lcm([p1,p2]) + +// Cas des doubles +i1 = 2*3^5; +i2 = 2^3*3^2; +[thegcd, U] = bezout(i1, i2) +V = [2^2*3^5 2^3*3^2 2^2*3^4*5]; +[thegcd, U] = gcd(V) +V*U +lcm(V) + +// Cas des entiers +i1 = int32(2*3^5); +i2 = int32(2^3*3^2); +[thegcd, U] = bezout(i1, i2) +V = int32([2^2*3^5 2^3*3^2 2^2*3^4*5]); +[thegcd, U] = gcd(V) +V*U +lcm(V) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="roots">roots</link> + </member> + <member> + <link linkend="simp">simp</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + <member> + <link linkend="lcm">lcm</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/cmndred.xml b/modules/polynomials/help/fr_FR/cmndred.xml new file mode 100755 index 000000000..502eeb02e --- /dev/null +++ b/modules/polynomials/help/fr_FR/cmndred.xml @@ -0,0 +1,47 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="cmndred"> + <refnamediv> + <refname>cmndred</refname> + <refpurpose>dénominateur commun </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[n,d]=cmndred(num,den)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>num, den </term> + <listitem> + <para>2 matrices de polynômes de mêmes dimensions + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[n,d]=cmndred(num,den)</literal> calcule une matrice de polynômes <literal>n</literal> et + un dénominateur commun <literal>d</literal> tels que : + </para> + <para> + <literal>n/d=num./den</literal> + </para> + <para> + La matrice de polynômes définie par <literal>num./den</literal> est <literal>n/d</literal>. + </para> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="simp">simp</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/coeff.xml b/modules/polynomials/help/fr_FR/coeff.xml new file mode 100755 index 000000000..c7f4a95a5 --- /dev/null +++ b/modules/polynomials/help/fr_FR/coeff.xml @@ -0,0 +1,83 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="coeff"> + <refnamediv> + <refname>coeff</refname> + <refpurpose>coefficients d'une matrice de polynômes </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[C]=coeff(Mp [,v])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>Mp </term> + <listitem> + <para>matrice de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>v </term> + <listitem> + <para>vecteur (ligne ou colonne) d'entiers des degrés choisis + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>C </term> + <listitem> + <para>grosse matrice de coefficients + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>C=coeff(Mp)</literal> + renvoie dans une grosse matrice <literal>C</literal> les coefficients de la + matrice de polynômes <literal>Mp</literal>. <literal>C</literal> est + partitionnée comme <literal>C=[C0,C1,...,Ck]</literal> + où les <literal>Ci</literal> sont arrangés dans l'ordre décroissant . + <literal>k = max(degree(Mp))</literal> + </para> + <para> + <literal>C=coeff(Mp,v)</literal> renvoie la matrice des coefficients avec les + degrés dans <literal>v</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +w=s*rand(10,10); +determ(w) +coeff(w,1) + +r = poly([0 -1+%i -1-%i],'s',"roots"); +coeff(r) + +r = poly([-1-%i -1+2*%i 0],'s',"roots"); +coeff(r) + + ]]></programlisting> + </refsection> + + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="degree">degree</link> + </member> + <member> + <link linkend="inv_coeff">inv_coeff</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/coffg.xml b/modules/polynomials/help/fr_FR/coffg.xml new file mode 100755 index 000000000..90611570c --- /dev/null +++ b/modules/polynomials/help/fr_FR/coffg.xml @@ -0,0 +1,67 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="coffg"> + <refnamediv> + <refname>coffg</refname> + <refpurpose>inverse d'une matrice de polynômes </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[Ns,d]=coffg(Fs)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>Fs </term> + <listitem> + <para>matrice carrée de polynômes + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>coffg</literal> calcule <literal>Fs^-1</literal> par la méthode des cofacteurs, où <literal>Fs</literal> est une matrice de polynômes. + </para> + <para> + inverse de <literal>Fs</literal> = <literal>Ns/d</literal> + </para> + <para> + <literal>d</literal> = dénominateur commun; <literal>Ns</literal> = numérateur (une matrice de polynômes). + </para> + <para> + (pour les grandes matrices, s'armer de patience... les résultats sont en général fiables) + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s') +a=[ s, s^2+1; s s^2-1]; +[a1,d]=coffg(a); +(a1/d)-inv(a) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="determ">determ</link> + </member> + <member> + <link linkend="detr">detr</link> + </member> + <member> + <link linkend="invr">invr</link> + </member> + <member> + <link linkend="penlaur">penlaur</link> + </member> + <member> + <link linkend="glever">glever</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/colcompr.xml b/modules/polynomials/help/fr_FR/colcompr.xml new file mode 100755 index 000000000..1bc4a6607 --- /dev/null +++ b/modules/polynomials/help/fr_FR/colcompr.xml @@ -0,0 +1,69 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="colcompr"> + <refnamediv> + <refname>colcompr</refname> + <refpurpose>compression des colonnes d'une matrice de polynômes </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[Y,rk,ac]=colcompr(A);</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Y </term> + <listitem> + <para>matrice carrée de polynômes (base unimodulaire à droite) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk </term> + <listitem> + <para> + rang normal de <literal>A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ac </term> + <listitem> + <para> + : <literal>Ac=A*Y</literal>, matrice de polynômes + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Compression de colonnes de la matrice de polynômes <literal>A</literal> (compression à gauche) + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +p=[s;s*(s+1)^2;2*s^2+s^3]; +[Y,rk,ac]=colcompr(p*p'); +p*p'*Y + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="rowcompr">rowcompr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/degree.xml b/modules/polynomials/help/fr_FR/degree.xml new file mode 100755 index 000000000..744ba9b7b --- /dev/null +++ b/modules/polynomials/help/fr_FR/degree.xml @@ -0,0 +1,62 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="degree"> + <refnamediv> + <refname>degree</refname> + <refpurpose>degrés d'une matrice de polynômes </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[D]=degree(M)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>M </term> + <listitem> + <para>matrice de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>D </term> + <listitem> + <para>matrice d'entiers + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + renvoie la matrice des plus hauts degrés de <literal>M</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +v=[-2-5*%s+%s^2;-6+11*%s-6*%s^2+%s^3]; +degree(v) // Devrait retourner 2 et 3 + +s=poly(0,"s"); +p=1+s+2*s^42; +degree(p) // Devrait retourner 42 + ]]></programlisting> + </refsection> + + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="coeff">coeff</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/denom.xml b/modules/polynomials/help/fr_FR/denom.xml new file mode 100755 index 000000000..2ae3d1f40 --- /dev/null +++ b/modules/polynomials/help/fr_FR/denom.xml @@ -0,0 +1,67 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="denom"> + <refnamediv> + <refname>denom</refname> + <refpurpose>dénominateur </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>den=denom(r)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>r </term> + <listitem> + <para>matrice de fractions rationnelles + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>den </term> + <listitem> + <para>matrice de polynômes + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>den=denom(r)</literal> renvoie le dénominateur d'une + matrice rationnelle <literal>R</literal> (<literal>R</literal> peut aussi être + une matrice constante ou une matrice de polynômes). + </para> + <para> + Puisque dans Scilab les matrices rationnelles sont représentées + comme + <literal>r=list(['r','num','den','dt'],num,den,[])</literal>, + <literal>denom(r</literal>) est équivalent à <literal>r(3)</literal>, + <literal>r('den')</literal> ou <literal>r.den)</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +h=(1+2*%s)/poly(1:4,'s','c'); +denom(h) +numer(h) + +s=poly(0,"s"); +p=1+s+2*s^2; +denom(p) // Devrait retourner 1 +numer(p) + ]]></programlisting> + </refsection> + + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="numer">numer</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/derivat.xml b/modules/polynomials/help/fr_FR/derivat.xml new file mode 100755 index 000000000..fedb6104a --- /dev/null +++ b/modules/polynomials/help/fr_FR/derivat.xml @@ -0,0 +1,57 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="derivat"> + <refnamediv> + <refname>derivat</refname> + <refpurpose>dérivée d'une matrice de polynômes </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>pd=derivat(p)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>p </term> + <listitem> + <para>polynôme, matrice de polynômes ou de fractions rationnelles + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Calcule la dérivée des polynômes ou fractions rationnelles contenus dans les termes de + la matrice p. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +derivat(1/s) // -1/s^2; + ]]></programlisting> + <programlisting role="example"><![CDATA[ +p1 = poly([1 -2 1], 'x', 'coeff') +derivat(p1) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +p2 = poly([1 -4 2], 'y', 'coeff') +derivat(p2) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +p3 = poly(ones(1, 10), 'z', 'coeff') +derivat(p3) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +p4 = poly([-1 1], 't', 'roots') +derivat(p4) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +s = %s; p5 = s^{-1} + 2 + 3*s +derivat(p5) + ]]></programlisting> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/determ.xml b/modules/polynomials/help/fr_FR/determ.xml new file mode 100755 index 000000000..d44339722 --- /dev/null +++ b/modules/polynomials/help/fr_FR/determ.xml @@ -0,0 +1,74 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="determ"> + <refnamediv> + <refname>determ</refname> + <refpurpose>déterminant d'une matrice de polynômes </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>res=determ(W [,k])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>W </term> + <listitem> + <para>matrice réelle de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>k </term> + <listitem> + <para>entier (borne supérieure pour le degré du déterminant de W) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>res=determ(W [,k])</literal> renvoie le déterminant d'une + matrice réelle de polynômes (calculs fait par FFT si la taille de W + est supérieure à 2*2). + </para> + <para> + <literal>k</literal> est un entier plus grand que le degré effectif du + déterminant. de <literal>W</literal>. + </para> + <para> + La valeur par défaut de <literal>k</literal> est la plus petite + puissance de 2 plus grande que <literal>n*max(degree(W))</literal>. + </para> + <para> + Méthode (pour les matrices dont la taille est supérieure à 2*2) : évaluation du déterminant de <literal>W</literal> aux + fréquences de Fourier et FFT inverse appliquée aux coefficients du + déterminant. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +w=s*rand(10,10); +determ(w) +det(coeff(w,1))*s^10 + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="det">det</link> + </member> + <member> + <link linkend="detr">detr</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/detr.xml b/modules/polynomials/help/fr_FR/detr.xml new file mode 100755 index 000000000..3d987428a --- /dev/null +++ b/modules/polynomials/help/fr_FR/detr.xml @@ -0,0 +1,64 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="detr"> + <refnamediv> + <refname>detr</refname> + <refpurpose>déterminant d'un polynôme </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>d=detr(h)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>h </term> + <listitem> + <para> + matrice carrée de doubles ou de polynômes ou de fractions rationnelles. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>d=detr(h)</literal> renvoie le déterminant <literal>d</literal> de la + matrice <literal>h</literal>. Basé sur l'algorithme de Leverrier. + </para> + </refsection> + <refsection> + <title>Examples</title> + <programlisting role="example"> + <![CDATA[ +// Matrice de doubles +A = rand(5,5); +detr(A) + +A = A+%i; +detr(A) + +// Matrice de polynômes +x = poly(0, 'x') +A = [1+x 2 5; 3 4-x 3+x; x^2 1 x]; +detr(A) + +// Matrice de fractions rationnelles +A = [1/x 2 3; 3 4/x 3/x; 1/x^2 1 1/x]; +detr(A) + ]]> + </programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="det">det</link> + </member> + <member> + <link linkend="determ">determ</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/diophant.xml b/modules/polynomials/help/fr_FR/diophant.xml new file mode 100755 index 000000000..816e26a4d --- /dev/null +++ b/modules/polynomials/help/fr_FR/diophant.xml @@ -0,0 +1,60 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="diophant"> + <refnamediv> + <refname>diophant</refname> + <refpurpose>équation diophantienne de Bezout </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[x,err]=diophant(p1p2,b)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>p1p2 </term> + <listitem> + <para> + vecteur de polynômes <literal>p1p2 = [p1 p2]</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>b </term> + <listitem> + <para>polynôme + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>x </term> + <listitem> + <para>vecteur de polynômes [x1;x2] + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal> diophant</literal> résout l'équation de Bezout : + </para> + <para> + <literal>p1*x1+p2*x2=b</literal> où <literal>p1p2</literal> est un vecteur de polynômes. + Si l'équation n'est pas soluble + </para> + <para> + sinon <literal>err=0</literal> + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s');p1=(s+3)^2;p2=(1+s); +x1=s;x2=(2+s); +[x,err]=diophant([p1,p2],p1*x1+p2*x2); +p1*x1+p2*x2-p1*x(1)-p2*x(2) + ]]></programlisting> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/factors.xml b/modules/polynomials/help/fr_FR/factors.xml new file mode 100755 index 000000000..e5e4a83f0 --- /dev/null +++ b/modules/polynomials/help/fr_FR/factors.xml @@ -0,0 +1,115 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="factors"> + <refnamediv> + <refname>factors</refname> + <refpurpose>factorisation réelle de polynômes </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[lnum,g]=factors(pol [,'flag']) + [lnum,lden,g]=factors(rat [,'flag']) + rat=factors(rat,'flag') + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>pol </term> + <listitem> + <para>polynôme réel + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rat </term> + <listitem> + <para> + fraction rationnelle (<literal>rat=pol1/pol2</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>lnum </term> + <listitem> + <para>liste de polynômes (de degrés 1 ou 2) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>lden </term> + <listitem> + <para>liste de polynômes (de degrés 1 ou 2) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>g </term> + <listitem> + <para>nombre réel + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag </term> + <listitem> + <para> + chaîne de caractères, <literal>'c'</literal> ou <literal>'d'</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + renvoie les facteurs du polynôme <literal>pol</literal> dans la liste <literal>lnum</literal> + et le "gain" g. + </para> + <para> + On a pol = g multiplié par le produit des termes de la liste <literal>lnum</literal> + (si <literal>flag</literal> n'est pas donné). Si <literal>flag='c'</literal>, on a <literal>|pol(i omega)|</literal> = <literal>|g*prod(lnum_j(i omega)|</literal>. + Si <literal>flag='d'</literal> alors + on a <literal>|pol(exp(i omega))|</literal> = <literal>|g*prod(lnum_i(exp(i omega))|</literal>. + Si l'argument de <literal>factors</literal> est une fraction rationnelle 1x1 <literal>rat=pol1/pol2</literal>, + les facteurs du numérateur <literal>pol1</literal> et le dénominateur <literal>pol2</literal> + sont renvoyés dans les listes <literal>lnum</literal> et <literal>lden</literal>, respectivement. + </para> + <para> + Le "gain" est renvoyé dans <literal>g</literal>, c'est à dire + rat = g multiplié par (produit des termes dans lnum) / (produit des termes dans lden). + </para> + <para> + Si <literal>flag</literal> vaut <literal>'c'</literal> (resp. <literal>'d'</literal>), les racines de <literal>pol</literal> + sont réfléchies par rapport à l'axe imaginaire (resp. le cercle unité), i.e. + les facteurs dans <literal>lnum</literal> sont des polynômes stables. + Idem si <literal>factors</literal> est appelé avec des arguments rationnels : + les termes dans <literal>lnum</literal> et <literal>lden</literal> sont des polynômes stables si + <literal>flag</literal> est donné. <literal>R2=factors(R1,'c')</literal> ou <literal>R2=factors(R1,'d')</literal> + avec <literal>R1</literal> une fraction rationnelle ou une liste <literal>syslin</literal> SISO : la sortie <literal>R2</literal> est rationnelle avec un numérateur et un dénominateur stables et + de même module que <literal>R1</literal> sur l'axe imaginaire (<literal>'c'</literal>) + ou le cercle unité (<literal>'d'</literal>). + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +n=poly([0.2,2,5],'z'); +d=poly([0.1,0.3,7],'z'); +R=syslin('d',n,d); +R1=factors(R,'d') +roots(R1('num')) +roots(R1('den')) +w=exp(2*%i*%pi*[0:0.1:1]); +norm(abs(horner(R1,w))-abs(horner(R,w))) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="simp">simp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/hermit.xml b/modules/polynomials/help/fr_FR/hermit.xml new file mode 100755 index 000000000..bdc1248ed --- /dev/null +++ b/modules/polynomials/help/fr_FR/hermit.xml @@ -0,0 +1,72 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="hermit"> + <refnamediv> + <refname>hermit</refname> + <refpurpose>forme d'Hermite </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[Ar,U]=hermit(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ar </term> + <listitem> + <para>matrice triangulaire de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>U </term> + <listitem> + <para>matrice unimodulaire de polynômes + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Forme d'Hermite : <literal>U</literal> est une matrice unimodulaire telle que <literal>A*U</literal> est sous la + forme d'Hermite triangulaire : + </para> + <para> + La variable de sortie est <literal>Ar=A*U</literal>. + </para> + <para> + <warning> + Attention : version expérimentale + </warning> + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +p=[s, s*(s+1)^2, 2*s^2+s^3]; +[Ar,U]=hermit(p'*p); +clean(p'*p*U), det(U) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="hrmt">hrmt</link> + </member> + <member> + <link linkend="htrianr">htrianr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/horner.xml b/modules/polynomials/help/fr_FR/horner.xml new file mode 100755 index 000000000..63ddeee19 --- /dev/null +++ b/modules/polynomials/help/fr_FR/horner.xml @@ -0,0 +1,84 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="horner"> + <refnamediv> + <refname>horner</refname> + <refpurpose>évaluation d'un polynôme ou d'une fraction rationnelle </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>horner(P,x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>P </term> + <listitem> + <para>polynôme ou matrice de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>x </term> + <listitem> + <para>vecteur de nombres , de polynômes ou de fractions rationnelles + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + évalue le polynôme ou la fraction rationnelle (ou matrice de fractions rationnelles) + <literal>P = P(s)</literal> quand la variable <literal>s</literal> du polynôme + est remplacée par <literal>x</literal> : + </para> + <para> + <literal>horner(P,x)</literal>=<literal>P(x)</literal> + </para> + <para> + Exemple (transformation bilinéaire) : supposons que <literal>P = P(s)</literal> est + une matrice de polynômes, alors la matrice de polynômes + <literal>P((1+s)/(1-s))</literal> est obtenue par <literal>horner(P,(1+s)/(1-s))</literal>. + </para> + <para> + Pour évaluer une matrice de polynômes à des fréquences données utiliser plutôt la primitive <literal>freq</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +//evaluation d'un polynôme pour un vecteur de nombres +P=poly(1:3,'x') +horner(P,[1 2 5]) +horner(P,[1 2 5]+%i) + +//evaluation d'un vecteur de fractions rationnelles +s=poly(0,'s');M=[s,1/s]; +horner(M,1) +horner(M,%i) +horner(M,1/s) + +//evaluation d'un polynôme pour une matrice de nombres +X= [1 2;3 4] +p=poly(1:3,'x','c') +m=horner(p, X) +1*X.^0+2*X.^1+3*X.