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Linear Combination for Resultant


R.<a, b, X> = ZZ[]
f = 1 - a*X^2
g = 1 - b*X^3

I need to compute polynomials u and v such that u f + v g = r where r = f.resultant(g, X).

Pari has a function polresultantext for that purpose, so one solution for my problem is

(u, v, r) = (R(p) for p in f._pari_().polresultantext(g._pari_(), 'X'))

Nevertheless, I have a few questions:

  • Is there a method in Sage which directly does this?
  • Is the detour via Pari the recommended solution? Or is there an alternative, e.g., in singular?
  • If there is currently no method in Sage for doing this directly, what name would you recommend? resultant_ext ?