On 06/12/2010 01:50 PM, Waldek Hebisch wrote:
> Bill Page wrote:
>> Ralf,
>>
>> I think that the map
>>
>> coerce : Fraction Polynomial Complex Integer -> %
>>
>> which is apparently x+-> [x,x]
>>
>> in
>>
>> )sh DirectProduct(2,Fraction Polynomial Complex Integer)
>>
>> should not be called a coercion.
>
> Good spot. AFAICS that coercion is defined because we have
>
> if R has SetCategory then FullyRetractableTo R
>
> in DirectProductCategory. IMHO this does not make sense.
> But before removing it one have to fix a few places in algebra
> (at least retract in SquareMatrix) where the retraction from direct
> product to scalars is used.
Waldek,
what exactly is the problem?
coerce: R -> %
or
retract % -> R
for % being DirectProduct(ndim, R)?
Bill and me discussed the coercion. If you check hyperdoc for
DirectProduct and click on "origin" for the function "coerce", then you
see that coerce: R -> % comes from Algebra(R). It just needs that R is a
CommutativeRing. Thus, removing FullyRetractableTo R will probably have
no effect on my original problem.
As for 'retract'. I think that this is not realy dangerous. It is
implemented as
if R has SetCategory then
same?: % -> Boolean
same? z == every?(x +-> x = z(minIndex z), z)
retract(z:%):R ==
same? z => z(minIndex z)
error "Not retractable"
So why do you think that it doesn't make sense?
I would have thought that one would naturally perhaps rather ask
if R has CommutativeRing then ...
in order to be in some sense the inverse for the coerce function, but I
cannot currently see that "R has SetCategory" is much of a problem.
Ralf
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