^2 + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="freq">freq</link> + </member> + <member> + <link linkend="repfreq">repfreq</link> + </member> + <member> + <link linkend="evstr">evstr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/hrmt.xml b/modules/polynomials/help/fr_FR/hrmt.xml new file mode 100755 index 000000000..af4aae393 --- /dev/null +++ b/modules/polynomials/help/fr_FR/hrmt.xml @@ -0,0 +1,64 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="hrmt"> + <refnamediv> + <refname>hrmt</refname> + <refpurpose>PGDC de plusieurs polynômes </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[pg,U]=hrmt(v)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>v </term> + <listitem> + <para>vecteur ligne de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>pg </term> + <listitem> + <para>polynôme + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>U </term> + <listitem> + <para>matrice unimodulaire de polynômes + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[pg,U]=hrmt(v)</literal> renvoie une matrice unimodulaire <literal>U</literal> et <literal>pg</literal> = PGDC de la ligne de + polynômes <literal>v</literal> tels que <literal>v*U = [pg,0]</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +x=poly(0,'x'); +v=[x*(x+1),x^2*(x+1),(x-2)*(x+1),(3*x^2+2)*(x+1)]; +[pg,U]=hrmt(v);U=clean(U) +det(U) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="gcd">gcd</link> + </member> + <member> + <link linkend="htrianr">htrianr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/htrianr.xml b/modules/polynomials/help/fr_FR/htrianr.xml new file mode 100755 index 000000000..5be1d43ca --- /dev/null +++ b/modules/polynomials/help/fr_FR/htrianr.xml @@ -0,0 +1,83 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="htrianr"> + <refnamediv> + <refname>htrianr</refname> + <refpurpose>triangularisation d'une matrice de polynômes </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[Ar,U,rk]=htrianr(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ar </term> + <listitem> + <para>matrice de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>U </term> + <listitem> + <para>matrice unimodulaire de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk </term> + <listitem> + <para> + entier, le rang normal de <literal>A</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + triangularisation de la matrice de polynômes <literal>A</literal>. + </para> + <para> + <literal>A</literal> de taille <literal>[m,n]</literal>, <literal>m <= n</literal>. + </para> + <para> + <literal>Ar=A*U</literal> + </para> + <para> + <warning> + Attention: il y a une élimination des "petits" termes (voir le code la fonction). + </warning> + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +x=poly(0,'x'); +M=[x;x^2;2+x^3]*[1,x-2,x^4]; +[Mu,U,rk]=htrianr(M) +det(U) +M*U(:,1:2) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="hrmt">hrmt</link> + </member> + <member> + <link linkend="colcompr">colcompr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/inv_coeff.xml b/modules/polynomials/help/fr_FR/inv_coeff.xml new file mode 100755 index 000000000..3165c9071 --- /dev/null +++ b/modules/polynomials/help/fr_FR/inv_coeff.xml @@ -0,0 +1,72 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="inv_coeff"> + <refnamediv> + <refname>inv_coeff</refname> + <refpurpose>construction d'une matrice polynomiale à partir des coefficients </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[P]=inv_coeff(C,[,d,[name])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>C </term> + <listitem> + <para>"grosse" matrice des coefficients + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>d </term> + <listitem> + <para> + degré de la matrice polynomiale (paramètre optionnel valant par défaut <literal>d=-1+size(C,'c')/size(C,'r')</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>name </term> + <listitem> + <para> + chaîne de caractères (indéterminée du polynôme, <literal>'x'</literal> par défaut). + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>P=inv_coeff(Mp,k)</literal>, quand <literal>k</literal> est compatible avec la taille de <literal>Mp</literal> renvoie une matrice polynomiale de degré k. <literal>C=[C0,C1,...,Ck]</literal> et + <literal>P= C0 + C1*x +... +Ck*x^k</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +A=int(10*rand(2,6)) +// construction d'une matrice polynomiale de degré 1 +P=inv_coeff(A,1) +norm(coeff(P)-A) +// utilisation de la valeur par défaut du degré +P1=inv_coeff(A) +norm(coeff(P1)-A) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="degree">degree</link> + </member> + <member> + <link linkend="coeff">coeff</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/invr.xml b/modules/polynomials/help/fr_FR/invr.xml new file mode 100755 index 000000000..7cdb58374 --- /dev/null +++ b/modules/polynomials/help/fr_FR/invr.xml @@ -0,0 +1,60 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="invr"> + <refnamediv> + <refname>invr</refname> + <refpurpose>inversion d'une matrice rationnelle (ou polynomiale) </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>F = invr(H)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>H </term> + <listitem> + <para>polynôme ou matrice de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>F </term> + <listitem> + <para>polynôme ou matrice de polynômes + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Si <literal>H</literal> est une matrice de polynômes ou de fractions rationnelles, <literal>invr</literal> + calcule <literal>H^(-1)</literal> avec l'algorithme de Leverrier (voir code de la fonction). + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s') +H=[s,s*s+2;1-s,1+s]; invr(H) +[Num,den]=coffg(H);Num/den +H=[1/s,(s+1);1/(s+2),(s+3)/s];invr(H) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="glever">glever</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + <member> + <link linkend="inv">inv</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/lcmdiag.xml b/modules/polynomials/help/fr_FR/lcmdiag.xml new file mode 100755 index 000000000..7c767c635 --- /dev/null +++ b/modules/polynomials/help/fr_FR/lcmdiag.xml @@ -0,0 +1,82 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="lcmdiag"> + <refnamediv> + <refname>lcmdiag</refname> + <refpurpose>factorisation diagonale par le plus petit commun multiple </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[N,D]=lcmdiag(H) + [N,D]=lcmdiag(H,flag) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>H </term> + <listitem> + <para>matrice de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>N </term> + <listitem> + <para>matrice de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>D </term> + <listitem> + <para>matrice diagonale de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag </term> + <listitem> + <para> + chaîne de caractères : <literal>'row'</literal> ou <literal>'col'</literal> (par défaut) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[kN,D]=lcmdiag(H,'row')</literal> calcule une factorisation <literal>D*H=N</literal>, + i.e. H=D^(-1)*N où D est une matrice diagonale avec D(k,k)=ppcm de la + k-ième ligne de H.den . + </para> + <para> + <literal>[N,D]=lcmdiag(H)</literal> ou <literal>[N,D]=lcmdiag(H,'col)</literal> renvoie + H=N*D^(-1) avec D diagonale et D(k,k)=ppcm de ma k-ième colonne de H.den . + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +H=[1/s,(s+2)/s/(s+1)^2;1/(s^2*(s+2)),2/(s+2)]; +[N,D]=lcmdiag(H); +N/D-H + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="lcm">lcm</link> + </member> + <member> + <link linkend="gcd">gcd</link> + </member> + <member> + <link linkend="bezout">bezout</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/ldiv.xml b/modules/polynomials/help/fr_FR/ldiv.xml new file mode 100755 index 000000000..eed04cba4 --- /dev/null +++ b/modules/polynomials/help/fr_FR/ldiv.xml @@ -0,0 +1,68 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="ldiv"> + <refnamediv> + <refname>ldiv</refname> + <refpurpose>division longue d'une matrice de polynômes </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[x]=ldiv(n,d,k)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>n,d </term> + <listitem> + <para>deux matrices réelles de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>k </term> + <listitem> + <para>entier + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>x=ldiv(n,d,k)</literal> donne les <literal>k</literal> premiers coefficients de la division longue + de <literal>n</literal> par <literal>d</literal> i.e. le développement de Taylor de la matrice rationnelle + <literal>[nij(z)/dij(z)]</literal> à l'infini. + </para> + <para> + Les coefficients du développement de <literal>nij/dij</literal> sont stockés dans + <literal>x((i-1)*n+k,j) k=1:n</literal> + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +wss=ssrand(1,1,3);[a,b,c,d]=abcd(wss); +wtf=ss2tf(wss); +x1=ldiv(numer(wtf),denom(wtf),5) +x2=[c*b;c*a*b;c*a^2*b;c*a^3*b;c*a^4*b] +wssbis=markp2ss(x1',5,1,1); +wtfbis=clean(ss2tf(wssbis)) +x3=ldiv(numer(wtfbis),denom(wtfbis),5) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="arl2">arl2</link> + </member> + <member> + <link linkend="markp2ss">markp2ss</link> + </member> + <member> + <link linkend="pdiv">pdiv</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/numer.xml b/modules/polynomials/help/fr_FR/numer.xml new file mode 100755 index 000000000..6375ba807 --- /dev/null +++ b/modules/polynomials/help/fr_FR/numer.xml @@ -0,0 +1,58 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="numer"> + <refnamediv> + <refname>numer</refname> + <refpurpose>numérateurs d'une matrice rationnelle </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>num=numer(R)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>R </term> + <listitem> + <para>matrice de fractions rationnelles + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>num </term> + <listitem> + <para>matrice de polynômes + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>num=numer(R)</literal> renvoie le numérateur <literal>num</literal> d'une matrice rationnelle <literal>R</literal> (<literal>R</literal> peut aussi être une matrice constante ou une matrice de polynômes). + <literal>numer(R)</literal> est équivalent à <literal>R(2)</literal>, <literal>R('num')</literal> ou <literal>R.num</literal> + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +h=(1+2*%s)/poly(1:4,'s','c'); +denom(h) +numer(h) + +s=poly(0,"s"); +p=1+s+2*s^2; +denom(p) // Devrait retourner 1 +numer(p) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="denom">denom</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/pdiv.xml b/modules/polynomials/help/fr_FR/pdiv.xml new file mode 100755 index 000000000..e36ec3630 --- /dev/null +++ b/modules/polynomials/help/fr_FR/pdiv.xml @@ -0,0 +1,71 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="pdiv"> + <refnamediv> + <refname>pdiv</refname> + <refpurpose>division de polynômes </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[R,Q]=pdiv(P1,P2) + [Q]=pdiv(P1,P2) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>P1 </term> + <listitem> + <para>matrice de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>P2 </term> + <listitem> + <para>polynôme ou matrice de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>R,Q </term> + <listitem> + <para>deux matrices de polynômes + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Division euclidienne élément par élément de la matrice de polynômes <literal>P1</literal> + par le polynôme <literal>P2</literal> ou par la matrice de polynômes <literal>P2</literal>. + <literal>Rij</literal> est la matrice des restes, <literal>Qij</literal> est la matrice + des quotients et <literal>P1ij = Qij*P2 + Rij</literal> ou <literal>P1ij = Qij*P2ij + Rij</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +x=poly(0,'x'); +p1=(1+x^2)*(1-x);p2=1-x; +[r,q]=pdiv(p1,p2) +p2*q-p1 +p2=1+x; +[r,q]=pdiv(p1,p2) +p2*q+r-p1 + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="ldiv">ldiv</link> + </member> + <member> + <link linkend="gcd">gcd</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/pol2str.xml b/modules/polynomials/help/fr_FR/pol2str.xml new file mode 100755 index 000000000..4cf6807be --- /dev/null +++ b/modules/polynomials/help/fr_FR/pol2str.xml @@ -0,0 +1,90 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * Copyright (C) 2013 - Samuel GOUGEON : upgrade for 5.5.0 + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="pol2str"> + <refnamediv> + <refname>pol2str</refname> + <refpurpose>conversion polynôme => texte</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>strs = pol2str(p)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>p </term> + <listitem> + <para>matrice ou hypermatrice de polynômes à coefficients réels ou complexes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>str </term> + <listitem> + <para>matrice ou hypermatrice texte + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + convertit les polynômes p en textes les représentant (fonction utilitaire). + </para> + <para> + <note> + Le format de sortie des coefficients est fixé par <link linkend="format">format(..)</link>. + </note> + </para> + </refsection> + + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +pol2str(%z) + +p = poly ([1, 2, 3], "x","coeff"); +pol2str(p) + +p = (1+%i+%z)^(1:4) +pol2str(p) + ]]></programlisting> + </refsection> + + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="string">string</link> + </member> + <member> + <link linkend="prettyprint">prettyprint</link> + </member> + <member> + <link linkend="sci2exp">sci2exp</link> + </member> + </simplelist> + </refsection> + <refsection role="history tag"> + <title>Historique</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revdescription>Extension aux polynômes à coefficients complexes et aux hypermatrices. Vectorisation du traitement du tableau de polynômes</revdescription> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/polfact.xml b/modules/polynomials/help/fr_FR/polfact.xml new file mode 100755 index 000000000..0ce33db2a --- /dev/null +++ b/modules/polynomials/help/fr_FR/polfact.xml @@ -0,0 +1,85 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="polfact"> + <refnamediv> + <refname>polfact</refname> + <refpurpose>facteurs minimaux </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[f]=polfact(p)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>p </term> + <listitem> + <para> + polynôme + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>f </term> + <listitem> + <para> + vecteur <literal>[f0 f1 ... fn]</literal> tel que <literal>p=prod(f)</literal> + </para> + <variablelist> + <varlistentry> + <term>f0 </term> + <listitem> + <para> + constante + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>fi </term> + <listitem> + <para> + polynôme + </para> + </listitem> + </varlistentry> + </variablelist> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>f=polfact(p)</literal> renvoie les facteurs minimaux de p + i.e. <literal>f=[f0 f1 ... fn]</literal> tel que <literal>p=prod(f)</literal> + </para> + </refsection> + + <refsection> + <title>Exemples</title> + <programlisting role="example"> + <![CDATA[ +x = poly(0, "x") +polfact(x^2-1) + +polfact(x^7-1) + + ]]> + </programlisting> + </refsection> + + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="lcm">lcm</link> + </member> + <member> + <link linkend="cmndred">cmndred</link> + </member> + <member> + <link linkend="factors">factors</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/poly.xml b/modules/polynomials/help/fr_FR/poly.xml new file mode 100755 index 000000000..924dc7957 --- /dev/null +++ b/modules/polynomials/help/fr_FR/poly.xml @@ -0,0 +1,125 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="poly"> + <refnamediv> + <refname>poly</refname> + <refpurpose>définition d'un polynôme </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[p]=poly(a,vname, ["flag"])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>a </term> + <listitem> + <para>matrice ou nombre réel.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>vname </term> + <listitem> + <para>chaîne de caractères, nom de l'indéterminée du + polynôme. La châine ne doit pas dépasser les 4 caractères. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>"flag"</term> + <listitem> + <para>chaîne de caractères ("roots" ou "r", "coeff" ou "c"), la + valeur par défaut est "roots". + </para> + <para> + Des raccourcis peuvent être aussi utilisés: <literal>"r"</literal> pour <literal>"roots"</literal> et <literal>"c"</literal> pour <literal>"coeff"</literal>. + </para> + + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <variablelist> + <varlistentry> + <term>Si a est une matrice,</term> + <listitem> + <para> + <literal>p</literal> est le polynôme + caractéristique de a, c'est à dire + <literal>déterminant(x*eye()-a)</literal>, <literal>x</literal> étant + l'indéterminée. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Si v est un vecteur,</term> + <listitem> + <itemizedlist> + <listitem> + <para> + <literal>poly(v,"x",["roots"])</literal> est le polynôme + dont les racines sont égales aux termes de <literal>v</literal> et + <literal>"x"</literal> l'indéterminée. Dans ce cas + <literal>roots</literal> et <literal>poly</literal> sont des fonctions inverses + l'une de l'autre. + <note> + Notez qye les racines infinies produisent des + coefficients de haut degré egaux a zéro. + </note> + </para> + </listitem> + <listitem> + <para> + <literal>poly(v,"x","coeff")</literal> crée le polynôme + d'indéterminée <literal>"x"</literal> dont les coefficients sont + les termes de <literal>v</literal> (v(1) est le terme constant). Dans ce + dernier cas, <literal>poly</literal> et <literal>coeff</literal> sont des fonctions + inverses l'une de l'autre. + </para> + </listitem> + </itemizedlist> + </listitem> + </varlistentry> + </variablelist> + <para> + <literal>s=poly(0,"s")</literal> permet de définir des polynômes en + utilisant les opérations usuelles (+,-,*,^).<literal>"s"</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,"s"); +p=1+s+2*s^2 +A=rand(2,2); +poly(A,"x") +//fractions rationnelles +h=(1+2*%s)/poly(1:4,'s','coeff') + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="coeff">coeff</link> + </member> + <member> + <link linkend="matrices">matrices</link> + </member> + <member> + <link linkend="rational">rational</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Historique</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>Les seules valeurs autorisées pour le troisième argument sont "roots", "coeff", "c" et "r".</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/rational.xml b/modules/polynomials/help/fr_FR/rational.xml new file mode 100755 index 000000000..9f96c3c62 --- /dev/null +++ b/modules/polynomials/help/fr_FR/rational.xml @@ -0,0 +1,46 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="rational"> + <refnamediv> + <refname>rational</refname> + <refpurpose>Objet Scilab, fraction rationnelle </refpurpose> + </refnamediv> + <refsection> + <title>Description</title> + <para> + Une fraction rationnelle <literal>r</literal> est le quotient de deux polynômes <literal>r=num/den</literal>. + La représentation interne d'une fraction rationnelle est une liste : + <literal>r=rlist(num,den,[])</literal> est identique à <literal>r=num/den</literal>. + Une matrice de fractions rationnelles peut être définie en utilisant la syntaxe habituelle : + <literal>[r11,r12;r21,r22]</literal> est une matrice 2x2 ou les <literal>rij</literal> sont des fractions rationnelles. + Une matrice de fractions rationnelles peut aussi être définie comme précédemment : <literal>tlist(['r','num','den','dt'],num,den,[])</literal> avec <literal>num</literal> et <literal>den</literal> deux matrices polynomiales. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +W=[1/s,1/(s+1)] +W'*W +Num=[s,s+2;1,s];Den=[s*s,s;s,s*s]; +rlist(Num,Den,[]) +H=Num./Den +syslin('c',Num,Den) +syslin('c',H) +[Num1,Den1]=simp(Num,Den) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="syslin">syslin</link> + </member> + <member> + <link linkend="simp">simp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/residu.xml b/modules/polynomials/help/fr_FR/residu.xml new file mode 100755 index 000000000..7e4a7316f --- /dev/null +++ b/modules/polynomials/help/fr_FR/residu.xml @@ -0,0 +1,73 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="residu"> + <refnamediv> + <refname>residu</refname> + <refpurpose>résidu </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[V]=residu(P,Q1,Q2)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>P, Q1, Q2 </term> + <listitem> + <para>polynômes ou matrice de polynômes à coefficients réels ou complexes. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>V=residu(P,Q1,Q2)</literal> renvoie la matrice <literal>V</literal> telle que <literal>V(i,j)</literal> + est la somme des résidus de la fraction rationnelle + <literal>P(i,j)/(Q1(i,j)*Q2(i,j))</literal> calculés aux zéros de <literal>Q1(i,j)</literal>. + </para> + <para> + <literal>Q1(i,j)</literal> et <literal>Q2(i,j)</literal> ne doivent pas avoir de racines communes. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +H=[s/(s+1)^2,1/(s+2)];N=numer(H);D=denom(H); +w=residu(N.*horner(N,-s),D,horner(D,-s)); //N(s) N(-s) / D(s) D(-s) +sqrt(sum(w)) // La norme H2 +h2norm(tf2ss(H)) + +p=(s-1)*(s+1)*(s+2)*(s+10);a=(s-5)*(s-1)*(s*s)*((s+1/2)**2); +b=(s-3)*(s+2/5)*(s+3); +residu(p,a,b)+531863/4410 // Exact +z=poly(0,'z');a=z^3+0.7*z^2+0.5*z-0.3;b=z^3+0.3*z^2+0.2*z+0.1; +atild=gtild(a,'d');btild=gtild(b,'d'); +residu(b*btild,z*a,atild)-2.9488038 // Exact +a=a+0*%i;b=b+0*%i; +real(residu(b*btild,z*a,atild)-2.9488038) // Cas complexe + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="pfss">pfss</link> + </member> + <member> + <link linkend="bdiag">bdiag</link> + </member> + <member> + <link linkend="roots">roots</link> + </member> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="gtild">gtild</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/roots.xml b/modules/polynomials/help/fr_FR/roots.xml new file mode 100755 index 000000000..ee108a747 --- /dev/null +++ b/modules/polynomials/help/fr_FR/roots.xml @@ -0,0 +1,170 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) ???? - 2008 - INRIA + * Copyright (C) 2011 - DIGITEO - Michael Baudin + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="roots" xml:lang="fr"> + <refnamediv> + <refname>roots</refname> + <refpurpose>racines d'un polynôme</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis> + x=roots(p) + x=roots(p,"algo") + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para> + un polynôme réel ou complexe, ou + une m-par-1 or 1-par-m matrice de doubles, les coefficients du polynômes par ordre de puissance décroissante. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>algo</term> + <listitem> + <para> + une chaîne de caractères, l'algorithme à utiliser (défaut algo="e"). + Si algo="e", alors les valeurs propres de la matrice compagnion sont utilisées. + Si algo="f", alors l'algorithme de Jenkins-Traub est utilisé (si les coefficients + du polynôme sont réels et que le degré du polynôme est plus petit que 100). + Si algo="f" et que le polynôme est complexe, alors une erreur est générée. + Si algo="f" et que le polynôme est de degré inférieur à 100, alors une erreur est + générée. