On 07/06/2010 04:13 PM, Martin Rubey wrote:
actually, why should PF 2 have Algebra Fraction Integer?
(1) -> PF 2 has Algebra INT
(1) false
(2) -> PF 2 has Algebra FRAC INT
(2) true
Oh.
That's really funny. :-(
But it seems to come from PF 2 being a DivisionRing. Since PF 2 is a
Field, it's also a DivisionRing, but why does DivisionRing export
Algebra(Fraction Integer)?
This comment in catdef.spad says it all...
-- Q-algebra is a lie, should be conditional on characteristic 0,
-- but knownInfo cannot handle the following commented
-- if % has CharacteristicZero then Algebra Fraction Integer
Would have been a surprise to me if the original programmers wouldn't
have known. So the problem is the compiler? But somehow, I wouldn't want
to have the above if-statement in the category, because it's a kind of
"I am also of type X if I am of type Y". But type Y can live far far
away and becomes only apparent in an actual implementation of a concrete
domain.
1) Better would be to declare Algebra(Fraction Integer) at the time of
implementation of the domain.
2) Or have additional categories DivisionRingCharacteristicZero and
DivisionRingCharacteristicNonZero.
I'd prefer (1).
Ralf
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