It might be helpful for non-experts if the documentation of Multivariate Polynomials were to mention explicitly that the ring being constructed is not the polynomial ring, but the polynomial ring wrt the term ordering, which is not always the same as the polynomial ring.
I found an explanation of the difference in Greuel & Pfister, "A Singular Introduction to Commutative Algebra".
My ignorance of the dependence of the ring on the term ordering was the source of my earlier question:
https://ask.sagemath.org/question/52623/find-quotient-of-two-multivariate-polynomials-which-are-divisible/
Daniel Friedan