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Cette fonction retourne dans le vecteur complexe + <literal>x</literal> les racines du polynôme <literal>p</literal>. + </para> + <para> + L'option "f" utilise l'algorithme rapide RPOLY, fondé sur la méthode de Jenkins-Traub. + </para> + <para> + Pour les polynôme réels de degré inférieur à 100, on peut utiliser + l'option "f", qui peut être plus rapide dans certains cas. + Toutefois, certains polynômes sont susceptibles de poser des problèmes + de convergences pour l'algorithme associé à l'option "f". + Par exemple, <literal>p=poly([1.e300,1.e0,1.e-300],'x');</literal> + provoque le bouclage infini de <literal>roots(p,"f")</literal> + </para> + </refsection> + <refsection> + <title>Exemples</title> + <para> + Dans les exemples suivants, on calcule des racines de polynômes. + </para> + <programlisting role="example"><![CDATA[ +// Un polynôme réel. +p = poly([1 2 3],"x") +roots(p) +// Les coefficients du polynôme sont donnés. +p = [3 2 1] +roots(p) +// Les racines d'un polynôme complexe. +p=poly([0,10,1+%i,1-%i],'x'); +roots(p) +// Les racines du polynôme caractéristique d'une matrice. +A=rand(3,3); +p = poly(A,'x') +roots(p) +spec(A) + ]]></programlisting> + <para> + La représentation polynômiale peut avoir un impact significatif sur les + racines. + Dans l'exemple suivant, suggéré par Wilkinson dans les années 60 et présenté + par Moler, on considère une matrice dont les termes diagonaux sont égaux + à 1, 2, ..., 20. + Bien entendu, les racines du polynôme caractéristique sont 1, 2, ..., 20. + Si on calcule le polynôme caractéristique associé et qu'on calcule ses + racines, on peut voir qu'elles sont significativement différentes des + valeurs attendues. + Cela montre que le seul fait de représenter les coefficients dans + des doubles IEEE change les racines. + </para> + <programlisting role="example"><![CDATA[ +A = diag(1:20); +p = poly(A,'x') +roots(p) + ]]></programlisting> + <para> + L'option "f" produit une erreur si le polynôme est complexe + ou que le degré est plus grand que 100. + </para> + <programlisting role="example"><![CDATA[ + // Le cas suivant produit une erreur + p = %i+%s; + roots(p,"f") + // Le cas suivant produit une erreur + p = ones(101,1); + roots(p,"f") + ]]></programlisting> + <para> + Le script suivant est une manière simple de vérifier que la matrice compagnon donne le même résultat que l'option "e". + Il utilise explicitement la matrice compagnon pour calculer les racines. + Il faut néanmoins inverser les coefficients du polynôme ; + en effet, "roots" les attend dans l'ordre de degré décroissant, + alors que "poly" les attend dans l'ordre croissant. + </para> + <programlisting role="example"><![CDATA[ +v= [1.12119799 0 3.512D+13 32 3.275D+27 0 1.117D+41 4.952D+27 1.722D+54 0 1.224D+67 0 3.262D+79 ]; +r1 = roots(v,"e"); // Avec l'option "e" +dv = size(v,"*"); +p = poly(v(dv:-1:1),"x","coeff"); // Inversion des coefficients de v +A = companion(p); +r2 = spec(A); // Avec la matrice compagnon +max(abs(r1-r2)) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="spec">spec</link> + </member> + <member> + <link linkend="companion">companion</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Bibliographie</title> + <para> + La routine RPOLY est decrite dans "Algorithm 493: Zeros of a Real + Polynomial", ACM TOMS Volume 1, Issue 2 (June 1975), pp. 178-189 + </para> + </refsection> + <refsection> + <title>Fonctions Utilisées</title> + <para> + Le code source de rpoly.f peut être trouvé dans le répertoire + SCI/modules/polynomials/src/fortran/ de la distribution source de Scilab. Dans le cas où la + matrix compagnon est utilisée, le calcul des valeurs propres est effectué + en utilisant les routines DGEEV et ZGEEV de LAPACK. + </para> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/rowcompr.xml b/modules/polynomials/help/fr_FR/rowcompr.xml new file mode 100755 index 000000000..d70e94624 --- /dev/null +++ b/modules/polynomials/help/fr_FR/rowcompr.xml @@ -0,0 +1,69 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="rowcompr"> + <refnamediv> + <refname>rowcompr</refname> + <refpurpose>compression de lignes d'une matrice de polynômes </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[X,rk,Ac]=rowcompr(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>A </term> + <listitem> + <para>matrice de polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Y </term> + <listitem> + <para>matrice carrée de polynômes (base unimodulaire à gauche) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk </term> + <listitem> + <para> + rang normal de <literal>A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ac </term> + <listitem> + <para> + : <literal>Ac=X*A</literal>, matrice de polynômes + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Compression de lignes de la matrice de polynômes <literal>A </literal>. + </para> + <para> + <literal>X</literal> est une base de polynômes unimodulaire à gauche qui compresse les lignes + de <literal>A</literal>. <literal>rk</literal> est le rang normal de A. + </para> + <para> + <warning> + Attention : élimination des termes "petits" (à utiliser avec précaution). + </warning> + </para> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="colcompr">colcompr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/sfact.xml b/modules/polynomials/help/fr_FR/sfact.xml new file mode 100755 index 000000000..711b38093 --- /dev/null +++ b/modules/polynomials/help/fr_FR/sfact.xml @@ -0,0 +1,82 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="sfact"> + <refnamediv> + <refname>sfact</refname> + <refpurpose>factorisation spectrale en temps discret </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>F=sfact(P)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>P </term> + <listitem> + <para>matrice de polynômes réels + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Trouve <literal>F</literal>, un facteur spectral de <literal>P</literal>. <literal>P</literal> est une + matrice de polynômes telle que chaque racine de <literal>P</literal> a une image miroir + par rapport au cercle unité. Le problème est singulier si une racine se trouve sur le cercle unité. + </para> + <para> + <literal>sfact(P)</literal> renvoie une matrice de polynômes <literal>F(z)</literal> antistable et telle que + </para> + <para> + <literal>P = F(z)* F(1/z) *z^n</literal> + </para> + <para> + Pour les polynômes scalaires un algorithme spécifique est utilisé. + Les algorithmes sont tirés du livre de Kucera. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +// polynôme simple +z=poly(0,'z'); +p=(z-1/2)*(2-z) +w=sfact(p); +w*numer(horner(w,1/z)) + +// exemple matriciel +F1=[z-1/2,z+1/2,z^2+2;1,z,-z;z^3+2*z,z,1/2-z]; +P=F1*gtild(F1,'d'); // P est symétrique +F=sfact(P) +roots(det(P)) +roots(det(gtild(F,'d'))) // Les racines stables +roots(det(F)) // Les racines antistables +clean(P-F*gtild(F,'d')) + +// Utilisation en temps continu +s=poly(0,'s'); +p=-3*(s+(1+%i))*(s+(1-%i))*(s+0.5)*(s-0.5)*(s-(1+%i))*(s-(1-%i));p=real(p); +// p(s) = polynôme dans s^2, cherche un f stable tel que p=f(s)*f(-s) +w=horner(p,(1-s)/(1+s)); // transformation bilinéaire w=p((1-s)/(1+s)) +wn=numer(w); // prend le numérateur +fn=sfact(wn);f=numer(horner(fn,(1-s)/(s+1))); // Factorisation et transformation inverse +f=f/sqrt(horner(f*gtild(f,'c'),0));f=f*sqrt(horner(p,0)); // normalisation +roots(f) // f est stable +clean(f*gtild(f,'c')-p) //f(s)*f(-s) est égal à p(s) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="gtild">gtild</link> + </member> + <member> + <link linkend="fspecg">fspecg</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/simp.xml b/modules/polynomials/help/fr_FR/simp.xml new file mode 100755 index 000000000..8998b15ed --- /dev/null +++ b/modules/polynomials/help/fr_FR/simp.xml @@ -0,0 +1,96 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="simp"> + <refnamediv> + <refname>simp</refname> + <refpurpose>simplification rationnelle </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[N1,D1]=simp(N,D) + H1=simp(H) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>N,D </term> + <listitem> + <para>polynômes réels ou matrices de polynômes réels + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>H </term> + <listitem> + <para> + matrice de fractions rationnelles (i.e matrice avec des termes <literal>n/d</literal>, <literal>n</literal> et <literal>d</literal> polynômes réels) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>[n1,d1]=simp(n,d)</literal> calcule deux polynômes <literal>n1</literal> et <literal>d1</literal> + tels que<literal>n1/d1 = n/d</literal>. + </para> + <para> + Si <literal>N</literal> et <literal>D</literal> sont des matrices de polynômes le calcul + est fait élément par élément. + </para> + <para> + <literal>H1=simp(H)</literal> est aussi valide (chaque terme de <literal>H</literal> est simplifié dans <literal>H1</literal>). + </para> + <para> + <warning> + Attention : + </warning> + </para> + <para> + - pas de seuil i.e. <literal>simp</literal> ne peut pas forcer une + simplification. + </para> + <para> + - Pour les systèmes dynamiques linéaires avec un intégrateur la simplification + change le gain statique. (<literal>H(0)</literal> pour les systèmes continus ou <literal>H(1)</literal> pour les systèmes discrets) + </para> + <para> + - Pour les données complexes, <literal>simp</literal> renvoie ses entrées. + </para> + <para> + - Une simplification est effectuée après la plupart des opérations rationnelles. Il est possible de la supprimer en utilisant la fonction <literal>simp_mode</literal>. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +[n,d]=simp((s+1)*(s+2),(s+1)*(s-2)) + +simp_mode(%F);hns=s/s +simp_mode(%T);hns=s/s + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="roots">roots</link> + </member> + <member> + <link linkend="trfmod">trfmod</link> + </member> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + <member> + <link linkend="simp_mode">simp_mode</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/simp_mode.xml b/modules/polynomials/help/fr_FR/simp_mode.xml new file mode 100755 index 000000000..4dd1aa3ed --- /dev/null +++ b/modules/polynomials/help/fr_FR/simp_mode.xml @@ -0,0 +1,58 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="simp_mode"> + <refnamediv> + <refname>simp_mode</refname> + <refpurpose>mode de simplification des fractions rationnelles </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>mod=simp_mode() + simp_mode(mod) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>mod </term> + <listitem> + <para>un booléen + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + Une simplification rationnelle est effectuée après chaque opération sur les fractions rationnelles. Il est possible de changer cela avec la fonction <literal>simp_mode</literal>. + </para> + <para> + <literal>simp_mode(%t)</literal> passe en mode de simplification systématique. + </para> + <para> + <literal>simp_mode(%f)</literal> empêche les simplifications. + </para> + <para> + <literal>mod=simp_mode()</literal> renvoie dans mod le mode de simplification courant. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +mod=simp_mode() +simp_mode(%f);hns=s/s +simp_mode(%t);hns=s/s +simp_mode(mod); + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="simp">simp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/sylm.xml b/modules/polynomials/help/fr_FR/sylm.xml new file mode 100755 index 000000000..b37fe06e8 --- /dev/null +++ b/modules/polynomials/help/fr_FR/sylm.xml @@ -0,0 +1,68 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="sylm"> + <refnamediv> + <refname>sylm</refname> + <refpurpose>matrice de Sylvester </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[S]=sylm(a,b)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>a,b </term> + <listitem> + <para>deux polynômes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>S </term> + <listitem> + <para>matrice + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>sylm(a,b)</literal> renvoie la matrice de Sylvester associée aux polynômes + <literal>a</literal> et <literal>b</literal>, i.e. la matrice <literal>S</literal> telle que : + </para> + <para> + <literal>coeff( a*x + b*y )' = S * [coeff(x)';coeff(y)']</literal>. + </para> + <para> + La dimension de <literal>S</literal> est égale à <literal>degree(a)+degree(b)</literal>. + </para> + <para> + Si <literal>a</literal> et <literal>b</literal> sont premiers entre eux alors + </para> + <para> + <literal>rank(sylm(a,b))=degree(a)+degree(b))</literal> et les instructions + </para> + <programlisting role="no-scilab-exec"><![CDATA[ +u = sylm(a,b) \ eye(na+nb,1) +x = poly(u(1:nb),'z','coeff') +y = poly(u(nb+1:na+nb),'z','coeff') + ]]></programlisting> + <para> + calculent les facteurs de Bezout <literal>x</literal> ainsi que <literal>y</literal> de degré minimum tels que + <literal>a*x+b*y = 1</literal> + </para> + + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +x = poly(0,"x") +y = poly ([1, 2, 3], "x","coeff"); +sylm(x,y) + + ]]></programlisting> + </refsection> + </refsection> +</refentry> diff --git a/modules/polynomials/help/fr_FR/varn.xml b/modules/polynomials/help/fr_FR/varn.xml new file mode 100755 index 000000000..f67068c45 --- /dev/null +++ b/modules/polynomials/help/fr_FR/varn.xml @@ -0,0 +1,96 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="varn"> + <refnamediv> + <refname>varn</refname> + <refpurpose>variable symbolique d'un polynôme ou d'une fraction rationnelle</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Séquence d'appel</title> + <synopsis>[symb]=varn(p) + [pm]=varn(p,varname) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Paramètres</title> + <variablelist> + <varlistentry> + <term>p </term> + <listitem> + <para>matrice de polynômes ou de fractions rationelles + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>symb </term> + <listitem> + <para> + chaîne de caractères: nom de l'indéterminée des éléments de <literal>p</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>varname </term> + <listitem> + <para> + chaîne de caractères: nouveau nom à attribuer à la variable des polynômes ou fractions rationnelles de <literal>p</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>pm </term> + <listitem> + <para> + matrice <literal>p</literal> actualisée avec le nouveau nom de variable <literal>varname</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Description</title> + <para> + <literal>symb=varn(p)</literal> renvoie dans <literal>symb</literal> l'indéterminée du polynôme <literal>p</literal> + (par exemple <literal>varn(poly(0,'x'))</literal> est égal à <literal>'x'</literal>). + </para> + <para> + <literal>varn(p,'s')</literal> renvoie une matrice polynomiale de même taille que <literal>p</literal> mais avec <literal>'s'</literal> comme indéterminée. + </para> + </refsection> + <refsection> + <title>Exemples</title> + <programlisting role="example"><![CDATA[ +s = poly(0,'s'); p = [s^2+1,s]; +varn(p) +varn(p,'x') + +f = %z / (%z-1); f = [f f^2] +varn(f) +varn(f,"x") + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Voir aussi</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="rlist">rlist</link> + </member> + <member> + <link linkend="horner">horner</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Historique</title> + <revhistory> + <revision> + <revnumber>5.5.1</revnumber> + <revdescription> + <para>Extension aux fractions rationnelles</para> + </revdescription> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/addchapter.sce b/modules/polynomials/help/ja_JP/addchapter.sce new file mode 100755 index 000000000..11643ae1d --- /dev/null +++ b/modules/polynomials/help/ja_JP/addchapter.sce @@ -0,0 +1,11 @@ +// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) 2009 - DIGITEO +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +add_help_chapter("Polynomials",SCI+"/modules/polynomials/help/ja_JP",%T); + diff --git a/modules/polynomials/help/ja_JP/bezout.xml b/modules/polynomials/help/ja_JP/bezout.xml new file mode 100755 index 000000000..a664cc253 --- /dev/null +++ b/modules/polynomials/help/ja_JP/bezout.xml @@ -0,0 +1,93 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Serge STEER + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="bezout"> + <refnamediv> + <refname>bezout</refname> + <refpurpose>多項式またｈ整数のべズー方程式</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis>[thegcd,U]=bezout(p1,p2)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parameters</title> + <variablelist> + <varlistentry> + <term>p1, p2</term> + <listitem> + <para>2つの実数多項式または2つの整数スカラー(8型)</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>[thegcd,U]=bezout(p1,p2)</literal> は GCD, + <literal>p1</literal> および <literal>p2</literal>の + <literal>thegcd</literal>および + 以下のような(2x2) ユニモジュラ行列<literal>U</literal> + を計算します: + </para> + <para> + <literal>[p1,p2]*U = [thegcd,0]</literal> + </para> + <para> + <literal>p1</literal>および<literal>p2</literal>のlcmは + 以下のように指定されます: + </para> + <para> + <literal>p1*U(1,2)</literal> (または <literal>-p2*U(2,2)</literal>) + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +// 多項式の場合 +x=poly(0,'x'); +p1=(x+1)*(x-3)^5;p2=(x-2)*(x-3)^3; +[thegcd,U]=bezout(p1,p2) +det(U) +clean([p1,p2]*U) +thelcm=p1*U(1,2) +lcm([p1,p2]) +// 整数の場合 +i1=int32(2*3^5); i2=int32(2^3*3^2); +[thegcd,U]=bezout(i1,i2) +V=int32([2^2*3^5, 2^3*3^2,2^2*3^4*5]); +[thegcd,U]=gcd(V) +V*U +lcm(V) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="roots">roots</link> + </member> + <member> + <link linkend="simp">simp</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + <member> + <link linkend="lcm">lcm</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/chepol.xml b/modules/polynomials/help/ja_JP/chepol.xml new file mode 100755 index 000000000..a919a365e --- /dev/null +++ b/modules/polynomials/help/ja_JP/chepol.xml @@ -0,0 +1,50 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="chepol"> + <refnamediv> + <refname>chepol</refname> + <refpurpose>チェビシェフ多項式 </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[Tn]=chepol(n,var)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>n</term> + <listitem> + <para>整数 : 多項式の次数</para> + </listitem> + </varlistentry> + <varlistentry> + <term>var</term> + <listitem> + <para>文字列 : 多項式の変数</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Tn</term> + <listitem> + <para> + 変数 <literal>var</literal>の多項式 + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + チェビシェフ多項式の再帰的実装. + <literal>T0=1</literal> および <literal>T1=poly(0,var)</literal>とした + <literal>Tn=2*poly(0,var)*chepol(n-1,var)-chepol(n-2,var)</literal>. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +chepol(4,'x') + ]]></programlisting> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/cmndred.xml b/modules/polynomials/help/ja_JP/cmndred.xml new file mode 100755 index 000000000..80b625038 --- /dev/null +++ b/modules/polynomials/help/ja_JP/cmndred.xml @@ -0,0 +1,60 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="cmndred"> + <refnamediv> + <refname>cmndred</refname> + <refpurpose>共通分母形式</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[n,d]=cmndred(num,den)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>num, den</term> + <listitem> + <para>同じ次元の2つの多項式行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>[n,d]=cmndred(num,den)</literal>は, + 以下のような + 多項式行列<literal>n</literal>および + 共通分母多項式<literal>d</literal>を計算します: + </para> + <para> + <literal>n/d=num./den</literal> + </para> + <para> + <literal>num./den</literal>により定義される有理行列は + <literal>n/d</literal>です. + </para> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="simp">simp</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/coeff.xml b/modules/polynomials/help/ja_JP/coeff.xml new file mode 100755 index 000000000..c1c8d1f54 --- /dev/null +++ b/modules/polynomials/help/ja_JP/coeff.xml @@ -0,0 +1,76 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Serge STEER + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="coeff"> + <refnamediv> + <refname>coeff</refname> + <refpurpose>多項式行列の係数</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[C]=coeff(Mp [,v])</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>Mp</term> + <listitem> + <para>多項式行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>v</term> + <listitem> + <para>整数 (行または列), 選択した次数のベクトル</para> + </listitem> + </varlistentry> + <varlistentry> + <term>C</term> + <listitem> + <para>大きな係数の行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>C=coeff(Mp)</literal> + 多項式行列<literal>Mp</literal>の係数である大きな + 行列<literal>C</literal>を返します. + <literal>C</literal>は<literal>C=[C0,C1,...,Ck]</literal>のように + 分割されます. + ただし,<literal>Ci</literal>は昇順 + <literal>k = max(degree(Mp))</literal>に並べられています. + </para> + <para> + <literal>C=coeff(Mp,v)</literal> は + <literal>v</literal>の次数の行列の係数を返します + (<literal>v</literal> は行または列ベクトルです). + </para> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="degree">degree</link> + </member> + <member> + <link linkend="inv_coeff">inv_coeff</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/coffg.xml b/modules/polynomials/help/ja_JP/coffg.xml new file mode 100755 index 000000000..2826d0db9 --- /dev/null +++ b/modules/polynomials/help/ja_JP/coffg.xml @@ -0,0 +1,78 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Francois DELBECQUE + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="coffg"> + <refnamediv> + <refname>coffg</refname> + <refpurpose>多項式行列の逆</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[Ns,d]=coffg(Fs)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>Fs</term> + <listitem> + <para>正方多項式行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>coffg</literal> は <literal>Fs^-1</literal> を計算します. + ただし, <literal>Fs</literal> は余因子法による多項式行列です. + </para> + <para> + <literal>Fs</literal> inverse = <literal>Ns/d</literal> + </para> + <para> + <literal>d</literal> = 共通分母; <literal>Ns</literal> = 分子 (多項式行列) + </para> + <para> + (大きな行列の場合,時間がかかりますが,結果は一般に信頼できます) + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s') +a=[ s, s^2+1; s s^2-1]; +[a1,d]=coffg(a); +(a1/d)-inv(a) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="determ">determ</link> + </member> + <member> + <link linkend="detr">detr</link> + </member> + <member> + <link linkend="invr">invr</link> + </member> + <member> + <link linkend="penlaur">penlaur</link> + </member> + <member> + <link linkend="glever">glever</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/colcompr.xml b/modules/polynomials/help/ja_JP/colcompr.xml new file mode 100755 index 000000000..6968786b5 --- /dev/null +++ b/modules/polynomials/help/ja_JP/colcompr.xml @@ -0,0 +1,78 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="colcompr"> + <refnamediv> + <refname>colcompr</refname> + <refpurpose>多項式行列の列圧縮 </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[Y,rk,ac]=colcompr(A);</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>多項式行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Y</term> + <listitem> + <para>正方多項式行列 (右ユニモジュラ基底)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + <literal>A</literal>の通常ランク + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ac</term> + <listitem> + <para> + <literal>Ac=A*Y</literal>, 多項式行列 + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + 多項式行列 <literal>A</literal>の列圧縮 (左への圧縮) + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +p=[s;s*(s+1)^2;2*s^2+s^3]; +[Y,rk,ac]=colcompr(p*p'); +p*p'*Y + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="rowcompr">rowcompr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/degree.xml b/modules/polynomials/help/ja_JP/degree.xml new file mode 100755 index 000000000..b3451fcfe --- /dev/null +++ b/modules/polynomials/help/ja_JP/degree.xml @@ -0,0 +1,59 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="degree"> + <refnamediv> + <refname>degree</refname> + <refpurpose>多項式行列の次数</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[D]=degree(M)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>M</term> + <listitem> + <para>多項式行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>D</term> + <listitem> + <para>整数行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>M</literal>の最高次数の行列を返します. + </para> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="coeff">coeff</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/denom.xml b/modules/polynomials/help/ja_JP/denom.xml new file mode 100755 index 000000000..0aacbe0de --- /dev/null +++ b/modules/polynomials/help/ja_JP/denom.xml @@ -0,0 +1,62 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="denom"> + <refnamediv> + <refname>denom</refname> + <refpurpose>分母</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>den=denom(r)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>r</term> + <listitem> + <para>有理または多項式または定数行列.