Ahh ok, thank you. Considering the following output I think a PR to make 
the degree of zero for these Laurent classes -Infinity is reasonable?

```
sage: R.<x> = LaurentSeriesRing(QQ)
sage: R.zero().valuation()
+Infinity
sage: R.zero().degree()
-1
sage: 
sage: R.<x> = LaurentPolynomialRing(QQ)
sage: R.zero().valuation()
+Infinity
sage: R.zero().degree()
-1
sage: 
sage: R.<x> = LazyLaurentSeriesRing(QQ)
sage: R.zero().valuation()
+Infinity
sage: R.zero().degree()
# Errors



On Wednesday, February 28, 2024 at 1:50:23 PM UTC Martin R 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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