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D.5.1.9 paraConic
Procedure from library paraplanecurves.lib (see paraplanecurves_lib).
- Usage:
- paraConic(q); q poly
- Assume:
- The basering must be a polynomial ring in three variables with
coefficients in Q.
The polynomial q must be homogeneous of degree 2 and absolutely
irreducible.
- Note:
- The procedure might fail or give a wrong output if the assumptions
do not hold.
- Return:
- ring with an ideal PARACONIC. The ring should be considered as the
homogeneous coordinate ring of PP^1, the ideal defines a rational
parametrization PP^1 --> C2 = {q=0}.
- Theory:
- We compute a point on C2 via rationalPointConic. The pencil of
lines through this point projects C2 birationally to PP^1. Inverting
the projection gives the result.
Example:
See also:
rationalPointConic.
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