On Fri, Mar 02, 2012 at 12:35:14PM +0100, Ralf Hemmecke wrote:
>> )abbrev domain SUP SparseUnivariatePolynomial
>> SparseUnivariatePolynomial(R : CommutativeRing):
>> with ...
>> Join(CommutativeRing,
>> R has IntegerLike or R has FiniteField or
>> R has SuchAndSuchCategory => UniqueFactorizationDomain
>> )
>> == add
>> Rep == ?
>> factor(f : UP R) : Factored (UP R) ==
>> R has IntegerLike => factorUPOverInteger f
>> R has FiniteField => factorUPByExtendedBerlekemp(R, f)
>> R has SuchAndSuchCategory => factorUPByGeneric(R, f)
>
> Of course that can be done. But I have the impression you haven't that
> you haven't got the point in me writing
>
> if R has Field then
> foo(r: R): % == (1/r) pretend %
> else
> foo(r: R): % == r pretend %
>
> instead of
>
> foo(r: R): % == if R has Field then
> (1/r) pretend %
> else
> r pretend %
>
> In the second case (as in your case above), calling factor will *always*
> perform the test "R has Field". In my version that test is only at
> instantiation time of the domain.
>
factorUPOverInteger f is an expensive loop, and the relative cost of
preliminary (R has IntegerLike) is usually small.
Still your solution looks indeed considerably better.
>> I am trying to find out whether the language allows, in principle, a clear
>> and efficient dispatching for such operations which have a complex set of
>> implementation cases overlapping non-trivially and having different
>> generality levels.
>
> I think my previous mail should have shown you how dispatching can be
> done on a domain level. The exports would simply list the function
> unconditionally.
Then, the next question is
why the `factor' instances are not so nicely
dispatched in the current FriCAS, Axiom ?
For I am a bit confused.
1. Waldek wrote about the category of Explicit...,
and of some performance problems related to dispatching `factor'.
2. I write in my testParse.spad :
factor(f) $UnivariateFactorize(UP(x,INT))
-- and this is by the advice read from e-mail.
Could I happen to call `factor' in this case from other place, where
its impementation is less efficient?
3. Waldek wrote, that it is not nicely dispatched -- if I understand
correct.
Is this by occasion or there are some fundamental reasons for this?
Regards,
------
Sergei
[email protected]
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