CASA Function: toImpl

Converts an algebraic set given in parametric or projected representation to an algebraic set in implicit representation in affine space.

Calling Sequence:

• B := toImpl(A)
• B := toImpl(A,vars)

Parameters:

A : {algset("para"),algset("proj"),algset("impl")}

• algebraic set in parametric implicit or projected representation

vars : list(name)

• List of variables.

Result:

B : algset("impl")

• The implicit representation of the algebraic set A.

Description:

• This function takes an algebraic set and converts it into an implicit representation in affine space. The dimension of the target space can be prescribed by the number of variables that can be given as a second argument.
• If no variables are given, the function tries to take the variables from the given algebraic set and add some more if necessary to embed the algebraic set into an affine space of lowest dimension.

Examples:

> A := mkParaAlgSet([t,t^2,t^3],[t]);

> toImpl(A,[x,y,z]);

> A := mkProjAlgSet([[u^2-v^3+v^2],[u+v,u-v,1/v]],[u,v]);

> toImpl(A);

> toImpl(A,[a,b,c]);

See Also: