On Thu, Mar 01, 2012 at 11:04:57PM +0100, Ralf Hemmecke wrote:
> On 03/01/2012 09:58 PM, Serge D. Mechveliani wrote:
>> Thus, can Spad handle (I) ? Something like this:
>>
>> Category(R : CommutativeRing) : WithDet ==
>> ...
>> with
>> det : SquareMatrix R -> R
>>
>> Default Implementation ==
>>
>> det mt = if rR has EuclideanRing then
>> gaussEliminationForEuclidean mt
>> else genericMethod mt -- expand by row
>>
>> -- correct the syntax if needed.
>
> ---rhxBEGIN foo.spad
> )abbrev domain FOO Foo
>
> Foo(R: Ring): with
> coerce: % -> OutputForm
> foo: R -> %
> == add
> Rep == R
> coerce(x: %): OutputForm ==
> "FoO"::OutputForm + (x pretend R)::OutputForm
> if R has Field then
> foo(r: R): % == (1/r) pretend %
> else
> foo(r: R): % == r pretend %
> ---rhxEND foo.spad
>
> Use it like this...
>
> (3) -> foo(3)$Foo(Integer)
>
> (3) FoO + 3
> Type: Foo(Integer)
>
> (5) -> foo(3)$Foo(Fraction Integer)
>
> 1
> (5) FoO + -
> 3
> Type: Foo(Fraction(Integer))
>
Thank you.
You changed from defining a Category to defining a Domain ...
All right, can `factor' be the dispatched by Axiom in this manner?
So that the user would not search which package among 20 fits the best
for `factor'.
------------------------------
)abbrev domain INT Integer
Integer(): with ...
Join(EuclideanDomain, UniqueFactorizationDomain ...)
== add
Rep == ?
factor n == factorInteger
)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)
------------------------------
Usage: factor(6) $INT,
(f := (x^2 - 1) :: SUP INT; factor(f) $SUP INT)
(F := ResidueRing(INT, 7); f := (x^7 +2) :: F; factor(f)$F)
So Axiom will dispatch itself to the `factor' version which is the most
efficient for this particular domain.
Can this be done?
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.
Regards,
------
Sergei
[email protected]
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