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 non-constant 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^2-y^2],[x,y]);
> type(a1,planecurve);
> a2:=mkImplAlgSet([x^2-c*y^2],[x,y]);
> type(a2,planecurve);
> type(a2,planecurve("system"));
See Also:
[CASA]
[mkImplAlgSet]