Prof. Dr. Johannes Grabmeier wrote:
>
> certainly, we do not really want Fraction from Fields, but where (certainly=
> not in algebra) is this kind of knowledge hidden in AXIOM?
>
AFAICS the check is done in 'isLegitimateMode' from 'clammed.boot'.
IMHO at least some check done by 'isLegitimateMode' are inappropriate
in algebra, but resonable for interactive use. More precisely,
'isLegitimateMode' claims that 'Polynomial(Polynomial(Integer))' is
bad, which is understandable, because users could easily get
confused by variables ending at wrong level. OTOH such domain
seem fine as representation for some other domain.
> one would suspect that Fraction could be defined in an algebraic was, somet=
> hing like=20
>
> Fraction F:=20
>
> F : IntegralDomain not Field
>
> In any case, AXIOM should be consistant:=20
>
> )sh Fraction Fraction Integer
>
> gives a valid answer.
FriCAS shows some consistency:
(1) -> ffQ := Fraction Fraction Integer
(1) Fraction(Fraction(Integer))
Type: Type
(2) -> (1/2)::ffQ
Fraction(Fraction(Integer)) is not a valid type.
(2) -> ffR := Fraction RADIX 2
(2) Fraction(RadixExpansion(2))
Type: Type
(3) -> (1/2)::ffR
Fraction(RadixExpansion(2)) is not a valid type.
that is, it allows you to form the type and complains only when
you try to use it at command line.
--
Waldek Hebisch
[email protected]
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