Main Page/Applications

Application Examples

Computing reduced Gröbner bases:

Use P ::= QQ[x,y,z], DegRevLex;
I := ideal(P,[y-x^2,z-x^3]);
GBasis(I); -- reduced DegRevLex Gröbner basis of I

Computing reduced SAGBI bases:

Use P ::= QQ[x,y,z], DegLex;
S := SB.Subalgebra(P,[y-x^2,z-x^3]);
SB.SAGBI(S); -- reduced DegLex-SAGBI basis of S

Solving polynomial equations over $\mathbb {Z} /2\mathbb {Z}$ using a SAT solver:

Use ZZ/(2)[x,y,z];
f1 := x*y + x*z + y*z + z;
f2 := y + 1;
f3 := x*y + z;
SAT.Solve([f1,f2,f3]); -- [0, 1, 0]