testParametrization -- Test if parametrization.

• Usage:

  testParametrization(a,p)

• Inputs:
  • I, an ideal, defining a rational curve C
  • phi, a matrix, with a parametrization of C, defined over \mathbb{P}^{1} or in the coordinate ring of a conic.
• Outputs:
  • a Boolean value, true if phi is a parametrization or false if not.

i1 : K=QQ;

i2 : R=K[v,u,z];

i3 : I=ideal(v^8-u^3*(z+u)^5);

o3 : Ideal of R

i4 : T=K[t_0,t_1]

o4 = T

o4 : PolynomialRing

i5 : phi=matrix {{t_0^3*t_1^5}, {-t_0^8}, {t_0^8-t_1^8}}

o5 = | t_0^3t_1^5  |
     | -t_0^8      |
     | t_0^8-t_1^8 |

             3       1
o5 : Matrix T  <--- T

i6 : testParametrization(I,phi)

o6 = true