The history of discussions about this issue reaches back over many years,
see #10708 <https://trac.sagemath.org/ticket/10708> and this sage-devel
thread
<https://groups.google.com/forum/#!searchin/sage-devel/artal/sage-devel/JQlb4bbBXjQ/7OgkbYIVNJQJ>
and it seems that they all broke down even though good suggestions where
made. So let me do another attempt by gathering and rephrasing those
suggestions, which I think should be realizable with a manageable effort.
May we can do that in three steps:
1. Change the default implementation if the user chooses a *local term
order*. The default implementation can't be longer *Singular* in this case,
since *Singular *operates on a different mathematical object (which is not
a polynomial ring), here. For example, this could be done in the following
way (shown relative to 9.1.beta9):
diff --git a/src/sage/rings/polynomial/polynomial_ring_constructor.py b/src/
sage/rings/polynomial/polynomial_ring_constructor.py
index 98af2c4..afe6720 100644
--- a/src/sage/rings/polynomial/polynomial_ring_constructor.py
+++ b/src/sage/rings/polynomial/polynomial_ring_constructor.py
@@ -772,7 +772,7 @@ def _multi_variate(base_ring, names, sparse=None, order=
"degrevlex", implementat
# yield the same implementation. We need this for caching.
implementation_names = set([implementation])
- if implementation is None or implementation == "singular":
+ if implementation is None and order.is_global() or implementation ==
"singular":
from sage.rings.polynomial.multi_polynomial_libsingular import
MPolynomialRing_libsingular
try:
R = MPolynomialRing_libsingular(base_ring, n, names, order)
diff --git a/src/sage/rings/polynomial/polynomial_singular_interface.py b/
src/sage/rings/polynomial/polynomial_singular_interface.py
index 74b8b82..8736c77 100644
--- a/src/sage/rings/polynomial/polynomial_singular_interface.py
+++ b/src/sage/rings/polynomial/polynomial_singular_interface.py
@@ -384,6 +384,10 @@ def can_convert_to_singular(R):
if R.ngens() == 0:
return False;
+ if hasattr(R, 'term_order'):
+ if R.term_order().is_local():
+ return False;
+
base_ring = R.base_ring()
if (base_ring is ZZ
or sage.rings.finite_rings.finite_field_constructor.is_FiniteField(
base_ring)
In the example of this thread, this would mean that an instance of
MPolynomialRing_polydict_domain will be created:
sage: R.<x,y> = PolynomialRing(QQ, order='negdeglex'); R
Multivariate Polynomial Ring in u, v over Rational Field
sage: type(R)
<class
'sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict_domain_with_category'
>
sage: f = 1 + x
sage: I = R.ideal(x^2)
sage: f.mod(I)
Traceback (most recent call last):
...
TypeError: Local/unknown orderings not supported by 'toy_buchberger'
implementation.
If a user still likes to work over the localization of the polynomial ring
via *Singular*, he has to give a corresponding *term order* and
implementation='singular' explicitly (so that we can assume, that he knows
what he is doing). In this case the representation string should make clear
that this instance does not represent a polynomial ring:
sage: S.<u,v> = PolynomialRing(QQ, order='neglex', implementation='singular'
); S
Multivariate Polynomial Ring in u, v over Rational Field localized at the
maximal idead centered at the origin
<class
'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular'
>
sage: g = 1 + u
sage: J = S.ideal(u^2)
sage: g.mod(J)
1
2. Deprecate implementation='singular' for *local term orders* and replace
it by a new construction function together with a new class inherited from
MPolynomialRing_libsingular with an appropriate name (LocalPolynomialRing
for instance).
3. Try to find a way, to use *Singular* again for applications according to
1. I'm not sure if this will be possible, but maybe this can be done using
a corresponding global order with *Singular* and perform transitions in
_richcmp_,
__reps__....
On Monday, April 6, 2020 at 9:46:26 AM UTC+2, Yang Zhou wrote:
>
> Hi,
>
> I am trying to truncate a multi-variable polynomial by moding out higher
> order term and found
> the following (simplified) example. I am wondering if it is a bug.
>
>
> *Reproducible Example: *
>
>> R.<x,y> = PolynomialRing(QQ, order='negdeglex')
>>
> f = 1 + x
>> I = R.ideal(x^2)
>> f.mod(I)
>>
> *Expected output:*
>
>> 1 + x
>>
> *Actual output:*
>
>> 1
>>
>
>
> *Note: *
> The actual output will be 1+x when I omit the "order='negdeglex" parameter.
>
> *SageMath version:*
> SageMath version 9.0, Release Date: 2020-01-01
>
> *Operating system:*
> OS: Ubuntu 19.10 x86_64
> Kernel: 5.3.0-45-generic
>
> Best regards,
> Yang
>
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