CASA Function: planecurve
Check for a plane algebraic curve or a system of plane algebraic curves.
Calling Sequence:
 b := type(expr,planecurve)
 b := type(expr,planecurve("system"))
Parameters:
 expr : expression

Result:
 b : boolean

Description:
 The call type(expr,planecurve) checks whether expr defines a plane algebraic curve, i.e., expr has to be an algebraic set in implicit representation represented by a single nonconstant polynomial.
 If the algebraic set is affine, the polynomial should be defined in the two variables specifying the algebraic set and should not contain any other indeterminates.
 If the algebraic set is projective the polynomial should be defined in the three variables specifying the algebraic set and should not contain any other indeterminates. Furthermore, it should be homogeneous.
 The call type(expr,planecurve("system")) checks whether expr is a system of plane curves. The defining polynomial of a system of plane curves can contain additional variables to the ones defining the algebraic set.
Examples:
> a1:=mkImplAlgSet([x^2y^2],[x,y]);
> type(a1,planecurve);
> a2:=mkImplAlgSet([x^2c*y^2],[x,y]);
> type(a2,planecurve);
> type(a2,planecurve("system"));
See Also:
[CASA]
[mkImplAlgSet]