algcurves
parametrization
find a parametrization for a curve with genus 0
Calling Sequence
Parameters
Description
Examples
parametrization(f, x, y, t)
f
-
irreducible polynomial in x and y, with genus 0
x, y, t
variables
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.
Now subs(t=any number,v) should be a point on the curve. Test the result (this should be 0):
See Also
AFactor
algcurves[genus]
algcurves[Weierstrassform]
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