I am trying to compute the rational parametrization of a plane curve. According to sage is irreducible and has genus 0, hence it should be possible.
B.<u,v> = AffineSpace(QQ,2)
p=Curve([2*u^2 + 2*u*v + 2*v^2 - 1],B)
p.rational_parameterization()
However, i get the following error
Singular crashed -- automatically restarting.
---------------------------------------------------------------------------
SingularError Traceback (most recent call last)
<ipython-input-10-db30bbca0c11> in <module>()
1 B = AffineSpace(QQ,Integer(2), names=('u', 'v',)); (u, v,) = B. _first_ngens(2)
2 p=Curve([Integer(2)*u**Integer(2) + Integer(2)*u*v + Integer(2) *v**Integer(2) - Integer(1)],B)
----> 3 p.rational_parameterization()
/home/mlainz/.local/SageMath/local/lib/python3.7/site-packages/sage/schemes/ curves/affine_curve.py in rational_parameterization(self)
1451 ((-7*t^2 + 7)/((-a)*t^2 + (-a)), 14*t/((-a)*t^2 + (-a)))
1452 """
-> 1453 para = self.projective_closure(i=0).rational_parameterization(). defining_polynomials()
1454 # these polynomials are homogeneous in two indeterminants, so dehomogenize wrt one of the variables
1455 R = para[0].parent()
/home/mlainz/.local/SageMath/local/lib/python3.7/site-packages/sage/schemes/ curves/projective_curve.py in rational_parameterization(self)
1569 singular.lib("paraplanecurves.lib")
1570 R = singular.paraPlaneCurve(self.defining_polynomial())
-> 1571 singular.setring(R)
1572 param = singular('PARA').sage().gens()
1573 R = R.sage()
/home/mlainz/.local/SageMath/local/lib/python3.7/site-packages/sage/interfaces/ singular.py in set_ring(self, R)
1097 if not isinstance(R, SingularElement):
1098 raise TypeError("R must be a singular ring")
-> 1099 self.eval("setring %s; short=0"%R.name(), allow_semicolon=True)
1100
1101 setring = set_ring
/home/mlainz/.local/SageMath/local/lib/python3.7/site-packages/sage/interfaces/ singular.py in eval(self, x, allow_semicolon, strip, **kwds)
657 # Singular actually does use that string
658 if s.find("error occurred") != -1 or s.find("Segment fault") != -1:
--> 659 raise SingularError('Singular error:\n%s'%s)
660
661 if get_verbose() > 0:
SingularError: Singular error:
? sage19 is no name of a ring/qring
? error occurred in or before STDIN line 11: `setring sage19; short=0;`
Is this a SAGE or a Singular bug or am I missing something?
