On 2017-10-16 18:41, Luca De Feo wrote: > 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.
It computes the polynomial "modulo" the given ideal (i.e. compute a Groebner basis of the ideal and reduce the given polynomial by this basis). My guess: If only a list of polynomials is given, then it is assumed that these form a Groebner basis, which seems not to be the case. >>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? Once we know what it does with lists, the documentation should be made precise. I am against underscoring, as for ideals as parameter, this is a standard operation. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
