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D.8.1.4 GBsolve
Procedure from library ffsolve.lib (see ffsolve_lib).
- Usage:
- GBsolve(I); I ideal
solve I (system of multivariate equations) over an
extension of Z/p by Groebner basis methods
- Return:
- list L, the common roots of I as ideal
- Assume:
- basering is a finite field of type (p^n,a)
Example:
| | LIB "ffsolve.lib";
ring R = (2,a),x(1..3),lp;
minpoly=a2+a+1;
ideal I;
I[1]=x(1)^2*x(2)+(a)*x(1)*x(2)^2+(a+1);
I[2]=x(1)^2*x(2)*x(3)^2+(a)*x(1);
I[3]=(a+1)*x(1)*x(3)+(a+1)*x(1);
GBsolve(I);
==> [1]:
==> _[1]=x(3)+1
==> _[2]=x(2)+(a)
==> _[3]=x(1)+1
==> [2]:
==> _[1]=x(3)+1
==> _[2]=x(2)+(a+1)
==> _[3]=x(1)+(a+1)
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