# CASA Function: mkAlgSet

Creates an algebraic set from a given one by applying some substitutions.

### Calling Sequence:

• B := mkAlgSet(A,s)
• B := mkAlgSet(A,s,vars)

### Parameters:

A : algset
• An algebraic set in some representation.
s : list(casaVariable=anything)
• List of substitutions.
vars : list(casaVariable)
• A list of new main variables.

### Result:

B : algset
• A Maple object representing an algebraic set.

### Description:

• The function applies the substitution s to the generators and the variable list of the algebraic set A and forms a new algebraic set from the resulting data.
• If the third parameter is not given, the variable list of the algebraic set A will be taken (even if one of the variables will be replaced in the substitution s.
• If A is affine/projective B will also be affine/projective.

### Examples:

> A := mkImplAlgSet([a^2+b-4],[a,b]);

> mkAlgSet(A,[b=3],[a]);

> mkAlgSet(A,[b=3]);

> mkAlgSet(A,[b=a,a=b],[a,b]);

> B := toPara(A);

> x := variableList(B)[1];

> mkAlgSet(B,[x=x+d]);