Hi everyone,
Here's a Sage session:
sage: A.<x,y> = QQ[]
sage: (x+y).reduce([(x-y), (x+y)])
0
sage: (x-y).reduce([(x-y), (x+y)])
-2*y
The docstring says reduce computes "the normal form of self w.r.t. I,
i.e. [...] the remainder of this polynomial with respect to the
polynomials in I".
Does anyone have any idea how this normal form is defined? It doesn't
seem to depend on the order of the polynomials in I.
>From the source code, I can only tell it calls Singular's kNF, but I
can't find any doc for it. Maybe this function should be underscored?
Cheers,
Luca
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