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>den</term> + <listitem> + <para>多項式行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>den=denom(r)</literal>は + 有理行列の分母を返します. + </para> + <para> + 有理数は,内部的に + <literal>r=list(['r','num','den','dt'],num,den,[])</literal>と + 表され, + <literal>denom(r</literal>) は <literal>r(3)</literal>, + <literal>r('den')</literal> または <literal>r.den</literal>と + 同じになります. + </para> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="numer">numer</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/derivat.xml b/modules/polynomials/help/ja_JP/derivat.xml new file mode 100755 index 000000000..fd87a229a --- /dev/null +++ b/modules/polynomials/help/ja_JP/derivat.xml @@ -0,0 +1,66 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="derivat"> + <refnamediv> + <refname>derivat</refname> + <refpurpose>有理行列の微分</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>pd=derivat(p)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>多項式または有理行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + 多項式または有理関数行列のダミー変数に関する微分を計算します. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +derivat(1/s) // -1/s^2; + ]]></programlisting> + <programlisting role="example"><![CDATA[ +p1 = poly([1 -2 1], 'x', 'coeff') +derivat(p1) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +p2 = poly([1 -4 2], 'y', 'coeff') +derivat(p2) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +p3 = poly(ones(1, 10), 'z', 'coeff') +derivat(p3) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +p4 = poly([-1 1], 't', 'roots') +derivat(p4) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +s = %s; p5 = s^{-1} + 2 + 3*s +derivat(p5) + ]]></programlisting> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/determ.xml b/modules/polynomials/help/ja_JP/determ.xml new file mode 100755 index 000000000..e02fb48fc --- /dev/null +++ b/modules/polynomials/help/ja_JP/determ.xml @@ -0,0 +1,83 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Francois DELBECQUE + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="determ"> + <refnamediv> + <refname>determ</refname> + <refpurpose>多項式行列の行列式</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>res=determ(W [,k])</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>W</term> + <listitem> + <para>実数正方多項式行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>k</term> + <listitem> + <para>整数 (Wの行列式の次数の上限</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + 実数多項式行列の行列式を返します + (Wの大きさが2*2より大きい場合,FFTにより計算されます). + </para> + <para> + <literal>res=determ(W [,k])</literal><literal>k</literal> は + <literal>W</literal>の行列式の実際の次数より大きな整数です. + </para> + <para> + <literal>k</literal>のデフォルト値は<literal>n*max(degree(W))</literal> + より大きな2の冪乗の最小値です. + </para> + <para> + 手法 (Wの大きさが 2*2より大きな場合のみ) : + フーリエ周波数に関して + <literal>W</literal>の行列式を評価し, + 行列式の係数に逆FFTを適用します. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +w=s*rand(10,10); +determ(w) +det(coeff(w,1))*s^10 + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="det">det</link> + </member> + <member> + <link linkend="detr">detr</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/detr.xml b/modules/polynomials/help/ja_JP/detr.xml new file mode 100755 index 000000000..51dcf419f --- /dev/null +++ b/modules/polynomials/help/ja_JP/detr.xml @@ -0,0 +1,53 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="detr"> + <refnamediv> + <refname>detr</refname> + <refpurpose>多項式の行列式</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>d=detr(h)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>h</term> + <listitem> + <para>多項式または有理正方行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>d=detr(h)</literal> は + 多項式または有理関数行列<literal>h</literal>の + 行列式<literal>d</literal>を返します. + Leverrierのアルゴリズムに基づきます. + </para> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="det">det</link> + </member> + <member> + <link linkend="determ">determ</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/diophant.xml b/modules/polynomials/help/ja_JP/diophant.xml new file mode 100755 index 000000000..8a04ddc5d --- /dev/null +++ b/modules/polynomials/help/ja_JP/diophant.xml @@ -0,0 +1,69 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="diophant"> + <refnamediv> + <refname>diophant</refname> + <refpurpose>ダイオファンタイン (べズー) 方程式</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[x,err]=diophant(p1p2,b)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>p1p2</term> + <listitem> + <para> + 多項式ベクトル <literal>p1p2 = [p1 p2]</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>b</term> + <listitem> + <para>多項式</para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para>多項式ベクトル [x1;x2]</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal> diophant</literal> は以下のべズー方程式を解きます: + </para> + <para> + 多項式ベクトル<literal>p1p2</literal>で指定した + <literal>p1*x1+p2*x2=b</literal> + </para> + <para>この方程式が可解の場合: + <literal>err=0</literal> + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s');p1=(s+3)^2;p2=(1+s); +x1=s;x2=(2+s); +[x,err]=diophant([p1,p2],p1*x1+p2*x2); +p1*x1+p2*x2-p1*x(1)-p2*x(2) + ]]></programlisting> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/factors.xml b/modules/polynomials/help/ja_JP/factors.xml new file mode 100755 index 000000000..213bdf1e8 --- /dev/null +++ b/modules/polynomials/help/ja_JP/factors.xml @@ -0,0 +1,133 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="factors"> + <refnamediv> + <refname>factors</refname> + <refpurpose>実数因数分解</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[lnum,g]=factors(pol [,'flag']) + [lnum,lden,g]=factors(rat [,'flag']) + rat=factors(rat,'flag') + </synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>pol</term> + <listitem> + <para>実数多項式</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rat</term> + <listitem> + <para> + 実数有理多項式 (<literal>rat=pol1/pol2</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>lnum</term> + <listitem> + <para>(1 または 2次の)多項式のリスト</para> + </listitem> + </varlistentry> + <varlistentry> + <term>lden</term> + <listitem> + <para>(1 または 2次の)多項式のリスト</para> + </listitem> + </varlistentry> + <varlistentry> + <term>g</term> + <listitem> + <para>実数</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + 文字列 <literal>'c'</literal>または <literal>'d'</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + 多項式<literal>pol</literal>の因数を + リスト<literal>lnum</literal>および"ゲイン" gに返します. + </para> + <para> + (<literal>flag</literal>が指定されない場合,) + pol= g にリスト<literal>lnum</literal>のエントリの積を乗じることになります. + <literal>flag='c'</literal>が指定された暴い, + <literal>|pol(i omega)|</literal> = <literal>|g*prod(lnum_j(i omega)|</literal> + となります. + <literal>flag='d'</literal>が指定された場合, + <literal>|pol(exp(i omega))|</literal> = <literal>|g*prod(lnum_i(exp(i omega))|</literal> + となります. + <literal>factors</literal>の引数が 1x1 有理数 <literal>rat=pol1/pol2</literal>の場合, + 分子<literal>pol1</literal> および分母 the denominator <literal>pol2</literal>の因数 + がそれぞれリスト<literal>lnum</literal> および <literal>lden</literal>に返されます. + </para> + <para> + "gain" は <literal>g</literal>に返されます. + すなわち: + rat= g times (lnumのエントリの積) / (ldenのエントリの積). + </para> + <para> + <literal>flag</literal> が<literal>'c'</literal> (または<literal>'d'</literal>)の場合, + <literal>pol</literal>の根は虚軸(または単位円)に関して折り返されます. + すなわち,<literal>lnum</literal>の因数は安定な多項式となります. + </para> + <para> + 有理数の引数を指定して<literal>factors</literal>がコールされた場合: + <literal>lnum</literal>および <literal>lden</literal>のエントリは, + <literal>flag</literal>が指定された場合に + 安定な多項式となります. + 有理関数<literal>R1</literal>またはSISOリスト<literal>syslin</literal>を指定する + <literal>R2=factors(R1,'c')</literal> または <literal>R2=factors(R1,'d')</literal> + の場合, + 出力<literal>R2</literal>は,安定な分子および分母を有し, + 虚軸(<literal>'c'</literal>)または単位円(<literal>'d'</literal>)に沿った + <literal>R1</literal>と同じ大きさの伝達関数となります. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +n=poly([0.2,2,5],'z'); +d=poly([0.1,0.3,7],'z'); +R=syslin('d',n,d); +R1=factors(R,'d') +roots(R1('num')) +roots(R1('den')) +w=exp(2*%i*%pi*[0:0.1:1]); +norm(abs(horner(R1,w))-abs(horner(R,w))) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="simp">simp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/hermit.xml b/modules/polynomials/help/ja_JP/hermit.xml new file mode 100755 index 000000000..0c4decbc6 --- /dev/null +++ b/modules/polynomials/help/ja_JP/hermit.xml @@ -0,0 +1,79 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="hermit"> + <refnamediv> + <refname>hermit</refname> + <refpurpose>エルミート形式</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[Ar,U]=hermit(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>多項式行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ar</term> + <listitem> + <para>三角多項式行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>ユニモジュラ多項式行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + エルミート形式: <literal>U</literal> は, + <literal>A*U</literal>がエルミート三角形式となるような + ユニモジュラ行列です: + </para> + <para> + 出力変数は <literal>Ar=A*U</literal>です. + </para> + <para> + 警告: 実験版 + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +p=[s, s*(s+1)^2, 2*s^2+s^3]; +[Ar,U]=hermit(p'*p); +clean(p'*p*U), det(U) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="hrmt">hrmt</link> + </member> + <member> + <link linkend="htrianr">htrianr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/horner.xml b/modules/polynomials/help/ja_JP/horner.xml new file mode 100755 index 000000000..f2dadaf45 --- /dev/null +++ b/modules/polynomials/help/ja_JP/horner.xml @@ -0,0 +1,92 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="horner"> + <refnamediv> + <refname>horner</refname> + <refpurpose>多項式/有理数の評価</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>horner(P,x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parameters</title> + <variablelist> + <varlistentry> + <term>P</term> + <listitem> + <para>多項式または有理数の行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para>数値または多項式または有理数の配列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + 多項式の変数<literal>s</literal>が<literal>x</literal>で + 置換される時, + 多項式または有理数行列<literal>P = P(s)</literal>を評価します: + </para> + <para> + <literal>horner(P,x)</literal>=<literal>P(x)</literal> + </para> + <para> + 例 (双一次変換): <literal>P = P(s)</literal> が有理行列と仮定すると, + 有理行列<literal>P((1+s)/(1-s))</literal>は + <literal>horner(P,(1+s)/(1-s))</literal>により得られます. + </para> + <para> + 指定した周波数で有理行列を評価する場合は, + <literal>freq</literal>プリミティブを使用する方が良いでしょう. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +//数値ベクトルに関する多項式の評価 +P=poly(1:3,'x') +horner(P,[1 2 5]) +horner(P,[1 2 5]+%i) +//有理数の評価 +s=poly(0,'s');M=[s,1/s]; +horner(M,1) +horner(M,%i) +horner(M,1/s) +//数値行列に関する多項式の評価 +X= [1 2;3 4] +p=poly(1:3,'x','c') +m=horner(p, X) +1*X.^0+2*X.^1+3*X.^2 + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="freq">freq</link> + </member> + <member> + <link linkend="repfreq">repfreq</link> + </member> + <member> + <link linkend="evstr">evstr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/hrmt.xml b/modules/polynomials/help/ja_JP/hrmt.xml new file mode 100755 index 000000000..08c39d027 --- /dev/null +++ b/modules/polynomials/help/ja_JP/hrmt.xml @@ -0,0 +1,76 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="hrmt"> + <refnamediv> + <refname>hrmt</refname> + <refpurpose>多項式の最大公約数</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[pg,U]=hrmt(v)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parameters</title> + <variablelist> + <varlistentry> + <term>v</term> + <listitem> + <para> + 多項式の行,すなわち,<literal>1</literal>x<literal>k</literal> 多項式行列 + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>pg</term> + <listitem> + <para>多項式</para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>ユニモジュラ多項式行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>[pg,U]=hrmt(v)</literal> は,多項式<literal>v</literal>について + ユニモジュラ行列<literal>U</literal>および + <literal>v*U = [pg,0]</literal>となるような, + <literal>pg</literal> = 多項式の行の最大公約数を返します. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +x=poly(0,'x'); +v=[x*(x+1),x^2*(x+1),(x-2)*(x+1),(3*x^2+2)*(x+1)]; +[pg,U]=hrmt(v);U=clean(U) +det(U) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="gcd">gcd</link> + </member> + <member> + <link linkend="htrianr">htrianr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/htrianr.xml b/modules/polynomials/help/ja_JP/htrianr.xml new file mode 100755 index 000000000..28b2c2232 --- /dev/null +++ b/modules/polynomials/help/ja_JP/htrianr.xml @@ -0,0 +1,89 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="htrianr"> + <refnamediv> + <refname>htrianr</refname> + <refpurpose>多項式行列の三角化</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[Ar,U,rk]=htrianr(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>多項式行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ar</term> + <listitem> + <para>多項式行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>ユニモジュラ多項式行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + 整数, <literal>A</literal>の通常ランク + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + 多項式行列 <literal>A</literal>の三角化. + </para> + <para> + <literal>A</literal> は <literal>[m,n]</literal> , <literal>m <= n</literal>です. + </para> + <para> + <literal>Ar=A*U</literal> + </para> + <para> + 警告: "小さい"項の削除が行われます(関数コードを参照). + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +x=poly(0,'x'); +M=[x;x^2;2+x^3]*[1,x-2,x^4]; +[Mu,U,rk]=htrianr(M) +det(U) +M*U(:,1:2) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="hrmt">hrmt</link> + </member> + <member> + <link linkend="colcompr">colcompr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/inv_coeff.xml b/modules/polynomials/help/ja_JP/inv_coeff.xml new file mode 100755 index 000000000..5ae293463 --- /dev/null +++ b/modules/polynomials/help/ja_JP/inv_coeff.xml @@ -0,0 +1,73 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="inv_coeff"> + <refnamediv> + <refname>inv_coeff</refname> + <refpurpose>係数を指定して多項式行列を作成</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[P]=inv_coeff(C,[,d,[name])</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>C</term> + <listitem> + <para>係数の行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>d</term> + <listitem> + <para>多項式行列の次数. + オプションのパラメータでデフォルト値は <literal>d=-1+size(C,'c')/size(C,'r')</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>name</term> + <listitem> + <para> + 多項式の変数名を指定する文字列 (デフォルト値: <literal>'x'</literal>). + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>P=inv_coeff(Mp,k)</literal>は, <literal>k</literal> が <literal>Mp</literal> の + 大きさと互換性がある場合, k次の多項式行列を返します. + <literal>C=[C0,C1,...,Ck]</literal> の時, + <literal>P= C0 + C1*x +... +Ck*x^k</literal>となります. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +A=int(10*rand(2,6)) +// 1次の多項式行列を作成 +P=inv_coeff(A,1) +norm(coeff(P)-A) +// 次数にデフォルト値を使用 +P1=inv_coeff(A) +norm(coeff(P1)-A) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="degree">degree</link> + </member> + <member> + <link linkend="coeff">coeff</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/invr.xml b/modules/polynomials/help/ja_JP/invr.xml new file mode 100755 index 000000000..41e1d9d28 --- /dev/null +++ b/modules/polynomials/help/ja_JP/invr.xml @@ -0,0 +1,69 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="invr"> + <refnamediv> + <refname>invr</refname> + <refpurpose>(有理) 行列の逆</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>F = invr(H)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>H</term> + <listitem> + <para>多項式または有理行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>F</term> + <listitem> + <para>多項式または有理行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>H</literal> が多項式または有理関数行列の場合, <literal>invr</literal> + はLeverrierのアルゴリズムにより <literal>H^(-1)</literal>を計算します (関数コード参照) + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s') +H=[s,s*s+2;1-s,1+s]; invr(H) +[Num,den]=coffg(H);Num/den +H=[1/s,(s+1);1/(s+2),(s+3)/s];invr(H) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="glever">glever</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + <member> + <link linkend="inv">inv</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/lcmdiag.xml b/modules/polynomials/help/ja_JP/lcmdiag.xml new file mode 100755 index 000000000..fb6d16e98 --- /dev/null +++ b/modules/polynomials/help/ja_JP/lcmdiag.xml @@ -0,0 +1,92 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="lcmdiag"> + <refnamediv> + <refname>lcmdiag</refname> + <refpurpose>最小公倍数対角分解</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[N,D]=lcmdiag(H) + [N,D]=lcmdiag(H,flag) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>H</term> + <listitem> + <para>有理行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>N</term> + <listitem> + <para>多項式行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>D</term> + <listitem> + <para>対角多項式行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + 文字列: <literal>'row'</literal> または <literal>'col'</literal> (デフォルト) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>[N,D]=lcmdiag(H,'row')</literal> は, + 分解<literal>D*H=N</literal>, + すなわち,<literal>H=D^(-1)*N</literal>を計算します + ただし, D は D(k,k)= H('den')のk行目の最小公倍数となる + 対角行列です. + </para> + <para> + <literal>[N,D]=lcmdiag(H)</literal> または <literal>[N,D]=lcmdiag(H,'col)</literal> + は,D(k,k)=H('den')のk列目の最小公倍数となる<literal>H=N*D^(-1)</literal>を返します. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +H=[1/s,(s+2)/s/(s+1)^2;1/(s^2*(s+2)),2/(s+2)]; +[N,D]=lcmdiag(H); +N/D-H + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="lcm">lcm</link> + </member> + <member> + <link linkend="gcd">gcd</link> + </member> + <member> + <link linkend="bezout">bezout</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/ldiv.xml b/modules/polynomials/help/ja_JP/ldiv.xml new file mode 100755 index 000000000..792c5cb5f --- /dev/null +++ b/modules/polynomials/help/ja_JP/ldiv.xml @@ -0,0 +1,79 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="ldiv"> + <refnamediv> + <refname>ldiv</refname> + <refpurpose>多項式行列の長除算</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[x]=ldiv(n,d,k)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>n,d</term> + <listitem> + <para>実数多項式行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>k</term> + <listitem> + <para>整数</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>x=ldiv(n,d,k)</literal> は, + <literal>n</literal>の<literal>d</literal>による長除算の + 最初の<literal>k</literal>個の係数を出力します. + すなわち,有理行列<literal>[nij(z)/dij(z)]</literal>の無限大近傍での + テイラー展開を出力します. + </para> + <para> + <literal>nij/dij</literal>の展開の係数は + <literal>x((i-1)*n+k,j) k=1:n</literal>に保存されます + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +wss=ssrand(1,1,3);[a,b,c,d]=abcd(wss); +wtf=ss2tf(wss); +x1=ldiv(numer(wtf),denom(wtf),5) +x2=[c*b;c*a*b;c*a^2*b;c*a^3*b;c*a^4*b] +wssbis=markp2ss(x1',5,1,1); +wtfbis=clean(ss2tf(wssbis)) +x3=ldiv(numer(wtfbis),denom(wtfbis),5) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="arl2">arl2</link> + </member> + <member> + <link linkend="markp2ss">markp2ss</link> + </member> + <member> + <link linkend="pdiv">pdiv</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/numer.xml b/modules/polynomials/help/ja_JP/numer.xml new file mode 100755 index 000000000..a83ef79f9 --- /dev/null +++ b/modules/polynomials/help/ja_JP/numer.xml @@ -0,0 +1,57 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="numer"> + <refnamediv> + <refname>numer</refname> + <refpurpose>分子</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>num=numer(R)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>R</term> + <listitem> + <para>有理または多項式または定数行列.</para> + </listitem> + </varlistentry> + <varlistentry> + <term>num</term> + <listitem> + <para>多項式行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + ユーティリティ関数. <literal>num=numer(R)</literal> は, + 有理関数行列<literal>R</literal>の + 分子<literal>num</literal>を返します + (<literal>R</literal> は定数または多項式行列とすることができます). + <literal>numer(R)</literal> は <literal>R(2)</literal>, <literal>R('num')</literal> または <literal>R.num</literal>に等しくなります + </para> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="denom">denom</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/pdiv.xml b/modules/polynomials/help/ja_JP/pdiv.xml new file mode 100755 index 000000000..a9723c766 --- /dev/null +++ b/modules/polynomials/help/ja_JP/pdiv.xml @@ -0,0 +1,82 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="pdiv"> + <refnamediv> + <refname>pdiv</refname> + <refpurpose>多項式の除算</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[R,Q]=pdiv(P1,P2) + [Q]=pdiv(P1,P2) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>P1</term> + <listitem> + <para>多項式の行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>P2</term> + <listitem> + <para>多項式または多項式行列 </para> + </listitem> + </varlistentry> + <varlistentry> + <term>R,Q</term> + <listitem> + <para>多項式行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + 多項式行列<literal>P1</literal>の多項式<literal>P2</literal>または + 多項式行列<literal>P2</literal>による + 要素毎のユークリッド除算. + <literal>Rij</literal>は余りの行列, + <literal>Qij</literal>は商の行列,そして, + <literal>P1ij = Qij*P2 + Rij</literal> または <literal>P1ij = Qij*P2ij + Rij</literal> + です. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +x=poly(0,'x'); +p1=(1+x^2)*(1-x);p2=1-x; +[r,q]=pdiv(p1,p2) +p2*q-p1 +p2=1+x; +[r,q]=pdiv(p1,p2) +p2*q+r-p1 + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="ldiv">ldiv</link> + </member> + <member> + <link linkend="gcd">gcd</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/pol2str.xml b/modules/polynomials/help/ja_JP/pol2str.xml new file mode 100755 index 000000000..6c2d70e29 --- /dev/null +++ b/modules/polynomials/help/ja_JP/pol2str.xml @@ -0,0 +1,87 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * Copyright (C) 2013 - Samuel GOUGEON : upgrade for 5.5.0 + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="pol2str"> + <refnamediv> + <refname>pol2str</refname> + <refpurpose>多項式を文字列に変換</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>strs = pol2str(p)</synopsis> + </refsynopsisdiv> + <refsection> + <title>引数</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>実数または複素係数の多項式の行列またはハイパー行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>strs</term> + <listitem> + <para>文字列の行列またはハイパー行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + 多項式を文字列に変換します (ユーティリティ関数). + </para> + <para> + <note> + 係数の出力フォーマットは、<link linkend="format">format(..)