I'm trying to learn more basics in Sage, and I'm struggling with polynomial rings with real and complex coefficients. Many of the basic functions seem to return errors from the Singular or Pari implementation, and I wonder if there is a simple workaround I'm missing. Here is an example:
P.<x,y> = PolynomialRing(RealField(), 2)
I = P.ideal(x^2 - y + 1, -x^2 - y - 1)
I.is_prime()
Returns an error:
TypeError: cannot call Singular function 'primdecSY' with ring parameter of type '<class 'sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict_domain_with_category'>'
Running the same code with QQ instead of RealField() works fine, so I assume the issue is that the Singular function can't work with Sage's implementation of Real numbers. Is there a way around this to do basic operations on polynomial rings with coefficients in numerically approximated fields like the reals and complexes?
