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:
[CASA]
[variableList]
[toProjective]