Not a "maths" why, but I know anything which uses singular currently
returns -1 because of the following snippet
cdef long singular_polynomial_deg(poly *p, poly *x, ring *r) noexcept:
cdef long _deg, deg
cdef int dummy
deg = -1
_deg = -1
if p == NULL:
return -1
...
I don't know the history of this choice or what we should be doing
generally. -1 for polynomials with only positive degree seems like a
computer science workaround, but for the LaurentPolynomialRing it just
seems wrong?
On Wednesday, February 28, 2024 at 3:29:25 PM UTC Dima Pasechnik wrote:
> in the polynomial case, the usual convention is deg(0)=-infinity
> I don't know why Sage uses -1 instead:
> R.<x,y>=QQ[]
> f=0*x*y
> f.degree()
>
> gives -1.
>
> On Wed, Feb 28, 2024 at 1:50 PM 'Martin R' via sage-devel <
> sage-...@googlegroups.com> wrote:
>
>> Sorry, I confused it with valuation, but I guess it is still a related
>> question.
>> On Wednesday 28 February 2024 at 14:36:35 UTC+1 Giacomo Pope wrote:
>>
>>> This is not what I see on the current beta:
>>>
>>> sage: R.<x> = LaurentSeriesRing(QQ)
>>> sage: R.zero().degree()
>>> -1
>>> sage: R.<x> = LazyLaurentSeriesRing(QQ)
>>> sage: R.zero().degree()
>>>
>>> ---------------------------------------------------------------------------
>>> AttributeError Traceback (most recent call
>>> last)
>>> Cell In[4], line 1
>>> ----> 1 R.zero().degree()
>>>
>>> File ~/sage/sage/src/sage/structure/element.pyx:489, in
>>> sage.structure.element.Element.__getattr__()
>>> 487 AttributeError:
>>> 'LeftZeroSemigroup_with_category.element_class' object has no attribute
>>> 'blah_blah'...
>>> 488 """
>>> --> 489 return self.getattr_from_category(name)
>>> 490
>>> 491 cdef getattr_from_category(self, name) noexcept:
>>>
>>> File ~/sage/sage/src/sage/structure/element.pyx:502, in
>>> sage.structure.element.Element.getattr_from_category()
>>> 500 else:
>>> 501 cls = P._abstract_element_class
>>> --> 502 return getattr_from_other_class(self, cls, name)
>>> 503
>>> 504 def __dir__(self):
>>>
>>> File ~/sage/sage/src/sage/cpython/getattr.pyx:357, in
>>> sage.cpython.getattr.getattr_from_other_class()
>>> 355 dummy_error_message.cls = type(self)
>>> 356 dummy_error_message.name = name
>>> --> 357 raise AttributeError(dummy_error_message)
>>> 358 cdef PyObject* attr = instance_getattr(cls, name)
>>> 359 if attr is NULL:
>>>
>>> AttributeError: 'LazyLaurentSeriesRing_with_category.element_class'
>>> object has no attribute 'degree'
>>>
>>> On Wednesday, February 28, 2024 at 12:05:32 PM UTC Martin R wrote:
>>>
>>>> LazyLaurentSeriesRing(QQ) currently gives +Infinity.
>>>>
>>>> On Wednesday 28 February 2024 at 12:50:45 UTC+1 Giacomo Pope wrote:
>>>>
>>>>> While chasing various bugs which appeared in the CI, I ended up adding
>>>>> a small method for computing random elements for the
>>>>> LaurentPolynomialRing
>>>>> class.
>>>>>
>>>>> When writing randomised testing I got myself confused about the degree
>>>>> of the zero polynomial. For the univariate and multivariate polynomial
>>>>> rings, we currently use that the degree for 0 (both R(0).degree() as well
>>>>> as R(0).degree(x)) is -1. This is unambiguous for the case of these types.
>>>>>
>>>>> However for the LaurentPolynomialRings, a polynomial with negative
>>>>> valuation is very natural. For example the following code snippet shows
>>>>> the
>>>>> ambiguity.
>>>>>
>>>>> sage: L.<x> = LaurentPolynomialRing(QQ)
>>>>> sage: f = (1/x); f
>>>>> x^-1
>>>>> sage: f.degree()
>>>>> -1
>>>>> sage: L.zero().degree()
>>>>> -1
>>>>>
>>>>> I don't feel familiar enough with the mathematics here and the usual
>>>>> use cases in sage to offer a PR "fixing" this, or whether it even needs
>>>>> fixing. However, I got confused so I thought maybe others might get
>>>>> confused and someone on this list might have a suggestion.
>>>>>
>>>>> I think the "usual" suggestion would be to have the degree as -infty,
>>>>> but then there's a question about whether this should be done for other
>>>>> polynomial rings...
>>>>>
>>>>> I made an issue for this on GitHub too:
>>>>>
>>>>> https://github.com/sagemath/sage/issues/37491
>>>>>
>>>> --
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>> .
>>
>
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