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