</link> によって設定されます. + </note> + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +pol2str(%z) +p = poly ([1, 2, 3], "x","coeff"); +pol2str(p) +p = (1+%i+%z)^(1:4) +pol2str(p) +]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="string">string</link> + </member> + <member> + <link linkend="prettyprint">prettyprint</link> + </member> + <member> + <link linkend="sci2exp">sci2exp</link> + </member> + </simplelist> + </refsection> + <refsection role="history tag"> + <title>履歴</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revdescription> + pol2str() は複素係数を有する多項式およびハイパー行列に拡張されました. + 配列処理がベクトル化されました. + </revdescription> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/polfact.xml b/modules/polynomials/help/ja_JP/polfact.xml new file mode 100755 index 000000000..315139cb1 --- /dev/null +++ b/modules/polynomials/help/ja_JP/polfact.xml @@ -0,0 +1,77 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Serge STEER + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="polfact"> + <refnamediv> + <refname>polfact</refname> + <refpurpose>最小因数</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[f]=polfact(p)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>多項式</para> + </listitem> + </varlistentry> + <varlistentry> + <term>f</term> + <listitem> + <para> + <literal>p=prod(f)</literal>となるようなベクトル <literal>[f0 f1 ... fn]</literal> + </para> + <variablelist> + <varlistentry> + <term>f0</term> + <listitem> + <para>定数</para> + </listitem> + </varlistentry> + <varlistentry> + <term>fi</term> + <listitem> + <para>多項式</para> + </listitem> + </varlistentry> + </variablelist> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>f=polfact(p)</literal> はpの最小因数,すなわち, + <literal>p=prod(f)</literal>となるような<literal>f=[f0 f1 ... fn]</literal> + を返します. + </para> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="lcm">lcm</link> + </member> + <member> + <link linkend="cmndred">cmndred</link> + </member> + <member> + <link linkend="factors">factors</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/poly.xml b/modules/polynomials/help/ja_JP/poly.xml new file mode 100755 index 000000000..9150a7b51 --- /dev/null +++ b/modules/polynomials/help/ja_JP/poly.xml @@ -0,0 +1,138 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="poly"> + <refnamediv> + <refname>poly</refname> + <refpurpose>多項式を定義する</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>p = poly(a, vname, ["flag"])</synopsis> + </refsynopsisdiv> + <refsection> + <title>引数</title> + <variablelist> + <varlistentry> + <term>a</term> + <listitem> + <para>行列または実数値</para> + </listitem> + </varlistentry> + <varlistentry> + <term>vname</term> + <listitem> + <para>文字列, 記号変数名を表します. 文字列は最大4文字とする必要があります. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>"flag" </term> + <listitem> + <para> + 文字列 (<literal>"roots"</literal>, <literal>"coeff"</literal>), + デフォルト値は<literal>"roots"</literal>です. + </para> + <para> + 短縮形も使用できます: + <literal>"roots"</literal> について <literal>"r"</literal>, + <literal>"coeff"</literal> について <literal>"c"</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <variablelist> + <varlistentry> + <term> + <literal>a</literal> が行列の場合, + </term> + <listitem> + <para> + <literal>p</literal> は特性多項式,すなわち + <code>determinant(x*eye()-a)</code> となり, <literal>x</literal>が + 記号変数となります. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term> + <literal>v</literal> がベクトルの場合, + </term> + <listitem> + <itemizedlist> + <listitem> + <para> + <code>poly(v,"x",["roots"])</code> は + <literal>v</literal>のエントリを<literal>根(roots)</literal>とし, + <literal>"x"</literal>を形式変数とする多項式となります + (この場合,<literal>roots</literal>と<literal>poly</literal>は逆関数となります). + <note> + 根が無限大の場合,最高次の係数がゼロになることに注意してください. + </note> + </para> + </listitem> + <listitem> + <para> + <literal>poly(v,"x","coeff")</literal> は記号を<literal>"x"</literal> + とし,<literal>v</literal>のエントリを係数とする多項式を作成します + (<code>v(1)</code>が多項式の定数項となります). + (この場合, <literal>poly</literal> と <literal>coeff</literal> が逆関数となります) + </para> + </listitem> + </itemizedlist> + </listitem> + </varlistentry> + </variablelist> + <para> + <literal>s=poly(0,"s")</literal> は記号<literal>"s"</literal>を + 用いた多項式を定義するための準備作業です. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +s=poly(0,"s"); +p=1+s+2*s^2 +A=rand(2,2); +poly(A,"x") +//有理分数 +h=(1+2*%s)/poly(1:4,'s','c') + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="coeff">coeff</link> + </member> + <member> + <link linkend="roots">roots</link> + </member> + <member> + <link linkend="varn">varn</link> + </member> + <member> + <link linkend="horner">horner</link> + </member> + <member> + <link linkend="derivat">derivat</link> + </member> + <member> + <link linkend="matrices">matrices</link> + </member> + <member> + <link linkend="rational">rational</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>履歴</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revremark>第3引数に指定可能な値は "roots", "coeff", "c" および "r"のみです.</revremark> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/rational.xml b/modules/polynomials/help/ja_JP/rational.xml new file mode 100755 index 000000000..2a5a2dd27 --- /dev/null +++ b/modules/polynomials/help/ja_JP/rational.xml @@ -0,0 +1,51 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="rational"> + <refnamediv> + <refname>rational</refname> + <refpurpose>Scilab オブジェクト, Scilabの有理数</refpurpose> + </refnamediv> + <refsection> + <title>説明</title> + <para> + 有理数 <literal>r</literal> は,2つの多項式の商<literal>r=num/den</literal>です. + 有理数の内部表現はリストです. + <literal>r=tlist(['r','num','den','dt'],num,den,[])</literal>は + <literal>r=num/den</literal>と同じです. + 有理行列は通常の構文で定義できます. + 例えば, <literal>[r11,r12;r21,r22]</literal>は 2x2 行列です. + ただし, <literal>rij</literal> は 1x1 有理数です. + 有理行列は, + <literal>num</literal> および <literal>den</literal>を多項式行列として + リスト<literal>rlist(num,den,[])</literal>により + 定義することも可能です. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +W=[1/s,1/(s+1)] +W'*W +Num=[s,s+2;1,s];Den=[s*s,s;s,s*s]; +rlist(Num,Den,[]) +H=Num./Den +syslin('c',Num,Den) +syslin('c',H) +[Num1,Den1]=simp(Num,Den) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="syslin">syslin</link> + </member> + <member> + <link linkend="simp">simp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/residu.xml b/modules/polynomials/help/ja_JP/residu.xml new file mode 100755 index 000000000..8a859a959 --- /dev/null +++ b/modules/polynomials/help/ja_JP/residu.xml @@ -0,0 +1,85 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Francois DELBECQUE + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="residu"> + <refnamediv> + <refname>residu</refname> + <refpurpose>残差</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[V]=residu(P,Q1,Q2)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>P, Q1, Q2</term> + <listitem> + <para>実数または複素数の係数を有する多項式または多項式の行列.</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>V=residu(P,Q1,Q2)</literal> は, + <literal>V(i,j)</literal>が + <literal>Q1(i,j)</literal>のゼロで計算される + 有理数<literal>P(i,j)/(Q1(i,j)*Q2(i,j))</literal> + の残差の合計となるような行列<literal>V</literal>を返します. + </para> + <para> + <literal>Q1(i,j)</literal> および <literal>Q2(i,j)</literal> は, + 共通の根を有さない必要があります. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +H=[s/(s+1)^2,1/(s+2)];N=numer(H);D=denom(H); +w=residu(N.*horner(N,-s),D,horner(D,-s)); //N(s) N(-s) / D(s) D(-s) +sqrt(sum(w)) //H2ノルムです +h2norm(tf2ss(H)) +p=(s-1)*(s+1)*(s+2)*(s+10);a=(s-5)*(s-1)*(s*s)*((s+1/2)**2); +b=(s-3)*(s+2/5)*(s+3); +residu(p,a,b)+531863/4410 //正確 +z=poly(0,'z');a=z^3+0.7*z^2+0.5*z-0.3;b=z^3+0.3*z^2+0.2*z+0.1; +atild=gtild(a,'d');btild=gtild(b,'d'); +residu(b*btild,z*a,atild)-2.9488038 //正確 +a=a+0*%i;b=b+0*%i; +real(residu(b*btild,z*a,atild)-2.9488038) //複素数の場合 + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="pfss">pfss</link> + </member> + <member> + <link linkend="bdiag">bdiag</link> + </member> + <member> + <link linkend="roots">roots</link> + </member> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="gtild">gtild</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/roots.xml b/modules/polynomials/help/ja_JP/roots.xml new file mode 100755 index 000000000..728ae3cd6 --- /dev/null +++ b/modules/polynomials/help/ja_JP/roots.xml @@ -0,0 +1,95 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="roots" xml:lang="ja"> + <refnamediv> + <refname>roots</refname> + <refpurpose>多項式の根</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[x]=roots(p) + [x]=roots(p,'e') + </synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>実数または複素係数の多項式 + または + 降順の多項式係数のベクトル(MATLAB互換用). + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>x=roots(p)</literal> は + 多項式<literal>p</literal>の<literal>x</literal>である + 複素ベクトルを返す. + 100次以下の実数多項式の場合,高速な(Jenkins-Traub法に基づく) + RPOLYアルゴリズムが使用される. + その他の場合, その根はコンパニオン行列の固有値として計算される. + どのような場合でもこのアルゴリズムを強制的に使用したい + 場合,<literal>x=roots(p,'e')</literal>を使用されたい. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +p=poly([0,10,1+%i,1-%i],'x'); +roots(p) +A=rand(3,3);roots(poly(A,'x')) // Evals by characteristic polynomial +spec(A) + ]]></programlisting> + </refsection> + <refsection> + <title>参考</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="spec">spec</link> + </member> + <member> + <link linkend="companion">companion</link> + </member> + </simplelist> + </refsection> + <refsection role="see also"> + <title>参照</title> + <para>RPOLYアルゴリズムは以下の文献に記述されている. + "Algorithm 493: Zeros of a Real + Polynomial", ACM TOMS Volume 1, Issue 2 (June 1975), pp. 178-189 + </para> + <para>Jenkins, M. A. and Traub, J. F. (1970), A Three-Stage Algorithm for + Real Polynomials Using Quadratic Iteration, SIAM J. Numer. Anal., 7(1970), 545-566. + </para> + <para>Jenkins, M. A. and Traub, J. F. (1970), Principles for Testing Polynomial Zerofinding Programs. + ACM TOMS 1, 1 (March 1975), pp. 26-34 + </para> + </refsection> + <refsection> + <title>使用される関数</title> + <para>ソースコードrpoly.f はScilabの配布ソースのディレクトリ + SCI/modules/polynomials/src/fortran にある. + コンパニオン行列が使用される場合,固有値計算は + LapackコードであるDGEEVおよびZGEEVにより行われる. + </para> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/rowcompr.xml b/modules/polynomials/help/ja_JP/rowcompr.xml new file mode 100755 index 000000000..02506f8b5 --- /dev/null +++ b/modules/polynomials/help/ja_JP/rowcompr.xml @@ -0,0 +1,78 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="rowcompr"> + <refnamediv> + <refname>rowcompr</refname> + <refpurpose>多項式行列の行圧縮</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[X,rk,Ac]=rowcompr(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>多項式行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Y</term> + <listitem> + <para>正方多項式行列 (左ユニモジュラ基底)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + <literal>A</literal>の通常のランク + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ac</term> + <listitem> + <para> + <literal>Ac=X*A</literal>, 多項式行列 + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + 多項式行列<literal>A</literal>の行圧縮. + </para> + <para> + <literal>X</literal> は, + 行圧縮された<literal>A</literal>の行である + 左多項式ユニモジュラ基底です. + <literal>rk</literal> は Aの通常ランクです. + </para> + <para> + 警告: "小さい"項は削除されます (注意して使用してください!). + </para> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="colcompr">colcompr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/sfact.xml b/modules/polynomials/help/ja_JP/sfact.xml new file mode 100755 index 000000000..f20edca8a --- /dev/null +++ b/modules/polynomials/help/ja_JP/sfact.xml @@ -0,0 +1,92 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="sfact"> + <refnamediv> + <refname>sfact</refname> + <refpurpose>離散時間スペクトル分解</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>F=sfact(P)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>P</term> + <listitem> + <para>実数多項式行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>P</literal>のスペクトル分解 <literal>F</literal>を求めます. + <literal>P</literal> は<literal>P</literal>の各根が単位円に関する + 鏡像となるような多項式行列です. + 単位円上に根がある時,問題は特異となります. + </para> + <para> + <literal>sfact(P)</literal> は,安定ではない以下のような + 多項式行列<literal>F(z)</literal>を返します. + </para> + <para> + <literal>P = F(z)* F(1/z) *z^n</literal> + </para> + <para> + スカラー多項式の場合,特殊なアルゴリズムが実装されています. + アルゴリズムはKuceraの本によるものです. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +//Simple polynomial example +z=poly(0,'z'); +p=(z-1/2)*(2-z) +w=sfact(p); +w*numer(horner(w,1/z)) +//matrix example +F1=[z-1/2,z+1/2,z^2+2;1,z,-z;z^3+2*z,z,1/2-z]; +P=F1*gtild(F1,'d'); //P is symmetric +F=sfact(P) +roots(det(P)) +roots(det(gtild(F,'d'))) //The stable roots +roots(det(F)) //The antistable roots +clean(P-F*gtild(F,'d')) +//Example of continuous time use +s=poly(0,'s'); +p=-3*(s+(1+%i))*(s+(1-%i))*(s+0.5)*(s-0.5)*(s-(1+%i))*(s-(1-%i));p=real(p); +//p(s) = polynomial in s^2 , looks for stable f such that p=f(s)*f(-s) +w=horner(p,(1-s)/(1+s)); // bilinear transform w=p((1-s)/(1+s)) +wn=numer(w); //take the numerator +fn=sfact(wn);f=numer(horner(fn,(1-s)/(s+1))); //Factor and back transform +f=f/sqrt(horner(f*gtild(f,'c'),0));f=f*sqrt(horner(p,0)); //normalization +roots(f) //f is stable +clean(f*gtild(f,'c')-p) //f(s)*f(-s) is p(s) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="gtild">gtild</link> + </member> + <member> + <link linkend="fspecg">fspecg</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/simp.xml b/modules/polynomials/help/ja_JP/simp.xml new file mode 100755 index 000000000..3bb4f06b0 --- /dev/null +++ b/modules/polynomials/help/ja_JP/simp.xml @@ -0,0 +1,109 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="simp"> + <refnamediv> + <refname>simp</refname> + <refpurpose>有理数の簡単化</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[N1,D1]=simp(N,D) + H1=simp(H) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>N,D</term> + <listitem> + <para>実数多項式または実数行列多項式</para> + </listitem> + </varlistentry> + <varlistentry> + <term>H</term> + <listitem> + <para>有理行列 (すなわち, + エントリ <literal>n/d</literal>を有する行列 ,実数多項式 + <literal>n</literal>および <literal>d</literal>) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>[n1,d1]=simp(n,d)</literal> は,<literal>n1/d1 = n/d</literal> + となるような多項式 + <literal>n1</literal> および <literal>d1</literal>を計算します. + </para> + <para> + <literal>N</literal> および <literal>D</literal> が多項式行列の場合, + 計算が要素毎に行われます. + </para> + <para> + <literal>H1=simp(H)</literal> も有効です (<literal>H</literal>の各エントリは + <literal>H1</literal>で簡単化されます). + </para> + <para> + 注意: + </para> + <para> + -閾値は指定されません. すなわち,<literal>simp</literal> は強制的に簡単かを + 行うことはできません. + </para> + <para> + -積分器を含む線形動的システムの場合,簡単化により定常ゲイン + (連続系の場合は<literal>H(0)</literal>,離散系の場合は <literal>H(1)</literal>) + が変化します. + </para> + <para> + -複素数のデータの場合, <literal>simp</literal> はその入力を返します. + </para> + <para> + -有理数の簡単化は,有理数に関するほぼ毎回の処理の後にコールされます. + <literal>simp_mode</literal>関数によりこの簡単化のオン/オフを切り替える + ことができます. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +[n,d]=simp((s+1)*(s+2),(s+1)*(s-2)) +simp_mode(%F);hns=s/s +simp_mode(%T);hns=s/s + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="roots">roots</link> + </member> + <member> + <link linkend="trfmod">trfmod</link> + </member> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + <member> + <link linkend="simp_mode">simp_mode</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/simp_mode.xml b/modules/polynomials/help/ja_JP/simp_mode.xml new file mode 100755 index 000000000..d6941fdce --- /dev/null +++ b/modules/polynomials/help/ja_JP/simp_mode.xml @@ -0,0 +1,71 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="simp_mode"> + <refnamediv> + <refname>simp_mode</refname> + <refpurpose>有理数の簡単化のオン/オフを切り替える</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>mod=simp_mode() + simp_mode(mod) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>mod</term> + <listitem> + <para>a boolean</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + 有理数に関する処理の後にほぼ毎回,有理数の簡単化が行われます. + <literal>simp_mode</literal> によりこの簡単化のオン/オフを切り替えることが + できます. + </para> + <para> + <literal>simp_mode(%t)</literal> は,有理数の簡単化をオンにします. + </para> + <para> + <literal>simp_mode(%f)</literal> は,有理数の簡単化をオフにします. + </para> + <para> + <literal>mod=simp_mode()</literal> は,カレントの + 有理数の簡単化モードをmodに返します. + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +mod=simp_mode() +simp_mode(%f);hns=s/s +simp_mode(%t);hns=s/s +simp_mode(mod); + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="simp">simp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/sylm.xml b/modules/polynomials/help/ja_JP/sylm.xml new file mode 100755 index 000000000..fe8b05fa3 --- /dev/null +++ b/modules/polynomials/help/ja_JP/sylm.xml @@ -0,0 +1,69 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="sylm"> + <refnamediv> + <refname>sylm</refname> + <refpurpose>シルベスタ行列</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[S]=sylm(a,b)</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>a,b</term> + <listitem> + <para>多項式</para> + </listitem> + </varlistentry> + <varlistentry> + <term>S</term> + <listitem> + <para>行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>sylm(a,b)</literal> は,多項式<literal>a</literal>および<literal>b</literal> + に関連するシルベスタ行列,すなわち, + 以下のような行列<literal>S</literal>を出力します: + </para> + <para> + <literal>coeff( a*x + b*y )' = S * [coeff(x)';coeff(y)']</literal>. + </para> + <para> + <literal>S</literal>の次元は<literal>degree(a)+degree(b)</literal>に等しくなります. + </para> + <para> + <literal>a</literal> および<literal>b</literal>が規約分解多項式の場合, + </para> + <para> + <literal>rank(sylm(a,b))=degree(a)+degree(b))</literal> となります. + また,以下の命令は, + </para> + <programlisting role=""><![CDATA[ +u = sylm(a,b) \ eye(na+nb,1) +x = poly(u(1:nb),'z','coeff') +y = poly(u(nb+1:na+nb),'z','coeff') + ]]></programlisting> + <para>べズー分解,つまり, + <literal>a*x+b*y = 1</literal>となるような最小次数の + <literal>x</literal> および <literal>y</literal>を計算します. + </para> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/systmat.xml b/modules/polynomials/help/ja_JP/systmat.xml new file mode 100755 index 000000000..d0ac07ab4 --- /dev/null +++ b/modules/polynomials/help/ja_JP/systmat.xml @@ -0,0 +1,74 @@ +<?xml version="1.0" encoding="UTF-8"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="systmat"> + <refnamediv> + <refname>systmat</refname> + <refpurpose>システム行列</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼び出し手順</title> + <synopsis>[Sm]=systmat(Sl);</synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>Sl</term> + <listitem> + <para> + 線形システム (<literal>syslin</literal>リスト) またはディスクリプタシステム + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Sm</term> + <listitem> + <para>行列ペンシル</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + 状態空間形式の線形システムのシステム行列 <literal>Sl</literal> (<literal>syslin</literal> リスト) + (ユーティリティ関数). + </para> + <programlisting role=""><![CDATA[ +Sm = [-sI + A B; + [ C D] + ]]></programlisting> + <para> + 離散系の場合(<literal>Sl=list('des',A,B,C,D,E)</literal>), <literal>systmat</literal> は + 以下を返します: + </para> + <programlisting role=""><![CDATA[ +Sm = [-sE + A B; + [ C D] + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="ss2des">ss2des</link> + </member> + <member> + <link linkend="sm2des">sm2des</link> + </member> + <member> + <link linkend="sm2ss">sm2ss</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ja_JP/varn.xml b/modules/polynomials/help/ja_JP/varn.xml new file mode 100755 index 000000000..df7953105 --- /dev/null +++ b/modules/polynomials/help/ja_JP/varn.xml @@ -0,0 +1,92 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="varn"> + <refnamediv> + <refname>varn</refname> + <refpurpose>多項式または有理分数のシンボリック変数</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>呼出し手順</title> + <synopsis>[symb]=varn(p) + [pm]=varn(p,varname) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>パラメータ</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>多項式のか合理的な画分の行列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>symb</term> + <listitem> + <para>文字列</para> + </listitem> + </varlistentry> + <varlistentry> + <term>varname</term> + <listitem> + <para>記号変数 (文字列)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>pm</term> + <listitem> + <para>多項式のか合理的な画分の行列</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>説明</title> + <para> + <literal>symb=varn(p)</literal> は, + 多項式<literal>p</literal>の記号変数 <literal>symb</literal>を返します + (すなわち,<literal>varn(poly(0,'x'))</literal> は <literal>'x'</literal> です). + </para> + <para> + <literal>varn(p,'s')</literal> は,<literal>p</literal>と + 同じ係数を有し,<literal>'s'</literal>を記号変数とする + 多項式行列を返します(変数名の変更). + </para> + </refsection> + <refsection> + <title>例</title> + <programlisting role="example"><![CDATA[ +s = poly(0,'s'); p = [s^2+1,s]; +varn(p) +varn(p,'x') + +f = %z / (%z-1); f = [f f^2] +varn(f) +varn(f,"x") + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>参照</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="rlist">rlist</link> + </member> + <member> + <link linkend="horner">horner</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>履歴</title> + <revhistory> + <revision> + <revnumber>5.5.1</revnumber> + <revdescription> + <para>Extension to rationals</para> + </revdescription> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/addchapter.sce b/modules/polynomials/help/pt_BR/addchapter.sce new file mode 100755 index 000000000..172ce21be --- /dev/null +++ b/modules/polynomials/help/pt_BR/addchapter.sce @@ -0,0 +1,11 @@ +// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) 2009 - DIGITEO +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +add_help_chapter("Polinômios",SCI+"/modules/polynomials/help/pt_BR",%T); + diff --git a/modules/polynomials/help/pt_BR/bezout.xml b/modules/polynomials/help/pt_BR/bezout.xml new file mode 100755 index 000000000..df9477aec --- /dev/null +++ b/modules/polynomials/help/pt_BR/bezout.xml @@ -0,0 +1,95 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Serge STEER + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="bezout" xml:lang="en"> + <refnamediv> + <refname>bezout</refname> + <refpurpose>equao de Bezout para polinmios ou inteiros</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento</title> + <synopsis>[thegcd,U]=bezout(p1,p2)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>p1, p2</term> + <listitem> + <para>dois polinmios reais ou dois escalares inteiros (tipo igual a + 8) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>[thegcd,U]=bezout(p1,p2)</literal> computa o MDC + <literal>thegcd</literal> de <literal>p1</literal> e <literal>p2</literal> + e tambm uma matriz (2x2) unimodular <literal>U</literal> tal quet: + </para> + <para> + <literal>[p1,p2]*U = [thegcd,0]</literal> + </para> + <para> + O MMC de <literal>p1</literal> e <literal>p2</literal> dado + por: + </para> + <para> + <literal>p1*U(1,2)</literal> (or + <literal>-p2*U(2,2)</literal>) + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +// caso polinomial +x=poly(0,'x'); +p1=(x+1)*(x-3)^5;p2=(x-2)*(x-3)^3; +[thegcd,U]=bezout(p1,p2) +det(U) +clean([p1,p2]*U) +thelcm=p1*U(1,2) +lcm([p1,p2]) + +// caso inteiro +i1=int32(2*3^5); i2=int32(2^3*3^2); +[thegcd,U]=bezout(i1,i2) +V=int32([2^2*3^5, 2^3*3^2,2^2*3^4*5]); +[thegcd,U]=gcd(V) +V*U +lcm(V) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="roots">roots</link> + </member> + <member> + <link linkend="simp">simp</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + <member> + <link linkend="lcm">lcm</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/cmndred.xml b/modules/polynomials/help/pt_BR/cmndred.xml new file mode 100755 index 000000000..0d5296f21 --- /dev/null +++ b/modules/polynomials/help/pt_BR/cmndred.xml @@ -0,0 +1,60 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="cmndred" xml:lang="en"> + <refnamediv> + <refname>cmndred</refname> + <refpurpose>forma de denominador comum</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[n,d]=cmndred(num,den)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>num, den</term> + <listitem> + <para>duas matrizes de polinmios de dimenses iguais</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>[n,d]=cmndred(num,den)</literal> computa uma matriz de + polinmios <literal>n</literal> e um polinmio denominador comum<literal> + d + </literal> + tais que: + </para> + <para> + <literal>n/d=num./den</literal> + </para> + <para>A matriz de razes de polinmios definida por + <literal>num./den</literal> <literal>n/d</literal> + </para> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="simp">simp</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/coeff.xml b/modules/polynomials/help/pt_BR/coeff.xml new file mode 100755 index 000000000..7822302f8 --- /dev/null +++ b/modules/polynomials/help/pt_BR/coeff.xml @@ -0,0 +1,77 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Serge STEER + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="coeff" xml:lang="en"> + <refnamediv> + <refname>coeff</refname> + <refpurpose>coeficientes de matrizes de polinmios</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[C]=coeff(Mp [,v])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>Mp</term> + <listitem> + <para>matriz de polinmios</para> + </listitem> + </varlistentry> + <varlistentry> + <term>v</term> + <listitem> + <para>vetor (linha ou coluna) de inteiros dos graus selecionados + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>C</term> + <listitem> + <para>matriz grande dos coeficientes</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>C=coeff(Mp)</literal> retorna em uma matriz grande + <literal>C</literal> os coeficientes da matriz de polinmios + <literal>Mp</literal> . <literal>C</literal> particionada como + <literal>C=[C0,C1,...,Ck]</literal> onde os <literal>Ci</literal> esto + dispostos em ordem crescente, <literal>k = + max(degree(Mp)) + </literal> + </para> + <para> + <literal>C=coeff(Mp,v)</literal> retorna a matriz de coeficientes + com graus em <literal>v</literal> . (<literal>v</literal> um vetor linha + ou coluna). + </para> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="degree">degree</link> + </member> + <member> + <link linkend="inv_coeff">inv_coeff</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/coffg.xml b/modules/polynomials/help/pt_BR/coffg.xml new file mode 100755 index 000000000..cd2891473 --- /dev/null +++ b/modules/polynomials/help/pt_BR/coffg.xml @@ -0,0 +1,80 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Francois DELBECQUE + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="coffg" xml:lang="en"> + <refnamediv> + <refname>coffg</refname> + <refpurpose>matriz inversa de polinmios</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[Ns,d]=coffg(Fs)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>Fs</term> + <listitem> + <para>matriz quadrada de polinmios</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>coffg</literal> computa <literal>Fs^-1</literal> onde + <literal>Fs</literal> uma matriz de polinmios, pelo mtodo dos + cofatores. + </para> + <para> + <literal>Fs</literal> inverse = <literal>Ns/d</literal> + </para> + <para> + <literal>d</literal> = denominador comum; <literal>Ns</literal> = + numerador (uma matriz de polinmios) + </para> + <para>(Para matrizes grandes, seja paciente... os resultados geralmente + so confiveis) + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s') +a=[ s, s^2+1; s s^2-1]; +[a1,d]=coffg(a); +(a1/d)-inv(a) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="determ">determ</link> + </member> + <member> + <link linkend="detr">detr</link> + </member> + <member> + <link linkend="invr">invr</link> + </member> + <member> + <link linkend="penlaur">penlaur</link> + </member> + <member> + <link linkend="glever">glever</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/colcompr.xml b/modules/polynomials/help/pt_BR/colcompr.xml new file mode 100755 index 000000000..704a1b161 --- /dev/null +++ b/modules/polynomials/help/pt_BR/colcompr.xml @@ -0,0 +1,80 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="colcompr" xml:lang="en"> + <refnamediv> + <refname>colcompr</refname> + <refpurpose>compresso de colunas de matrizes de polinmios</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[Y,rk,ac]=colcompr(A);</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz de polinmios </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Y</term> + <listitem> + <para>matriz de polinmios quadrada (base unimodular direita) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + posto normal de <literal>A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ac</term> + <listitem> + <para> + <literal>Ac=A*Y</literal>, matriz de polinmios + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + Compresso de colunas da matriz de polinmios <literal>A</literal> + (compresso para a esquerda). + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +p=[s;s*(s+1)^2;2*s^2+s^3]; +[Y,rk,ac]=colcompr(p*p'); +p*p'*Y + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="rowcompr">rowcompr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/degree.xml b/modules/polynomials/help/pt_BR/degree.xml new file mode 100755 index 000000000..d9d0790ce --- /dev/null +++ b/modules/polynomials/help/pt_BR/degree.xml @@ -0,0 +1,59 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="degree" xml:lang="en"> + <refnamediv> + <refname>degree</refname> + <refpurpose>grau da matriz de polinmios</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[D]=degree(M)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>M</term> + <listitem> + <para>matriz de polinmios </para> + </listitem> + </varlistentry> + <varlistentry> + <term>D</term> + <listitem> + <para>matriz de inteiros</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para>Retorna a matriz de graus mais elevados de + <literal>M</literal>. + </para> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="coeff">coeff</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/denom.xml b/modules/polynomials/help/pt_BR/denom.xml new file mode 100755 index 000000000..a0c07161e --- /dev/null +++ b/modules/polynomials/help/pt_BR/denom.xml @@ -0,0 +1,61 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="denom" xml:lang="en"> + <refnamediv> + <refname>denom</refname> + <refpurpose>denominador</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>den=denom(r)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>r</term> + <listitem> + <para>matriz de polinmios, de razes de polinmios ou de + constantes. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>den</term> + <listitem> + <para>matriz de polinmios</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>den=denom(r)</literal> retorna o denominador de uma matriz + de razes de polinmios. + </para> + <para>Desde que razes de polinmios so representadas internamente como + <literal>r=list(['r','num','den','dt'],num,den,[])</literal>, + <literal>denom(r</literal>) o mesmo que <literal>r(3)</literal>, + <literal>r('den')</literal> ou <literal>r.den</literal> + </para> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="numer">numer</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/derivat.xml b/modules/polynomials/help/pt_BR/derivat.xml new file mode 100755 index 000000000..0595ed529 --- /dev/null +++ b/modules/polynomials/help/pt_BR/derivat.xml @@ -0,0 +1,66 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="derivat" xml:lang="en"> + <refnamediv> + <refname>derivat</refname> + <refpurpose>derivada de matriz de razes de polinmios</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>pd=derivat(p)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>matriz de polinmios ou de razes de polinmios</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para>Computa a derivada da matriz de polinmios ou de funes racionais + em relao varivel livre. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +derivat(1/s) // -1/s^2; + ]]></programlisting> + <programlisting role="example"><![CDATA[ +p1 = poly([1 -2 1], 'x', 'coeff') +derivat(p1) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +p2 = poly([1 -4 2], 'y', 'coeff') +derivat(p2) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +p3 = poly(ones(1, 10), 'z', 'coeff') +derivat(p3) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +p4 = poly([-1 1], 't', 'roots') +derivat(p4) + ]]></programlisting> + <programlisting role="example"><![CDATA[ +s = %s; p5 = s^{-1} + 2 + 3*s +derivat(p5) + ]]></programlisting> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/determ.xml b/modules/polynomials/help/pt_BR/determ.xml new file mode 100755 index 000000000..1729ecdcc --- /dev/null +++ b/modules/polynomials/help/pt_BR/determ.xml @@ -0,0 +1,84 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Francois DELBECQUE + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="determ" xml:lang="en"> + <refnamediv> + <refname>determ</refname> + <refpurpose>determinante de matrizes de polinmios</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>res=determ(W [,k])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>W</term> + <listitem> + <para>matriz quadrada de polinmios reais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>k</term> + <listitem> + <para>inteiro (limite superior para o grau do determinante de + W) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para>Retorna o determinante de uma matriz de polinmios reais (computao + feita por Transformada Rpida de Fourier (TRF) se W possuir tamanho maior + do que 2*2). + </para> + <para> + <literal>res=determ(W [,k])</literal><literal>k</literal> um + inteiro maior do que o grau verdadeiro do determinante de + <literal>W</literal>. + </para> + <para> + O valor padro de <literal>k</literal> a menor potncia de 2 que + maior que <literal>n*max(degree(W))</literal>. + </para> + <para>Mtodo (apenas se o tamanho de W for maior que 2*2) : avalia o + determinante de W para as freqncias de Fourier e aplica a TRF inversa + para os coeficientes do determinante. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +w=s*rand(10,10); +determ(w) +det(coeff(w,1))*s^10 + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="det">det</link> + </member> + <member> + <link linkend="detr">detr</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/detr.xml b/modules/polynomials/help/pt_BR/detr.xml new file mode 100755 index 000000000..438afc7e1 --- /dev/null +++ b/modules/polynomials/help/pt_BR/detr.xml @@ -0,0 +1,54 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="detr" xml:lang="en"> + <refnamediv> + <refname>detr</refname> + <refpurpose>determinante polinomial</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>d=detr(h)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>h</term> + <listitem> + <para>matriz quadrada de polinmios ou de razes de + polinmios + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>d=detr(h)</literal> retorna o determinante + <literal>d</literal> da matriz de funes polinomiais ou racionais + <literal>h</literal>. baseado no algoritmo de Leverrier. + </para> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="det">det</link> + </member> + <member> + <link linkend="determ">determ</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/diophant.xml b/modules/polynomials/help/pt_BR/diophant.xml new file mode 100755 index 000000000..8704911fd --- /dev/null +++ b/modules/polynomials/help/pt_BR/diophant.xml @@ -0,0 +1,69 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="diophant" xml:lang="en"> + <refnamediv> + <refname>diophant</refname> + <refpurpose>equao (de Bezout) diofantina</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[x,err]=diophant(p1p2,b)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>p1p2</term> + <listitem> + <para> + vetor de polinmios <literal>p1p2 = [p1 p2]</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>b</term> + <listitem> + <para>polinmio</para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para>vetor de polinmios [x1;x2]</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal> diophant</literal> resolve a equao de Bezout: + </para> + <para> + <literal>p1*x1+p2*x2=b</literal> com <literal>p1p2</literal> um + vetor de polinmios. Se a equao no for solvel + </para> + <para> + de outro modo <literal>err=0</literal> + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s');p1=(s+3)^2;p2=(1+s); +x1=s;x2=(2+s); +[x,err]=diophant([p1,p2],p1*x1+p2*x2); +p1*x1+p2*x2-p1*x(1)-p2*x(2) + ]]></programlisting> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/factors.xml b/modules/polynomials/help/pt_BR/factors.xml new file mode 100755 index 000000000..b61daaa0d --- /dev/null +++ b/modules/polynomials/help/pt_BR/factors.xml @@ -0,0 +1,138 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="factors" xml:lang="en"> + <refnamediv> + <refname>factors</refname> + <refpurpose>fatorao numrica real</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[lnum,g]=factors(pol [,'flag']) + [lnum,lden,g]=factors(rat [,'flag']) + rat=factors(rat,'flag') + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>pol</term> + <listitem> + <para>polinmio real</para> + </listitem> + </varlistentry> + <varlistentry> + <term>rat</term> + <listitem> + <para>razo de polinmios reais + (<literal>rat=pol1/pol2</literal>) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>lnum</term> + <listitem> + <para>lista de polinmios (de graus 1 ou 2) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>lden</term> + <listitem> + <para>lista de polinmios (de graus 1 ou 2) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>g</term> + <listitem> + <para>nmero real </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + string <literal>'c'</literal> ou <literal>'d'</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + Retorna os fatores do polinmio <literal>pol</literal> na lista + <literal>lnum</literal> e o "ganho" g. + </para> + <para>Tem-se pol= g vezes o produto das entradas da lista + <literal>lnum</literal> (se <literal>flag</literal> no for fornecido). Se + <literal>flag='c'</literal> for dado, ento tem-se <literal>|pol(i + omega)| + </literal> + =<literal>|g*prod(lnum_j(i omega)|</literal>. Se + <literal>flag='d'</literal> for dado, ento tem-se <literal>|pol(exp(i + omega))| + </literal> + =<literal>|g*prod(lnum_i(exp(i omega))|</literal>. Se + o argumento de <literal>factors</literal> for uma razo + <literal>rat=pol1/pol2</literal>, os fatores do numerador + <literal>pol1</literal> e do denominador <literal>pol2</literal> so + retornados nas listas <literal>lnum</literal> e <literal>lden</literal> + respectivamente. + </para> + <para> + O "ganho" retornado como <literal>g</literal>, i.e. tem-se: rat= g + vezes (produto das entradas de lnum) / (produto das entradas de + lden). + </para> + <para> + Se <literal>flag</literal> for <literal>'c'</literal> + (respectivamente, <literal>'d'</literal>), as razes + <literal>pol</literal> sero refletidas em relao em relao ao eixo + imaginrio (respectivamente, ao crculo unitrio), i.e. os fatores em + <literal>lnum</literal> so polinmios estveis. + </para> + <para> + A mesma coisa se <literal>factors</literal> for invocado com + argumentos racionais: as entradas em <literal>lnum</literal> e + <literal>lden</literal> so polinmios estveis se <literal>flag</literal> + for dado. <literal>R2=factors(R1,'c')</literal> ou + <literal>R2=factors(R1,'d')</literal> com <literal>R1</literal> uma funo + racional ou lista <literal>syslin</literal> SISO, ento a sada + <literal>R2</literal> uma transferncia com com numerador e denominador + estveis e com a mesma magnitude de <literal>R1</literal> ao longo do eixo + imaginrio (<literal>'c'</literal>) ou do crculo unitrio + (<literal>'d'</literal>). + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +n=poly([0.2,2,5],'z'); +d=poly([0.1,0.3,7],'z'); +R=syslin('d',n,d); +R1=factors(R,'d') +roots(R1('num')) +roots(R1('den')) +w=exp(2*%i*%pi*[0:0.1:1]); +norm(abs(horner(R1,w))-abs(horner(R,w))) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="simp">simp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/hermit.xml b/modules/polynomials/help/pt_BR/hermit.xml new file mode 100755 index 000000000..e4511c75f --- /dev/null +++ b/modules/polynomials/help/pt_BR/hermit.xml @@ -0,0 +1,76 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="hermit" xml:lang="en"> + <refnamediv> + <refname>hermit</refname> + <refpurpose>forma hermitiana</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[Ar,U]=hermit(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz de polinmios </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ar</term> + <listitem> + <para>matriz de polinmios triangular </para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>matriz de polinmios unimodular</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + Forma hermitiana: <literal>U</literal> uma matriz unimodular tal + que <literal>A*U</literal> est na forma triangular de Hermite: + </para> + <para> + A varivel de sada <literal>Ar=A*U</literal>. + </para> + <para>Aviso: verso experimental</para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +p=[s, s*(s+1)^2, 2*s^2+s^3]; +[Ar,U]=hermit(p'*p); +clean(p'*p*U), det(U) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="hrmt">hrmt</link> + </member> + <member> + <link linkend="htrianr">htrianr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/horner.xml b/modules/polynomials/help/pt_BR/horner.xml new file mode 100755 index 000000000..ecdca16e5 --- /dev/null +++ b/modules/polynomials/help/pt_BR/horner.xml @@ -0,0 +1,98 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="horner" xml:lang="en"> + <refnamediv> + <refname>horner</refname> + <refpurpose>avaliao polinomial/racional</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>horner(P,x)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>P</term> + <listitem> + <para>matriz de polinmios ou de razes de polinmios</para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para>nmero real, polinmio ou razo de polinmios</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + Avalia a matriz de polinmios ou de razes de polinmios <literal>P + = P(s) + </literal> + quando a varivel <literal>s</literal> do polinmio + substituida por <literal>x</literal>: + </para> + <para> + <literal>horner(P,x)</literal>=<literal>P(x)</literal> + </para> + <para> + Exemplo (transformao bilinear): admita que <literal>P= + P(s) + </literal> + uma matriz de razes de polinmios, ento a matriz de + razes de polinmios <literal>P((1+s)/(1-s))</literal> obtida por + <literal>horner(P,(1+s)/(1-s))</literal>. + </para> + <para>Para avaliar uma matriz de razes de polinmios em dadas freqncias + use preferivelmente a primitiva <literal>freq</literal> . + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +//avaliao de um polinmio para um vetor de nmeros +P=poly(1:3,'x') +horner(P,[1 2 5]) +horner(P,[1 2 5]+%i) + +//avaliao de uma razo +s=poly(0,'s');M=[s,1/s]; +horner(M,1) +horner(M,%i) +horner(M,1/s) + +//avaliao de um polinmio para uma matriz de nmeros +X= [1 2;3 4] +p=poly(1:3,'x','c') +m=horner(p, X) +1*X.^0+2*X.^1+3*X.