parametrization - Maple Help
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algcurves

  

parametrization

  

find a parametrization for a curve with genus 0

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

parametrization(f, x, y, t)

Parameters

f

-

irreducible polynomial in x and y, with genus 0

x, y, t

-

variables

Description

• 

This procedure computes, if it exists, a parametrization of an algebraic curve f. A parametrization is a birational equivalence from a projective line to the given curve f. Such a parametrization exists if and only if the genus is 0 and the curve is irreducible (which can be checked by AIrreduc).

• 

The output of the procedure is a list  of rational functions in t, such that  is a point on the curve f for every value of t.

• 

For a description of the method used see M. van Hoeij, "Rational Parametrizations of Algebraic Curves using a Canonical Divisor", 23, p. 209-227, JSC 1997.

Examples

(1)

Now subs(t=any number,v) should be a point on the curve. Test the result (this should be 0):

(2)

(3)

See Also

AFactor

algcurves[genus]

algcurves[Weierstrassform]

 


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