# rParametrizeConic -- Compute a rational parametrization of a conic.

## Synopsis

• Usage:
rParametrizeConic(I)
• Inputs:
• I, an ideal, of an irreducible conic.
• Outputs:
• , with the rational parametrization, or the 0-matrix if the conic does not have a rational point.

## Description

Computes a rational parametrization of a conic or returns the 0-matrix if the conic does not have a rational point.

 i1 : K=QQ; i2 : R=K[y_0..y_2]; i3 : I=ideal(y_0*y_2-y_1^2+y_2^2); o3 : Ideal of R i4 : rParametrizeConic(I) o4 = | t_0^2-t_1^2 | | -t_0t_1 | | -t_0^2 | 3 1 o4 : Matrix (QQ[t , t ]) <--- (QQ[t , t ]) 0 1 0 1

## Caveat

If the conic does not have a rational point the field extension of degree 2 should be implemented.

## Ways to use rParametrizeConic :

• "rParametrizeConic(Ideal)"

## For the programmer

The object rParametrizeConic is .