Dear Vincent,
On 2012-08-16, Vincent Delecroix <20100.delecr...@gmail.com> wrote:
> It breaks many test in sage.combinat.*. Note that if we adopt the
> strict convention (ie int(2) not in Integers/IntegerRange/...) then it
> will be impossible to do the following
> {{{
> sage: W = Words("positive integers")
> sage: W([int(1), int(2)])
> word: 12
> }}}
>
> I have two options
> * modify all files in sage.combinat.* in order to fit the new implementation
> * make PositiveIntegers and IntegerRange accepts silently Python int
The default behaviour of "x in P" for any parent P in Sage is:
x in P
<=>
P(x)==x is True (and does not raise an error)
Hence, according to the default, if P=PositiveIntegers(), then we want
the following:
1) P(int(1)) works
2) Coercion between P and int works (this is implicitly used in "==")
But currently, we have:
* P(int(1)) raises an error (hence, "int(1) in P" is false by default)
* P(1).parent() is ZZ, not P
* sage.categories.pushout.pushout(P,ZZ) raises an error.
* The coercion model finds that there is a multiplication action of
P on ZZ, but it is not able to tell about addition.
I think that's a mess. P should at least know that it is a subset of ZZ.
Hence, its embedding into ZZ should be registered as a coercion. And it
should be able to convert a positive python int.
Cheers,
Simon
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