Singular

D.8.1.5 XLsolve

Usage:

XLsolve(I[, d]); I ideal, d optional integer
solve I (system of multivariate polynomials) with a
variant of the linearization technique, multiplying
the polynomials with monomials of degree at most d
(default is 2)

Return:

list L of the common roots of I as ideals

Assume:

basering is a finite field of type (p^n,a)

LIB "ffsolve.lib";
ring R = (2,a),x(1..3),lp;
minpoly=a2+a+1;
ideal I;
I[1]=(a)*x(1)^2+x(2)^2+(a+1);
I[2]=(a)*x(1)^2+(a)*x(1)*x(3)+(a)*x(2)^2+1;
I[3]=(a)*x(1)*x(3)+1;
I[4]=x(1)^2+x(1)*x(3)+(a);
XLsolve(I, 3);
==> [1]:
==>    _[1]=x(3)+(a+1)
==>    _[2]=x(2)+1
==>    _[3]=x(1)+1