Hello,
I am having a hard time understanding the precise semantics of
multivariate polynomial quo_rem(). The documentation only says "Returns
quotient and remainder of self and right" which is absolutely not helpful.
Example:
R.<x,y> = PolynomialRing(QQ, order="lex")
f = x^2
g = x^2 + y
f.quo_rem(g)
This gives me (0, x^2) where I would have expected (1, -y) since the
leading term of f is divisible by the leading term of g.
Is multivariate division in the sense of
https://en.wikipedia.org/wiki/Gr%C3%B6bner_basis#Reduction implemented
somewhere in Sage?
Jeroen.
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