On 11/10/2008 10:31 PM, koffie wrote:
>> sage: C = VectorSpaces(GF(5))
>> sage: C
>> Category of vector spaces over Finite Field of size 5
>> sage: W = (ZZ^3).span([[1,2,3],[4,5,3]])
>> sage: W
>>
>> Free module of degree 3 and rank 2 over Integer Ring
>> Echelon basis matrix:
>> [1 2 3]
>> [0 3 9]
>> sage: C(W)
>>
>> Vector space of degree 3 and dimension 2 over Finite Field of size 5
>> Basis matrix:
>> [1 0 2]
>> [0 1 3]
>>
>> That looks to me as if C is like a coercion function.
>
>> Ralf
>
> Wel looking at it mathematically, you would like C to be some functor
> from free modules over Z to vectorspases over Finite Fields of size 5.
I have nothing against functors. However, as I understand, C is a
>> Category of vector spaces over Finite Field of size 5
and that does not sound like a "functor".
> And taking this in mind I think this is a good behaviour of C(W),
> since this behaviour is for example similar to that of F5(x) in the
> example below:
> sage: F5=GF(5)
> sage: F5
> Finite Field of size 5
> sage: x=ZZ(102)
> sage: F5(x)
> 2
> That is F5() tries to make an element in F5() of 102 as C tries to
> make a vectorfield over GF(5) out of W. So maybe it is also not bad to
> have coercion functions defined for categories.
In in the above form "ZZ(102)" and "F5(x)" you basically use ZZ and F5
to denote a type cast. That is what I called "coercion" (which is
basically a function ZZ -> F5).
My question now (still being a bit unfamiliar with python) would be,
where can I find the documentation of what is allowed for x in something
like F5(x). I guess F5("some string") does not work. I'd like to be sure
that code I write does not break at runtime. A pointer to the
documentation is highly appreciated.
Thank you
Ralf
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