#15223: Let the `TestSuite` test that the construction of a parent returns the
parent
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Reporter: SimonKing | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-5.12
Component: coercion | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/SimonKing/ticket/15223 | a81fcc1072df88cc369d7aa0b7ae423fd97d7f02
Dependencies: | Stopgaps:
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Comment (by SimonKing):
Hm. But the more I think about it...:
In the `__cmp__` method of `IntegerModRing`, it is said:
{{{
if type(other) is not type(self): # so that GF(p) =/= Z/pZ
return cmp(type(self), type(other))
return cmp(self.__order, other.__order)
}}}
Note the comment: The aim is to let `GF(p)` and `Z/pZ` evaluate unequal.
This gives rise to two questions:
1. Do we really want that the evaluate unequal?
We have
{{{
sage: GF(5).has_coerce_map_from(IntegerModRing(5))
True
sage: IntegerModRing(5).has_coerce_map_from(GF(5))
False
}}}
Since there is no coercion in both directions, the two rings can not be
equal. So, I'd say `GF(5)!=IntegerModRing(5)` is correct
2. Do we really want that `IntegerModRing(5)` and
`IntegerModRing(5,category=Fields())` evaluate unequal?
This time, the coercions exist in both directions:
{{{
sage: IntegerModRing(5).has_coerce_map_from(IntegerModRing(5,
category=Fields()))
True
sage: IntegerModRing(5,
category=Fields()).has_coerce_map_from(IntegerModRing(5))
True
}}}
Hence, we might want to let them evaluate equal.
I see the following options:
- Make it so that integer mod rings with the same modulus evaluate equal,
regardless of their type and category. This would be in spite of the
comment in the code of `__cmp__`.
- Change `__cmp__` so that integer mod rings evaluate equal if and only if
there is a coercion in both directions. Hence, `GF(5)` and `ZZ.quo(5)`
would evaluate unequal, but `IntegerModRing(5, category=...)` would all
evaluate equal, independent of the category.
- Change `_coerce_map_from_`, so that there is a coercion in both
directions if and only if the two integer mod rings evaluate equal. Hence,
`IntegerModRing(5, category=...)` would all be distinct, for different
categories.
- Do not allow to put in a "category" argument. But then, we might want to
learn the rationale of introducing the argument in the first place. After
all, if the modulus of integer mod ring R is a prime number, then asking
`R in Fields()` will return true. So, if one knows during creation of the
ring that the modulus is prime, one might use `GF(p)` instead of
`IntegerModRing(p,category=Fields())`.
Further ways to go? In any case, there should be a new ticket.
--
Ticket URL: <http://trac.sagemath.org/ticket/15223#comment:21>
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