CASA Function: implEmpty

Tests whether an algebraic set is empty.

Calling Sequence:

• b := implEmpty(A)

Parameters:

A : algset("impl")

• Algebraic set in implicit representation.

Result:

b : boolean

• A boolean value indicating whether the given algebraic set is empty or not.

Description:

• The function tests if an algebraic set in implicit form is empty. It is tested whether `1' is in the Groebner basis for the ideal of A.

Examples:

> a1 := mkImplAlgSet([x^3+x^2*y-x,y^2+z^2-1,x,z],[x,y,z]);

> implEmpty(a1);

> a2 := mkImplAlgSet([x^2-1,x^2-3],[x,y,z]);

> implEmpty(a2);

See Also: