// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 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

function [f,sexp]=trianfml(f,sexp)
    // [f [,sexp]]=trianfml(f [,sexp])  Triangularization of the symbolic matrix
    // f ; Triangularization is performed by elementary row operations;
    // sexp is a set of common expressions stored by the algorithm.
    //!
    //

    [lhs,rhs]=argn(0)
    [mf,nf]=size(f)
    f_tra=f
    //
    // row loop
    // ------------------------------
    //
    for nli=1:mf
        //
        [mf_tra,nf_tra]=size(f_tra)
        //recherche du pivot  dans la premiere colonne
        c1=f_tra(:,1);
        lc=length(c1);[lc,klc]=gsort(lc);
        pivot="0";l=mf_tra+1;
        while (pivot=="0"&l>1),
            l=l-1;
            if c1(klc(l))<>"0" then pivot=c1(klc(l)),end,
        end
        if pivot<>"0" then
            l=klc(l)
            //
            if l<>1 then f_tra([1 l],:)=f_tra([l 1],:);c1([1 l])=c1([l 1]);end
            //
            for k=2:mf_tra,
                if c1(k)<>"0" then
                    f_tra(k,:)=cmb_lin(pivot,f_tra(k,:),c1(k),f_tra(1,:))
                    f_tra(k,1)="0"
                    if rhs==2 then
                        ns=prod(size(sexp)),
                        for kl=2:nf_tra
                            if length(f_tra(k,kl))>20 then
                                ns=ns+1
                                sexp(ns)=f_tra(k,kl)
                                f_tra(k,kl)="%("+string(ns)+")"
                            end;
                        end;
                    end;
                end;
            end;
            f(mf-mf_tra+1:mf,nf-nf_tra+1:nf)=f_tra
            f_tra=f_tra(2:mf_tra,2:nf_tra)
        end
    end;
endfunction