Is this a bug:
sage: K.=QQ[]
sage: (x^6+y^9)%(x^3-y^2-1)
x^12*y - 4*x^9*y + 6*x^6*y + x^6 - 4*x^3*y + y
In pari:
? (x^6+y^9)%(x^3-y^2-1)
%1 = y^9 + y^4 + 2*y^2 + 1
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Surely it is just a question of precedence of variables. In Sage you are
dividing by a quadratic in y and getting a remainder which is linear in y.
In pari you are dividing by a cubic in x and getting a remainder which is
of degree <3 in x.
If you swap x and y in both polynomials, sage's remaind
John is right.
Dividing a by b means finding q and r such that a = q*b + r and r is either
0 or "smaller" than b.
The question is the meaning of "smaller".
For univariate polynomials, one says that r is smaller than b if deg(r) <
deg(b) (one can include r = 0 by defining deg(0) = –∞).
For multiv
On Thu, Mar 9, 2023 at 2:07 PM G. M.-S. wrote:
>
>
> John is right.
>
> Dividing a by b means finding q and r such that a = q*b + r and r is either 0
> or "smaller" than b.
> The question is the meaning of "smaller".
>
> For univariate polynomials, one says that r is smaller than b if deg(r) <
>
Could you elaborate, Dima?
It seems to me that *quo_rem* ignores the ordering and always uses *invlex*.
Would this be a bug or a feature?
Guillermo
On Thu, 9 Mar 2023 at 17:45, Dima Pasechnik wrote:
> On Thu, Mar 9, 2023 at 2:07 PM G. M.-S. wrote:
> >
> >
> > John is right.
> >
> > Dividing
On Thu, Mar 9, 2023 at 5:29 PM G. M.-S. wrote:
>
>
> Could you elaborate, Dima?
>
> It seems to me that quo_rem ignores the ordering and always uses invlex.
Sorry, I was not thinking clearly.
In fact, I think, '%' shoud work for ideals on the right-hand side,
not just for polynomials (i.e. princ
