Hi there,
this is already documented:
“ Return the normal form of self w.r.t. "I", i.e. return the
remainder of this polynomial with respect to the polynomials in
"I". If the polynomial set/list "I" is not a (strong) Groebner
basis the result is not canonical.
”
Cheers,
Martin
Daniel Krenn <kr...@aon.at> writes:
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.
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