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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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            User manual for Singular version 3-1-6, Dec 2012, generated by texi2html.