I'm writing some new Sage code to do partial fraction decompositions of multivariate rational expressions and want to use the Sequence() and algebraic_dependence() methods from sage.rings.polynomial.multi_polynomial_sequence. What's the best import call to use?
I've played around with various import calls, and most recently tried the following from within the function i'm writing.
from sage.structure.sequence import * from sage.rings.polynomial.polynomial_ring_constructor import * from sage.rings.polynomial.multi_polynomial_sequence import *
I thought that would work and be overkill, but i got the error message
/Applications/sage/local/lib/python2.6/site-packages/sage/rings/polynomial/multi_polynomial_sequence.pyc in algebraic_dependence(self) 600 T = T+'T' 601 Ts = [T + str(j) for j in range(r)] --> 602 RR = PolynomialRing(K,d+r,tuple(Xs+Ts)) 603 Vs = list(RR.gens()) 604 Xs = Vs[0 :d] NameError: global name 'PolynomialRing' is not defined
Any advice on this particular import or imports in general would be appreciated.