^2 + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="freq">freq</link> + </member> + <member> + <link linkend="repfreq">repfreq</link> + </member> + <member> + <link linkend="evstr">evstr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/hrmt.xml b/modules/polynomials/help/pt_BR/hrmt.xml new file mode 100755 index 000000000..7e0b2b834 --- /dev/null +++ b/modules/polynomials/help/pt_BR/hrmt.xml @@ -0,0 +1,78 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="hrmt" xml:lang="en"> + <refnamediv> + <refname>hrmt</refname> + <refpurpose>mximo divisor comum de polinmios</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[pg,U]=hrmt(v)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>v</term> + <listitem> + <para>vetor linha de polinmios, i.e. matriz de polinmios + <literal>1</literal>x<literal>k</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>pg</term> + <listitem> + <para>polinmio</para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>matriz de polinmios unimodular</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>[pg,U]=hrmt(v)</literal> retorna uma matriz unimodular + <literal>U</literal> e <literal>pg</literal> = MDC do vetor linha de + polinmios <literal>v</literal> tais que <literal>v*U = + [pg,0] + </literal> + . + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +x=poly(0,'x'); +v=[x*(x+1),x^2*(x+1),(x-2)*(x+1),(3*x^2+2)*(x+1)]; +[pg,U]=hrmt(v);U=clean(U) +det(U) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="gcd">gcd</link> + </member> + <member> + <link linkend="htrianr">htrianr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/htrianr.xml b/modules/polynomials/help/pt_BR/htrianr.xml new file mode 100755 index 000000000..f05a268fb --- /dev/null +++ b/modules/polynomials/help/pt_BR/htrianr.xml @@ -0,0 +1,92 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="htrianr" xml:lang="en"> + <refnamediv> + <refname>htrianr</refname> + <refpurpose>triangularizao de matrizes de polinmios</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[Ar,U,rk]=htrianr(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title> Parmetros </title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz de polinmios</para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ar</term> + <listitem> + <para>matriz de polinmios</para> + </listitem> + </varlistentry> + <varlistentry> + <term>U</term> + <listitem> + <para>matriz unimodular de polinmios </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + inteiro, posto normal def <literal>A</literal> + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para>Triangularizao da matriz de polinmios + <literal>A</literal>. + </para> + <para> + <literal>A</literal> is <literal>[m,n]</literal> , <literal>m <= + n + </literal> + . + </para> + <para> + <literal>Ar=A*U</literal> + </para> + <para>Aviso: h eliminao de termos "pequenos" (ver cdigo da + funo). + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +x=poly(0,'x'); +M=[x;x^2;2+x^3]*[1,x-2,x^4]; +[Mu,U,rk]=htrianr(M) +det(U) +M*U(:,1:2) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="hrmt">hrmt</link> + </member> + <member> + <link linkend="colcompr">colcompr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/inv_coeff.xml b/modules/polynomials/help/pt_BR/inv_coeff.xml new file mode 100755 index 000000000..50ab8f2f6 --- /dev/null +++ b/modules/polynomials/help/pt_BR/inv_coeff.xml @@ -0,0 +1,75 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="inv_coeff" xml:lang="en"> + <refnamediv> + <refname>inv_coeff</refname> + <refpurpose>constri uma matriz de polinmios a partir de seus + coeficientes + </refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqncia de Chamamento</title> + <synopsis>[P]=inv_coeff(C,[,d,[name])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>C</term> + <listitem> + <para>matriz grande de coeficientes</para> + </listitem> + </varlistentry> + <varlistentry> + <term>d</term> + <listitem> + <para>grau da matriz de polinmios. Parmetro opcional com valor + padro <literal>d=-1+size(C,'c')/size(C,'r')</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>name</term> + <listitem> + <para>string fornecendo o nome da varivel polinomial (valor padro + <literal>'x'</literal>). + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>P=inv_coeff(Mp,k)</literal>, quando <literal>k</literal> + compatvel com o tamanho de <literal>Mp</literal> size, retorna uma matriz + de polinmios de grau k. <literal>C=[C0,C1,...,Ck]</literal> and + <literal>P= C0 + C1*x +... +Ck*x^k</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +A=int(10*rand(2,6)) +// Construindo uma matriz de polinmios de grau 1 +P=inv_coeff(A,1) +norm(coeff(P)-A) +// Usando valor padro para o grau +P1=inv_coeff(A) +norm(coeff(P1)-A) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="degree">degree</link> + </member> + <member> + <link linkend="coeff">coeff</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/invr.xml b/modules/polynomials/help/pt_BR/invr.xml new file mode 100755 index 000000000..4a6569f61 --- /dev/null +++ b/modules/polynomials/help/pt_BR/invr.xml @@ -0,0 +1,70 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="invr" xml:lang="en"> + <refnamediv> + <refname>invr</refname> + <refpurpose>inverso de matrizes (de razes de polinmios)</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>F = invr(H)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>H</term> + <listitem> + <para>matriz de polinmios ou de razes de polinmios </para> + </listitem> + </varlistentry> + <varlistentry> + <term>F</term> + <listitem> + <para>matriz de polinmios ou de razes de polinmios</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + Se <literal>H</literal> uma matriz de polinmios ou de razes de + polinmios, <literal>invr</literal> computa <literal>H^(-1)</literal> + utilizando o algoritmo de Leverrier (ver cdigo da funo). + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s') +H=[s,s*s+2;1-s,1+s]; invr(H) +[Num,den]=coffg(H);Num/den +H=[1/s,(s+1);1/(s+2),(s+3)/s];invr(H) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="glever">glever</link> + </member> + <member> + <link linkend="coffg">coffg</link> + </member> + <member> + <link linkend="inv">inv</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/lcmdiag.xml b/modules/polynomials/help/pt_BR/lcmdiag.xml new file mode 100755 index 000000000..c3e2fd12c --- /dev/null +++ b/modules/polynomials/help/pt_BR/lcmdiag.xml @@ -0,0 +1,93 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="lcmdiag" xml:lang="en"> + <refnamediv> + <refname>lcmdiag</refname> + <refpurpose>fatorao diagonal por MMC</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[N,D]=lcmdiag(H) + [N,D]=lcmdiag(H,flag) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>H</term> + <listitem> + <para>matriz de razes de polinmios </para> + </listitem> + </varlistentry> + <varlistentry> + <term>N</term> + <listitem> + <para>matriz de polinmios </para> + </listitem> + </varlistentry> + <varlistentry> + <term>D</term> + <listitem> + <para>matriz de polinmios diagonal </para> + </listitem> + </varlistentry> + <varlistentry> + <term>flag</term> + <listitem> + <para> + string: <literal>'row'</literal> ou <literal>'col'</literal> + (padro) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>[N,D]=lcmdiag(H,'row')</literal> computa uma fatorao + <literal>D*H=N</literal>, i.e. <literal>H=D^(-1)*N</literal> onde D uma + matriz diagonal com D(k,k)=MMC da k-sima linha de H('den'). + </para> + <para> + <literal>[N,D]=lcmdiag(H)</literal> ou + <literal>[N,D]=lcmdiag(H,'col)</literal> retorna + <literal>H=N*D^(-1)</literal> com matriz diagonal D e D(k,k)=MMC da + k-sima coluna de H('den') + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +H=[1/s,(s+2)/s/(s+1)^2;1/(s^2*(s+2)),2/(s+2)]; +[N,D]=lcmdiag(H); +N/D-H + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="lcm">lcm</link> + </member> + <member> + <link linkend="gcd">gcd</link> + </member> + <member> + <link linkend="bezout">bezout</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/ldiv.xml b/modules/polynomials/help/pt_BR/ldiv.xml new file mode 100755 index 000000000..270e51fde --- /dev/null +++ b/modules/polynomials/help/pt_BR/ldiv.xml @@ -0,0 +1,79 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="ldiv" xml:lang="en"> + <refnamediv> + <refname>ldiv</refname> + <refpurpose>diviso longa entre matrizes de polinmios</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[x]=ldiv(n,d,k)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>n,d</term> + <listitem> + <para>duas matrizes de polinmios reais </para> + </listitem> + </varlistentry> + <varlistentry> + <term>k</term> + <listitem> + <para>inteiro</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>x=ldiv(n,d,k)</literal> fornece os <literal>k</literal> + primeiros coeficientes da diviso longa de <literal>n</literal> por + <literal>d</literal> i.e. the a expanso de Taylor da matriz de razes de + polinmios <literal>[nij(z)/dij(z)]</literal> aproximando-se do + infinito. + </para> + <para> + Os coeficientes de expanso de <literal>nij/dij</literal> so + armazenados em <literal>x((i-1)*n+k,j) k=1:n</literal> + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +wss=ssrand(1,1,3);[a,b,c,d]=abcd(wss); +wtf=ss2tf(wss); +x1=ldiv(numer(wtf),denom(wtf),5) +x2=[c*b;c*a*b;c*a^2*b;c*a^3*b;c*a^4*b] +wssbis=markp2ss(x1',5,1,1); +wtfbis=clean(ss2tf(wssbis)) +x3=ldiv(numer(wtfbis),denom(wtfbis),5) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="arl2">arl2</link> + </member> + <member> + <link linkend="markp2ss">markp2ss</link> + </member> + <member> + <link linkend="pdiv">pdiv</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/numer.xml b/modules/polynomials/help/pt_BR/numer.xml new file mode 100755 index 000000000..7a9fa45b9 --- /dev/null +++ b/modules/polynomials/help/pt_BR/numer.xml @@ -0,0 +1,59 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="numer" xml:lang="en"> + <refnamediv> + <refname>numer</refname> + <refpurpose>numerador</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>num=numer(R)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>R</term> + <listitem> + <para>matriz de polinmios, de razes de polinmios ou de constantes + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>num</term> + <listitem> + <para>matriz de polinmios</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + Funo utilitria. <literal>num=numer(R)</literal> retorna o + numerador <literal>num</literal> de uma matriz de funes racionais + <literal>R</literal> (<literal>R</literal> tambm pode ser uma matriz de + polinmios ou de constantes). <literal>numer(R)</literal> equivalente a + <literal>R(2)</literal>, <literal>R('num')</literal> ou + <literal>R.num</literal> + </para> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="denom">denom</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/pdiv.xml b/modules/polynomials/help/pt_BR/pdiv.xml new file mode 100755 index 000000000..5ccbbf620 --- /dev/null +++ b/modules/polynomials/help/pt_BR/pdiv.xml @@ -0,0 +1,81 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="pdiv" xml:lang="en"> + <refnamediv> + <refname>pdiv</refname> + <refpurpose>diviso polinomial</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[R,Q]=pdiv(P1,P2) + [Q]=pdiv(P1,P2) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>P1</term> + <listitem> + <para>matriz de polinmios </para> + </listitem> + </varlistentry> + <varlistentry> + <term>P2</term> + <listitem> + <para>polinmio ou matriz de polinmios</para> + </listitem> + </varlistentry> + <varlistentry> + <term>R,Q</term> + <listitem> + <para>duas matrizes de polinmios</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para>Diviso euclidiana elemento a elemento da matriz de polinmios + <literal>P1</literal> pelo polinmio <literal>P2</literal> ou pela matriz + de polinmios <literal>P2</literal>. <literal>Rij</literal> a matriz de + restos, <literal>Qij</literal> a matriz de quocientes e <literal>P1ij = + Qij*P2 + Rij + </literal> + ou <literal>P1ij = Qij*P2ij + Rij</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +x=poly(0,'x'); +p1=(1+x^2)*(1-x);p2=1-x; +[r,q]=pdiv(p1,p2) +p2*q-p1 +p2=1+x; +[r,q]=pdiv(p1,p2) +p2*q+r-p1 + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="ldiv">ldiv</link> + </member> + <member> + <link linkend="gcd">gcd</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/pol2str.xml b/modules/polynomials/help/pt_BR/pol2str.xml new file mode 100755 index 000000000..07422088d --- /dev/null +++ b/modules/polynomials/help/pt_BR/pol2str.xml @@ -0,0 +1,84 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * Copyright (C) 2013 - Samuel GOUGEON : upgrade for 5.5.0 + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="pol2str" xml:lang="en"> +<refnamediv> + <refname>pol2str</refname> + <refpurpose>converso de polinmio para string</refpurpose> +</refnamediv> +<refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[str] = pol2str(p)</synopsis> +</refsynopsisdiv> +<refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>Matriz ou hipermatriz polinmios com coeficientes reais ou complexos</para> + </listitem> + </varlistentry> + <varlistentry> + <term>str</term> + <listitem> + <para>string</para> + </listitem> + </varlistentry> + </variablelist> +</refsection> +<refsection> + <title>Descrio</title> + <para> Converte um polinmio para um string (funo utilitria).</para> + <para> + <note> + O formato dos coeficientes de sada definida atravs <link linkend="format">format(..)</link>. + </note> + </para> +</refsection> +<refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +pol2str(%z) + +p = poly ([1, 2, 3], "x","coeff"); +pol2str(p) + +p = (1+%i+%z)^(1:4) +pol2str(p) + ]]></programlisting> +</refsection> +<refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="string">string</link> + </member> + <member> + <link linkend="prettyprint">prettyprint</link> + </member> + <member> + <link linkend="sci2exp">sci2exp</link> + </member> + </simplelist> +</refsection> +<refsection role="history tag"> + <title>Histrico</title> + <revhistory> + <revision> + <revnumber>5.5.0</revnumber> + <revdescription>pol2str () estendido para polinmios com coeficientes complexos e para hipermatriz. Processamento de matriz vetorizado.</revdescription> + </revision> + </revhistory> +</refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/polfact.xml b/modules/polynomials/help/pt_BR/polfact.xml new file mode 100755 index 000000000..5fc18b36a --- /dev/null +++ b/modules/polynomials/help/pt_BR/polfact.xml @@ -0,0 +1,78 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Serge STEER + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="polfact" xml:lang="en"> + <refnamediv> + <refname>polfact</refname> + <refpurpose>fatores mnimos</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[f]=polfact(p)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>polinmio </para> + </listitem> + </varlistentry> + <varlistentry> + <term>f</term> + <listitem> + <para> + vetor <literal>[f0 f1 ... fn]</literal> tal que + <literal>p=prod(f)</literal> + </para> + <variablelist> + <varlistentry> + <term>f0</term> + <listitem> + <para>constante</para> + </listitem> + </varlistentry> + <varlistentry> + <term>fi</term> + <listitem> + <para>polinmio</para> + </listitem> + </varlistentry> + </variablelist> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>f=polfact(p)</literal> retorna os valores mnimos de p, + i.e., <literal>f=[f0 f1 ... fn]</literal> tal que + <literal>p=prod(f)</literal> + </para> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="lcm">lcm</link> + </member> + <member> + <link linkend="cmndred">cmndred</link> + </member> + <member> + <link linkend="factors">factors</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/poly.xml b/modules/polynomials/help/pt_BR/poly.xml new file mode 100755 index 000000000..9cdf1a5dd --- /dev/null +++ b/modules/polynomials/help/pt_BR/poly.xml @@ -0,0 +1,119 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="poly" xml:lang="en"> + <refnamediv> + <refname>poly</refname> + <refpurpose>definio de polinmios</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqncia de Chamamento</title> + <synopsis>p=poly(a,x, ["flag"])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>a</term> + <listitem> + <para>matriz ou nmero real </para> + </listitem> + </varlistentry> + <varlistentry> + <term>x</term> + <listitem> + <para>String, o nome da varivel simblica. Se o string tiver mais + de 4 caracteres, apenas os quatro primeiros sero levados em + conta. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>"flag"</term> + <listitem> + <para>string ("roots", "coeff"), valor padro "roots".</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <variablelist> + <varlistentry> + <term>Se a uma matriz,</term> + <listitem> + <para> + <literal>p</literal> o polinmio caracterstico, i.e., + <literal>determinant(x*eye()-a)</literal>, <literal>x</literal> + sendo a varivel simblica. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Se v um vetor,</term> + <listitem> + <itemizedlist> + <listitem> + <para> + <literal>poly(v,"x",["roots"])</literal> o polinmio com + entradas de <literal>v</literal> como razes e + <literal>"x"</literal> como varivel formal (neste caso, + <literal>roots</literal> e <literal>poly</literal> so funes + inversas). Note que infinitas razes fornecem zero coeficientes + de grau mais elevado. + </para> + </listitem> + <listitem> + <para> + <literal>poly(v,"x","coeff")</literal> cria o polinmio + com smbolo <literal>"x"</literal> e com entradas de + <literal>v</literal> como coeficientes (v(1) o termo constante + do polinmio). (aqui <literal>poly</literal> e + <literal>coeff</literal> so funes inversas). + </para> + </listitem> + </itemizedlist> + </listitem> + </varlistentry> + </variablelist> + <para> + <literal>s=poly(0,"s")</literal> a fonte para definir polinmios + com smbolo <literal>"s"</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +s=poly(0,"s"); +p=1+s+2*s^2 +A=rand(2,2); +poly(A,"x") +//fraes racionais +h=(1+2*%s)/poly(1:4,'s','c') + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>See Also</title> + <simplelist type="inline"> + <member> + <link linkend="coeff">coeff</link> + </member> + <member> + <link linkend="roots">roots</link> + </member> + <member> + <link linkend="varn">varn</link> + </member> + <member> + <link linkend="horner">horner</link> + </member> + <member> + <link linkend="derivat">derivat</link> + </member> + <member> + <link linkend="matrices">matrices</link> + </member> + <member> + <link linkend="rational">rational</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/rational.xml b/modules/polynomials/help/pt_BR/rational.xml new file mode 100755 index 000000000..6743c4f27 --- /dev/null +++ b/modules/polynomials/help/pt_BR/rational.xml @@ -0,0 +1,52 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="rational" xml:lang="en"> + <refnamediv> + <refname>rational</refname> + <refpurpose>objeto do Scilab, razo de polinmios</refpurpose> + </refnamediv> + <refsection> + <title>Descrio</title> + <para> + Um razo de polinmios <literal>r</literal> um quociente entre + dois polinmios <literal>r=num/den</literal>. A representao interna de + uma razo de polinmios uma lista. + <literal>r = rlist(num,den,[])</literal> o mesmo + que <literal>r=num/den</literal>. Uma matriz de razes de polinmios pode + ser definida pela sintaxe usual, por exemplo: + <literal>[r11,r12;r21,r22]</literal> i uma matriz 2x2 onde + <literal>rij</literal> so razes 1x1. Uma matriz de razes de polinmios + tambm pode ser definida como acima como uma lista + <literal>tlist(['r','num','den','dt'],num,den,[])</literal> com + <literal>num</literal> e <literal>den</literal> matrizes de + polinmios. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +W=[1/s,1/(s+1)] +W'*W +Num=[s,s+2;1,s];Den=[s*s,s;s,s*s]; +rlist(Num,Den,[]) +H=Num./Den +syslin('c',Num,Den) +syslin('c',H) +[Num1,Den1]=simp(Num,Den) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="syslin">syslin</link> + </member> + <member> + <link linkend="simp">simp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/residu.xml b/modules/polynomials/help/pt_BR/residu.xml new file mode 100755 index 000000000..bbe0c17f5 --- /dev/null +++ b/modules/polynomials/help/pt_BR/residu.xml @@ -0,0 +1,87 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA - Francois DELBECQUE + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="residu" xml:lang="en"> + <refnamediv> + <refname>residu</refname> + <refpurpose>resduo</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[V]=residu(P,Q1,Q2)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>P, Q1, Q2</term> + <listitem> + <para>polinmios ou matrizes de polinmios de coeficientes reais ou + complexos. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>V=residu(P,Q1,Q2)</literal> retorna a matriz + <literal>V</literal> tal que <literal>V(i,j)</literal> a soma dos + resduos da frao racional <literal>P(i,j)/(Q1(i,j)*Q2(i,j))</literal> + calculada nos zeros de <literal>Q1(i,j)</literal>. + </para> + <para> + <literal>Q1(i,j)</literal> e <literal>Q2(i,j)</literal> no devem + possuir razes em comum. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +H=[s/(s+1)^2,1/(s+2)];N=numer(H);D=denom(H); +w=residu(N.*horner(N,-s),D,horner(D,-s)); //N(s) N(-s) / D(s) D(-s) +sqrt(sum(w)) //This is H2 norm +h2norm(tf2ss(H)) +// +p=(s-1)*(s+1)*(s+2)*(s+10);a=(s-5)*(s-1)*(s*s)*((s+1/2)**2); +b=(s-3)*(s+2/5)*(s+3); +residu(p,a,b)+531863/4410 //Exato +z=poly(0,'z');a=z^3+0.7*z^2+0.5*z-0.3;b=z^3+0.3*z^2+0.2*z+0.1; +atild=gtild(a,'d');btild=gtild(b,'d'); +residu(b*btild,z*a,atild)-2.9488038 //Exato +a=a+0*%i;b=b+0*%i; +real(residu(b*btild,z*a,atild)-2.9488038) //Caso complexo + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="pfss">pfss</link> + </member> + <member> + <link linkend="bdiag">bdiag</link> + </member> + <member> + <link linkend="roots">roots</link> + </member> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="gtild">gtild</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/roots.xml b/modules/polynomials/help/pt_BR/roots.xml new file mode 100755 index 000000000..a73585db0 --- /dev/null +++ b/modules/polynomials/help/pt_BR/roots.xml @@ -0,0 +1,93 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="roots" xml:lang="en"> + <refnamediv> + <refname>roots</refname> + <refpurpose>razes de polinmios</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[x]=roots(p) + [x]=roots(p,'e') + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>polinmio com coeficientes reais ou complexos ou vetor dos + coeficientes do polinmio em ordem de graus decrescentes (para + compatibilidade com o Matlab). + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>x=roots(p)</literal> retorna no vetor de complexos + <literal>x</literal> as razes do polinmio <literal>p</literal>. Para + polinmios reais de grau<= 100 o algoritmo rpido RPOLY utilizado. Em + outros casos, as razes so computadas como os autovalores da matriz + companheira associada. Use <literal>x=roots(p,'e')</literal> para forar + este algoritmo em qualquer caso. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +p=poly([0,10,1+%i,1-%i],'x'); +roots(p) +A=rand(3,3);roots(poly(A,'x')) // avaliaes por polinmios caractersticos +spec(A) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="spec">spec</link> + </member> + <member> + <link linkend="companion">companion</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>References</title> + <para>O algoritmo RPOLY descrito em "Algorithm 493: Zeros of a Real + Polynomial", ACM TOMS Volume 1, edio 2 (Junho 1975), pp. 178-189 + </para> + <para>Jenkins, M. A. e Traub, J. F. (1970), A Three-Stage Algorithm for + Real Polynomials Using Quadratic Iteration, SIAM J. Numer. Anal., 7(1970), + 545-566. + </para> + <para>Jenkins, M. A. e Traub, J. F. (1970), Principles for Testing + Polynomial Zerofinding Programs. ACM TOMS 1, 1 (Maro1975), pp. + 26-34 + </para> + </refsection> + <refsection> + <title> Funes Utilizadas </title> + <para>O cdigo fonte de rpoly.f pode ser achado no diretrio + SCI/modules/polynomials/src/fortran de uma distribuio fonte do Scilab. A computao de + autovalores feita utilizando-se os cdigos do LAPACK DGEEV e ZGEEV. + </para> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/rowcompr.xml b/modules/polynomials/help/pt_BR/rowcompr.xml new file mode 100755 index 000000000..fb1ed8862 --- /dev/null +++ b/modules/polynomials/help/pt_BR/rowcompr.xml @@ -0,0 +1,78 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="rowcompr" xml:lang="en"> + <refnamediv> + <refname>rowcompr</refname> + <refpurpose>compresso de linhas de uma matriz de polinmios</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[X,rk,Ac]=rowcompr(A)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>A</term> + <listitem> + <para>matriz de polinmios </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Y</term> + <listitem> + <para>matriz de polinmios quadrada (base unimodular esquerda) + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>rk</term> + <listitem> + <para> + posto normal de <literal>A</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Ac</term> + <listitem> + <para> + <literal>Ac=X*A</literal>, matriz de polinmios + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para>Compresso de linhas da matriz de polinmios + <literal>A</literal>. + </para> + <para> + <literal>X</literal> uma base polinomial unimodular esquerda que + comprime as linhas de <literal>A</literal>. <literal>rk</literal> o + posto normal de A. + </para> + <para> Aviso: h eliminao de termos "pequenos" (utilize com + cuidado!). + </para> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="colcompr">colcompr</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/sfact.xml b/modules/polynomials/help/pt_BR/sfact.xml new file mode 100755 index 000000000..ef86abb07 --- /dev/null +++ b/modules/polynomials/help/pt_BR/sfact.xml @@ -0,0 +1,95 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="sfact" xml:lang="en"> + <refnamediv> + <refname>sfact</refname> + <refpurpose>fatorao espectral em tempo discreto</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>F=sfact(P)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>P</term> + <listitem> + <para>matriz de polinmios reais</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + Acha <literal>F</literal>, um fator espectral de + <literal>P</literal>. <literal>P</literal> uma matriz de polinmios tal + que cada raiz de <literal>P</literal> possui uma imagem simtrica em + relao ao crculo unitrio. O problema singular se uma raiz estiver no + crculo unitrio. + </para> + <para> + <literal>sfact(P)</literal> retorna uma matriz de polinmios + <literal>F(z)</literal> que anti-estvel e tal que + </para> + <para> + <literal>P = F(z)* F(1/z) *z^n</literal> + </para> + <para> Para polinmios escalares um algorimto especfico implementado. + Os algoritmos so implementados do livro de Kucera. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +//exemplo polinomial +z=poly(0,'z'); +p=(z-1/2)*(2-z) +w=sfact(p); +w*numer(horner(w,1/z)) + +//exemplo matricial +F1=[z-1/2,z+1/2,z^2+2;1,z,-z;z^3+2*z,z,1/2-z]; +P=F1*gtild(F1,'d'); //P simtrica +F=sfact(P) +roots(det(P)) +roots(det(gtild(F,'d'))) //as razes estveis +roots(det(F)) //as razes anti-estveis +clean(P-F*gtild(F,'d')) + +//exemplo de uso de tempo contnuo +s=poly(0,'s'); +p=-3*(s+(1+%i))*(s+(1-%i))*(s+0.5)*(s-0.5)*(s-(1+%i))*(s-(1-%i));p=real(p); + +//p(s) = polinmio em s^2 , procura por f estvel tal que p=f(s)*f(-s) +w=horner(p,(1-s)/(1+s)); // transformao bilinear w=p((1-s)/(1+s)) +wn=numer(w); //tomando o numerador +fn=sfact(wn);f=numer(horner(fn,(1-s)/(s+1))); //fator e transformao de volta +f=f/sqrt(horner(f*gtild(f,'c'),0));f=f*sqrt(horner(p,0)); //normalizao +roots(f) //f estvel +clean(f*gtild(f,'c')-p) //f(s)*f(-s) p(s) + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="gtild">gtild</link> + </member> + <member> + <link linkend="fspecg">fspecg</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/simp.xml b/modules/polynomials/help/pt_BR/simp.xml new file mode 100755 index 000000000..11e093fb8 --- /dev/null +++ b/modules/polynomials/help/pt_BR/simp.xml @@ -0,0 +1,110 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="simp" xml:lang="en"> + <refnamediv> + <refname>simp</refname> + <refpurpose>simplificao racional</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[N1,D1]=simp(N,D) + H1=simp(H) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>N,D</term> + <listitem> + <para>polinmios reais ou matrizes de polinmios reais</para> + </listitem> + </varlistentry> + <varlistentry> + <term>H</term> + <listitem> + <para>matriz de razes de polinmios (i.e matriz com entradas + <literal>n/d</literal> ,<literal>n</literal> e <literal>d</literal> + polinmios reais) + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>[n1,d1]=simp(n,d)</literal> calcula dois polinmios + <literal>n1</literal> e <literal>d1</literal> tais que <literal>n1/d1 = + n/d + </literal> + . + </para> + <para> + Se <literal>N</literal> e <literal>D</literal> so matrizes de + polinmios, os clculos so feitos elemento a elemento. + </para> + <para> + <literal>H1=simp(H)</literal> tambm vlido (cada entrada de + <literal>H</literal> simplificada em <literal>H1</literal>). + </para> + <para>Cuidado:</para> + <para> + -Nenhum limiar dado i.e. <literal>simp</literal> no pode forar + uma simplificao. + </para> + <para>-Para sistemas lineares dinmicos que incluem integrador(es), a + simplificao modifica o ganho esttico. (<literal>H(0)</literal> para + sistemas contnuos <literal>H(1)</literal> para sistemas discretos) + </para> + <para> + -Para dados complexos, <literal>simp</literal> retorna sua(s) + entrada(s). + </para> + <para>-Uma simplificao racional chamada aps aproximadamente cada + operao sobre razes de polinmios. possvel alternar o modo de + simplificao entre "on" e "off" (ligado e desligado) utilizando a funo + <literal>simp_mode</literal>. + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +[n,d]=simp((s+1)*(s+2),(s+1)*(s-2)) + +simp_mode(%F);hns=s/s +simp_mode(%T);hns=s/s + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="roots">roots</link> + </member> + <member> + <link linkend="trfmod">trfmod</link> + </member> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="clean">clean</link> + </member> + <member> + <link linkend="simp_mode">simp_mode</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/simp_mode.xml b/modules/polynomials/help/pt_BR/simp_mode.xml new file mode 100755 index 000000000..89c83e0d2 --- /dev/null +++ b/modules/polynomials/help/pt_BR/simp_mode.xml @@ -0,0 +1,73 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="simp_mode" xml:lang="en"> + <refnamediv> + <refname>simp_mode</refname> + <refpurpose>modifica o modo de simplificao racional</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>mod=simp_mode() + simp_mode(mod) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>mod</term> + <listitem> + <para>um booleano</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para>A simplificao racional chamada aps quase cada operao sobre + razes de polinmios. possvel alternar o modo de simplificao entre + "on" e "off" (ligado e desligado) utilizando a funo + <literal>simp_mode</literal>. + </para> + <para> + <literal>simp_mode(%t)</literal> ajusta o modo de simplificao + racional para "on" + </para> + <para> + <literal>simp_mode(%f)</literal> ajusta o modo de simplificao + racional para "off" + </para> + <para> + <literal>mod=simp_mode()</literal> retorna em mod o modo de + simplificao racional corrente + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +mod=simp_mode() +simp_mode(%f);hns=s/s +simp_mode(%t);hns=s/s +simp_mode(mod); + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Tambm </title> + <simplelist type="inline"> + <member> + <link linkend="simp">simp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/sylm.xml b/modules/polynomials/help/pt_BR/sylm.xml new file mode 100755 index 000000000..21a48ed8e --- /dev/null +++ b/modules/polynomials/help/pt_BR/sylm.xml @@ -0,0 +1,76 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="sylm" xml:lang="en"> + <refnamediv> + <refname>sylm</refname> + <refpurpose>matriz de Sylvester</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqncia de Chamamento </title> + <synopsis>[S]=sylm(a,b)</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>a,b</term> + <listitem> + <para>duas matrizes de polinmios </para> + </listitem> + </varlistentry> + <varlistentry> + <term>S</term> + <listitem> + <para>matriz</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + <literal>sylm(a,b)</literal> fornece a matriz de Sylvester associada + aos polinmios <literal>a</literal> e <literal>b</literal>, i.e. a matriz + <literal>S</literal> tal que: + </para> + <para> + <literal>coeff( a*x + b*y )' = S * + [coeff(x)';coeff(y)'] + </literal> + . + </para> + <para> + A dimenso de <literal>S</literal> igual a + <literal>degree(a)+degree(b)</literal>. + </para> + <para> + Se <literal>a</literal> e <literal>b</literal> so polinmios primos + entre si, ento + </para> + <para> + <literal>rank(sylm(a,b))=degree(a)+degree(b))</literal> e as + instrues + </para> + <programlisting role=""><![CDATA[ +u = sylm(a,b) \ eye(na+nb,1) +x = poly(u(1:nb),'z','coeff') +y = poly(u(nb+1:na+nb),'z','coeff') + ]]></programlisting> + <para> + computam os fatores de Bezout <literal>x</literal> e + <literal>y</literal> de graus mnimos tais que <literal>a*x+b*y = + 1 + </literal> + </para> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/systmat.xml b/modules/polynomials/help/pt_BR/systmat.xml new file mode 100755 index 000000000..a945e3f6c --- /dev/null +++ b/modules/polynomials/help/pt_BR/systmat.xml @@ -0,0 +1,76 @@ +<?xml version="1.0" encoding="ISO-8859-1"?> +<!-- + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2006-2008 - INRIA + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + * + --> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="systmat" xml:lang="en"> + <refnamediv> + <refname>systmat</refname> + <refpurpose>matriz sistema</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Seqncia de Chamamento</title> + <synopsis>[Sm]=systmat(Sl);</synopsis> + </refsynopsisdiv> + <refsection> + <title>Parmetros</title> + <variablelist> + <varlistentry> + <term>Sl</term> + <listitem> + <para> + sistema linear (lista <literal>syslin</literal> ) ou sistema + descritor + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>Sm</term> + <listitem> + <para>feixe de matrizes</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrio</title> + <para> + Matriz sistema do sistema linear <literal>Sl</literal> (lista + <literal>syslin</literal>) em forma de espao de estados (funo + utilitria). + </para> + <programlisting role=""><![CDATA[ +Sm = [-sI + A B; + [ C D] + ]]></programlisting> + <para>Para um sistema descritor + (<literal>Sl=list('des',A,B,C,D,E)</literal>), <literal>systmat</literal> + retorna: + </para> + <programlisting role=""><![CDATA[ +Sm = [-sE + A B; + [ C D] + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Ver Tambm</title> + <simplelist type="inline"> + <member> + <link linkend="ss2des">ss2des</link> + </member> + <member> + <link linkend="sm2des">sm2des</link> + </member> + <member> + <link linkend="sm2ss">sm2ss</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/pt_BR/varn.xml b/modules/polynomials/help/pt_BR/varn.xml new file mode 100755 index 000000000..b4c8266c5 --- /dev/null +++ b/modules/polynomials/help/pt_BR/varn.xml @@ -0,0 +1,93 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="varn" xml:lang="pt"> + <refnamediv> + <refname>varn</refname> + <refpurpose>variável simbólica de polinômios ou de frações racionais</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title> Seqüência de Chamamento </title> + <synopsis>[symb]=varn(p) + [pm]=varn(p,varname) + </synopsis> + </refsynopsisdiv> + <refsection> + <title> Parâmetros </title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>matriz de polinômios ou de frações racionais</para> + </listitem> + </varlistentry> + <varlistentry> + <term>symb</term> + <listitem> + <para>string</para> + </listitem> + </varlistentry> + <varlistentry> + <term>var</term> + <listitem> + <para>variável simbólica (string) </para> + </listitem> + </varlistentry> + <varlistentry> + <term>pm</term> + <listitem> + <para>matriz de polinômios ou de frações racionais</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Descrição</title> + <para> + <literal>symb=varn(p)</literal> retorna em <literal>symb</literal> a + variável simbólica de <literal>p</literal> (i.e. + <literal>varn(poly(0,'x'))</literal> is <literal>'x'</literal>). + </para> + <para> + <literal>varn(p,'s')</literal> retorna uma matriz de polinômios com + os mesmos coeficientes que <literal>p</literal> mas com <literal>'s' + </literal> + como variável simbólica (mudança do nome de variável). + </para> + </refsection> + <refsection> + <title>Exemplos</title> + <programlisting role="example"><![CDATA[ +s = poly(0,'s'); p = [s^2+1,s]; +varn(p) +varn(p,'x') + +f = %z / (%z-1); f = [f f^2] +varn(f) +varn(f,"x") + ]]></programlisting> + </refsection> + <refsection> + <title> Ver Também </title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="rlist">rlist</link> + </member> + <member> + <link linkend="horner">horner</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>Histórico</title> + <revhistory> + <revision> + <revnumber>5.5.1</revnumber> + <revdescription> + <para>Extensão de frações racionais</para> + </revdescription> + </revision> + </revhistory> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ru_RU/addchapter.sce b/modules/polynomials/help/ru_RU/addchapter.sce new file mode 100755 index 000000000..539f015e6 --- /dev/null +++ b/modules/polynomials/help/ru_RU/addchapter.sce @@ -0,0 +1,11 @@ +// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) 2009 - DIGITEO +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +add_help_chapter("Polynomials",SCI+"/modules/polynomials/help/ru_RU",%T); + diff --git a/modules/polynomials/help/ru_RU/inv_coeff.xml b/modules/polynomials/help/ru_RU/inv_coeff.xml new file mode 100755 index 000000000..31dcadeb5 --- /dev/null +++ b/modules/polynomials/help/ru_RU/inv_coeff.xml @@ -0,0 +1,73 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ru" xml:id="inv_coeff"> + <refnamediv> + <refname>inv_coeff</refname> + <refpurpose>построение матрицы полиномов по их коэффициентам</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Последовательность вызова</title> + <synopsis>[P]=inv_coeff(C,[,d,[name])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Аргументы</title> + <variablelist> + <varlistentry> + <term>C</term> + <listitem> + <para>большая матрица коэффициентов</para> + </listitem> + </varlistentry> + <varlistentry> + <term>d</term> + <listitem> + <para> + степень матрицы полиномов. Это необязательный параметр, у которого значение + по умолчанию <literal>d=-1+size(C,'c')/size(C,'r')</literal> + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>name</term> + <listitem> + <para> + строковое значение, указывающее имя полиномиальной переменной (значение по умолчанию <literal>'x'</literal>). + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Описание</title> + <para> + <literal>P=inv_coeff(Mp,k)</literal>, когда <literal>k</literal> совместима с размером <literal>Mp</literal>, + возвращает полиномиальную матрицу степени <literal>k</literal>. <literal>C=[C0,C1,...,Ck]</literal> и + <literal>P= C0 + C1*x +... +Ck*x^k</literal>. + </para> + </refsection> + <refsection> + <title>Примеры</title> + <programlisting role="example"><![CDATA[ +A=int(10*rand(2,6)) +// Building a degree 1 polynomial matrix +P=inv_coeff(A,1) +norm(coeff(P)-A) +// Using default value for degree +P1=inv_coeff(A) +norm(coeff(P1)-A) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Смотрите также</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="degree">degree</link> + </member> + <member> + <link linkend="coeff">coeff</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ru_RU/poly.xml b/modules/polynomials/help/ru_RU/poly.xml new file mode 100755 index 000000000..e0d25792c --- /dev/null +++ b/modules/polynomials/help/ru_RU/poly.xml @@ -0,0 +1,131 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ru" xml:id="poly"> + <refnamediv> + <refname>poly</refname> + <refpurpose>определение полинома</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Последовательность вызова</title> + <synopsis>p = poly(a, vname, ["flag"])</synopsis> + </refsynopsisdiv> + <refsection> + <title>Аргументы</title> + <variablelist> + <varlistentry> + <term>a</term> + <listitem> + <para>матрица или вещественное число</para> + </listitem> + </varlistentry> + <varlistentry> + <term>vname</term> + <listitem> + <para> + Строка, имя символьной переменной. Если строка больше 4 символов, то из них + учитываются только 4 первых. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term>"flag"</term> + <listitem> + <para> + символьная строка ( <literal>"roots"</literal>, + <literal>"coeff"</literal>), значение по + умолчанию <literal>"roots"</literal>. + </para> + <para> + Также могут быть использованы сокращения: + <literal>"r"</literal> для <literal>"roots"</literal> + и <literal>"c"</literal> для <literal>"coeff"</literal>. + </para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Описание</title> + <variablelist> + <varlistentry> + <term> + Если <literal>a</literal> - матрица, то + </term> + <listitem> + <para> + <varname>p</varname> является характеристическим полиномом, то есть + <code>determinant(x*eye()-a)</code>, где <literal>x</literal> является + символьной переменной. + </para> + </listitem> + </varlistentry> + <varlistentry> + <term> + Если <literal>v</literal> - вектор, то + </term> + <listitem> + <itemizedlist> + <listitem> + <para> + <code>poly(v,"x",["roots"])</code> является полиномом с корнями, хранящимися в элементах <varname>v</varname> и + <literal>"x"</literal> в качестве формальной переменной. (В этом случае + <function>roots</function> и <function>poly</function> являются обратными функциями). + <note> + Заметьте, что бесконечные корни дают нулевые коэффициенты наивысшей степени. + </note> + </para> + </listitem> + <listitem> + <para> + <code>poly(v,"x","coeff")</code> создаёт полином с символом + <literal>"x"</literal> и с коэффициентами, хранящимися в элементах + <varname>v</varname> (<code>v(1)</code> - постоянный член полинома). Здесь + <function>poly</function> и <function>coeff</function> являются обратными функциями. + </para> + </listitem> + </itemizedlist> + </listitem> + </varlistentry> + </variablelist> + <para> + <code>s=poly(0,"s")</code> является семенем для определения полиномов с символом + <literal>"s"</literal>. + </para> + </refsection> + <refsection> + <title>Примеры</title> + <programlisting role="example"><![CDATA[ +s=poly(0,"s"); +p=1+s+2*s^2 +A=rand(2,2); +poly(A,"x") +//рациональные дроби +h=(1+2*%s)/poly(1:4,'s','c') + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Смотрите также</title> + <simplelist type="inline"> + <member> + <link linkend="coeff">coeff</link> + </member> + <member> + <link linkend="roots">roots</link> + </member> + <member> + <link linkend="varn">varn</link> + </member> + <member> + <link linkend="horner">horner</link> + </member> + <member> + <link linkend="derivat">derivat</link> + </member> + <member> + <link linkend="matrices">матрицы</link> + </member> + <member> + <link linkend="rational">рациональное число</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ru_RU/rational.xml b/modules/polynomials/help/ru_RU/rational.xml new file mode 100755 index 000000000..ef61eecff --- /dev/null +++ b/modules/polynomials/help/ru_RU/rational.xml @@ -0,0 +1,48 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ru" xml:id="rational"> + <refnamediv> + <refname>рациональное число</refname> + <refpurpose>объекты Scilab, рациональное число в Scilab</refpurpose> + </refnamediv> + <refsection> + <title>Описание</title> + <para> + Рациональное число <literal>r</literal> является частным двух полиномов <literal>r=num/den</literal>. + Внутреннее представление рационального число является списком. + <literal>r=rlist(num,den,[])</literal> -- это то же самое, что и <literal>r=num/den</literal>. + Матрица рациональных чисел может быть определена обычным синтаксисом, + например, <literal>[r11,r12;r21,r22]</literal> является матрицей размером 2x2, где <literal>rij</literal> -- рациональные + числа размером 1x1. + Матрица рациональных чисел может быть, также определена в виде вышеупомянутого списка, + <literal>tlist(['r','num','den','dt'],num,den,[])</literal>, где <literal>num</literal> и <literal>den</literal> матрицы полиномов. + </para> + </refsection> + <refsection> + <title>Примеры</title> + <programlisting role="example"><![CDATA[ +s=poly(0,'s'); +W=[1/s,1/(s+1)] +W'*W +Num=[s,s+2;1,s];Den=[s*s,s;s,s*s]; +rlist(Num,Den,[]) +H=Num./Den +syslin('c',Num,Den) +syslin('c',H) +[Num1,Den1]=simp(Num,Den) + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Смотрите также</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="syslin">syslin</link> + </member> + <member> + <link linkend="simp">simp</link> + </member> + </simplelist> + </refsection> +</refentry> diff --git a/modules/polynomials/help/ru_RU/varn.xml b/modules/polynomials/help/ru_RU/varn.xml new file mode 100755 index 000000000..c1bc84453 --- /dev/null +++ b/modules/polynomials/help/ru_RU/varn.xml @@ -0,0 +1,93 @@ +<?xml version="1.0" encoding="UTF-8"?> +<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ru" xml:id="varn"> + <refnamediv> + <refname>varn</refname> + <refpurpose>Символические переменных полиномами или рациональные дроби</refpurpose> + </refnamediv> + <refsynopsisdiv> + <title>Последовательность вызова</title> + <synopsis> + [symb]=varn(p) + [pm]=varn(p, varname) + </synopsis> + </refsynopsisdiv> + <refsection> + <title>Аргументы</title> + <variablelist> + <varlistentry> + <term>p</term> + <listitem> + <para>Матрица полиномов или рациональных дробей</para> + </listitem> + </varlistentry> + <varlistentry> + <term>symb</term> + <listitem> + <para>символьная строка</para> + </listitem> + </varlistentry> + <varlistentry> + <term>varname</term> + <listitem> + <para>символическая переменная (символьная строка)</para> + </listitem> + </varlistentry> + <varlistentry> + <term>pm</term> + <listitem> + <para>Матрица полиномов или рациональных дробей</para> + </listitem> + </varlistentry> + </variablelist> + </refsection> + <refsection> + <title>Описание</title> + <para> + <literal>symb=varn(p)</literal> возвращает в <literal>symb</literal> символическую + переменную полинома <literal>p</literal> (т. е., если + <literal>varn(poly(0,'x'))</literal>, то <literal>'x'</literal>). + </para> + <para> + <literal>varn(p,'s')</literal> возвращает матрицу полиномов с теми же коэффициентами, + что и <literal>p</literal>, но с <literal>'s'</literal> в качестве символической + переменой (смена имени переменной). + </para> + </refsection> + <refsection> + <title>Примеры</title> + <programlisting role="example"><![CDATA[ +s = poly(0,'s'); p = [s^2+1,s]; +varn(p) +varn(p,'x') + +f = %z / (%z-1); f = [f f^2] +varn(f) +varn(f,"x") + ]]></programlisting> + </refsection> + <refsection role="see also"> + <title>Смотрите также</title> + <simplelist type="inline"> + <member> + <link linkend="poly">poly</link> + </member> + <member> + <link linkend="rlist">rlist</link> + </member> + <member> + <link linkend="horner">horner</link> + </member> + </simplelist> + </refsection> + <refsection> + <title>История</title> + <revhistory> + <revision> + <revnumber>5.5.1</revnumber> + <revdescription> + <para>Расширение для рациональных дробей</para> + </revdescription> + </revision> + </revhistory> + </refsection> +</refentry> |