Hans added that one should not rely on the behaviour that Singular reorders the list. This may change in a future version of Singular. He mentioned it only to explain the behaviour that is currently observed.
On Thursday, 19 October 2017 11:20:05 UTC+2, Bill Hart wrote: > > According to Hans Schoenemann: > > "Usually (i.e. in a ring with a well ordering and no additional flags) > reduce/kNF (p,I) computes p' (with p a polynomial and I a list of > polynomials) > with p-p' is in the ideal generated by I and no monomial of p' is > divisible by any L(f) for f in I. > If I is a standard basis then p' is unique. > Otherwise, the result depends on the internally used algorithm. > In Singular's implementation p' does not depend on the order of the > polynomials in I because it starts with sorting I > (wrt. to the monomial ordering or the total degree)." > > On Monday, 16 October 2017 18:41:50 UTC+2, Luca De Feo wrote: >> >> 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 >> > -- 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.
