# Main Page/Applications

From ApCoCoAWiki

### 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 QQ[x,y], DegLex; SB.SAGBI([x^2*y, x^2 -y^2, x^2*y^2 -y^4, x^2*y^4]);

Solving polynomial equations over 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]);