CASA Function: RPHcurve

Checks if there exists an RPH (rational Phytagorean hodograph) parametrization of the given curve.

Calling Sequence:

• B := RPHcurve(C,phi)

Parameters:

C : algset("para")

• Rational curve in parametric representation.

phi : name

• An unevaluated name which will store the reparametrizing function upon return.

Result:

B : boolean

• The function returns true if the given curve has an RPH parametrization and false otherwise.

Description:

• The function checks if there exists an RPH (Rational Phytagorean hodograph) parametrization of the algebraic curve C by analyzing the reducibility and rationality of the reparametrizing curve. If the reparametrizing curve is irreducible and rational then a quadratic reparametrizing function is assigned to the parameter phi.

Examples:

> a:=mkParaAlgSet([t^7,t^6],[t]);

> RPHcurve(a,p);

> p;

See Also: