CASA Function: implSubSet

Test whether an algebraic set is contained in another one.

Calling Sequence:

• b := implSubSet(A,B)

Parameters:

A : algset("impl")

• An algebraic set in implicit representation.

B : algset("impl")

• An algebraic set in implicit representation.

Result:

b : boolean

• A boolean value indicating whether the algebraic set A is a subset of the algebraic set B.

Description:

• The function tests if an algebraic set is a subset of another algebraic set in implicit form.
• An algebraic set A is a subset of B if and only if rad(I( B)) is a subset of rad(I( A)), where I(x) denotes the ideal of the algebraic set x and rad(I) denotes the radical ideal of I.

Examples:

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

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

> a3 := implIntersect(a1,a2);

> implSubSet(a3,a1);

> implSubSet(a2,a3);

See Also: