Ticket #3330 (new enhancement)

Opened 7 months ago

multivariate polynomial GCD should work over more base rings

Reported by: cwitty Assigned to: malb
Priority: major Milestone: sage-wishlist
Component: commutative algebra Keywords:
Cc:

Description

Consider this example: 

  R.<a,b> = NumberField(x^2-3,'g').extension(x^2-7,'h')[]
  h = R.base_ring().gen()    
  S.<y> = R.fraction_field()[]
  xgcd(y^2, a*h*y+b)

(reported by Gaëtan Bisson here: http://groups.google.com/group/sage-support/browse_thread/thread/5338608bd7508b00/cd1d6555592e472f#cd1d6555592e472f)

This fails because Sage attempts to find the GCD of multivariate polynomials over a relative number field using Singular, and Singular does not support relative number fields. This should be implemented in Sage (probably by converting the relative number field into an absolute field, performing the computation, and converting back).

See also #3329, which is about the exact same test case, but requests only a better error message.