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D.5.1.5 rationalPointConic

Procedure from library paraplanecurves.lib (see paraplanecurves_lib).

Usage:
rationalPointConic(p); p poly

Assume:
assumes that p is an irreducible quadratic polynomial in the first three ring variables;
ground field is expected to be Q.

Return:
The method finds a point on the given conic. There are two possibilities:
1) There is a rational point on the curve.
2) There is no rational point on the curve.
In the second case, the method creates a modification of the current basering which is a polynomial ring over some quadratic field extension Q(a) of Q. Apart from the replacement of Q by Q(a), the new polynomial ring, R say, is the same as the original basering. (In the first case, R is identical with the basering.) In both cases, the method will then define a (1x3) matrix named 'point' which lives in R and which contains the coordinates of the desired point on q.
Finally, the method returns the ring R (which will in the 1st case be the original base ring).

Example:
 


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