Hi Luca,
On 2017-10-16, Luca De Feo wrote:
> On Mon, Oct 16, 2017 at 7:35 PM, 'Martin R. Albrecht' via sage-devel
> wrote:
>> 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 polyno
On 2017-10-17, Daniel Krenn wrote:
> What about the following fix: When the input is a list/tuple, we check
> if it is a Groebner basis or not.
Too expensive.
Cheers,
Simon
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On 2017-10-17, Luca De Feo wrote:
>> It takes I as the generators of the ideal and uses that as the reduction
>> set.
>
> That's not a definition. I'm in front of a class asking what this
> function does, and I'm unable to give a mathematical definition of
> what Sage means by "reduction" modulo s
Hi Luca,
On 2017-10-18, Luca De Feo wrote:
> I hate to sound snarky, but...
No offence taken...
> Yet, none of us seems to be able to second guess what kind of normal
> form is actually implemented by .reduce() (Singular's kNF, actually).
> And from the answers to this thread, it seems to me th
Hi Luca,
On 2017-10-18, Luca De Feo wrote:
> However, what's the use of such a function with
> implementation-dependent outputs?
>
> If I understand Martin's argument correctly, he is saying that
> .reduce() *could* be used for a schoolbook "implementation of Gröbner
> basis algorithms in Sage wh
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 standa
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 Sch
Hi Simon,
I hate to sound snarky, but...
> When reading `normal form` and `Groebner basis` in the same sentence,
> the meaning should be clear to anybody who took a course in commutative
> algebra. So, the question is: Whom should documentation be addressed to?
>
> I do *not* think that documenta
> I agree that Sage devs don't (need to) know what *exact* algorithm is
> used. But at least it is clear that the .reduce() method does polynomial
> reductions and continues till no further reduction is possible; all this
> for a fixed monomial ordering (determined by the polynomial ring), in
> *so
> I would formulate it more precisely as "no monomial in the output is
> divisible by the leading monomial of any polynomial in I". This seems
> to be true given the examples I have, it would be good to have a
> confirmation (hidden somewhere in Singular's docs?)
>
Curiously, the definition
Thanks everyone for the discussion.
I opened https://trac.sagemath.org/ticket/24071 to improve the
docstring of reduce().
It's ready for review, let's continue the discussion there.
> In Singular's implementation p' does not depend on the order of the
> polynomials in I because it starts with so
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