Many thanks for all replies.
GMS suggested to use Ideal.reduce(), but from the documentation:
"Requires computation of a Groebner basis, which can be a very
expensive operation"
I suspected that polynomial division is significantly more
cheap than groebner basis.
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On Fri, 10 Mar 2023, 09:53 Georgi Guninski, wrote:
> Many thanks for all replies.
>
> GMS suggested to use Ideal.reduce(), but from the documentation:
> "Requires computation of a Groebner basis, which can be a very
> expensive operation"
>
> I suspected that polynomial division is significantly
Hi Georgi.
In the case of a principal ideal, to get a Gröbner basis the only thing you
may need is making the generator monic, so there is almost nothing to do.
Then you do an ordered division of the other polynomial by this one, which
is straightforward.
HTH,
Guillermo
On Fri, 10 Mar 2023 at 1
I think grobner basis which contain non-zero constant and polynomials
is a bug.
sage: K.=ZZ[]
sage: l=[x^2+y^2+x+4,x^2+y^2+4*y+2,x^2-13*y^2+x]
sage: I=Ideal(l);gb=I.groebner_basis();gb
[y^2 + 4*y + 198, x + 1036*y + 2, 8*y + 544, 1040]
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This result is correct, as you are working over ℤ.
If you try over ℚ, you will get [1].
Guillermo
On Fri, 10 Mar 2023 at 11:57, Georgi Guninski wrote:
> I think grobner basis which contain non-zero constant and polynomials
> is a bug.
>
> sage: K.=ZZ[]
> sage: l=[x^2+y^2+x+4,x^2+y^2+4*y+2,x^2-1
Not a bug, but a (nice) feature: Gröbner bases for rings of polynomials
with integers coefficients, documented in:
https://doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/multi_polynomial_ideal.html
El vie, 10 mar 2023 a las 11:57, Georgi Guninski ()
escribió:
> I thin
