CASA Function: toAffine

Converts the algebraic set to the corresponding algebraic set in affine space.

Calling Sequence:

• A := toAffine(a)
• A := toAffine(a,x)

Parameters:

a : algset("impl")

• Algebraic set in affine or projective implicit representation.

x : name

• The variable with respect to which the dehomogenization of the defining polynomials will be done. This variable must be among the variables in the variable list of a.

Result:

A : algset("impl")

• The corresponding algebraic set in affine space.

Description:

• The function converts an algebraic set in implicit representation to the corresponding algebraic set in implicit form but lying in affine space.
• If the dehomogenization variable is not provided, the last variable of the variable list of a will be taken.
• If the given algebraic set is already in affines space, it is returned immediately.

Examples:

> a:=mkImplAlgSet([x^2*z-2*y^3+4*x*y^2],[x,y,z],

> ["basespace"="projective"]);

> b:=toAffine(a,x);

> c:=toAffine(a,y);

> [isProjective(a),isProjective(b),isProjective(c)];

See Also: