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//Author: Parthasarathi Panda
//parthasarathipanda314@gmail.com
function [zerosort,g]=sosbreak(p)
//function for breaking a polynomial in second order polynomials and an extra linear term (g)
//where
//g:-the interger multiple obtained after breaking the polynomial
//zerosort:-the array of the broken polynomials
//p:-the input polynomial
//EXAMPLE:
//v=[1+4*%s+6*%s^2+4*%s^3+%s^4];
// [zerosort,g]=sosbreak(v);
//OUTPUT:
// g =1.
//zerosort =
// zerosort(1)
// 2
// 1 + 2s + s
// zerosort(2)
// 2
//1.0000000 + 2s + s
//NOTE :To verify the output use coeff(zerosort(1)) and coeff(zerosort(2))
[zero,g]=factors(p);//factorising into real coefficient polynomials
degn=degree(p);
zerosort=list();
//to segregate linear and quadratic factors
for i=[1:length(zero)]
q=zero(i);
//putting the quadratic factor at the front
if degree(q)==2 then
zerosort(0)=q;
//putting the linear factor at the end
else
zerosort($+1)=q;
end
end
if (modulo(degn,2))==0 then
e=length(zerosort);
//leave the last linear element if an odd degree polynomial
else
e=length(zerosort)-1;
end
for i=[e:-2:1]
q=zerosort(i);
if degree(q)==2 then
break;
end
zerosort(i)=q.*zerosort(i-1);//combining 2 linear polynomial into one quadratic polynomial
zerosort(i-1)=null();//removing leftover linear polynomial
end
endfunction
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