Serge D. Mechveliani wrote:
>
> On Thu, Mar 22, 2012 at 04:13:33PM +0400, Serge D. Mechveliani wrote:
> > People,
> > I search in Axiom for an equivalent for the domain constructor
> > ResidueE
> > -- residue ring of an Euclidean ring R by an ideal generated by a
> > generator g : R.
> >
> > I see ResidueRing, but it is said to be for a polynomial ring R.
> > But Integer, GaussianInteger, some of quadratic integer rings --
> > are all Euclidean, and are not presented as a polynomial ring,
> > and their residues can be treated uniformly by ResidueE.
> > I expect that Axiom has something for this, may be, under a different
> > name.
> > Can you point at it?
> >
>
> May be, it is ModularRing(R, Mod, reduction, merge, exactQuo)
> ?
> My Spad program has R : EuclideanRing and g : R,
> and needs to build R/Ideal(g).
> Probably, it needs to
> 1) build Mod as an additive monoid generated by g,
> 2) define `reduction' as a map of taking a remainder by g,
> etc.
> Can ModularRing be used this way?
Yes. Note that you probably want to take R as Mod. Also
ModularRing is different than say IntegerMod, because
in case of IntegerMod you get different ring for each
different modulus, while ModularRing normally gives you
a single ring for all moduli (typically it is used in
such way that user gets runtime error when attempting
operation between two elements with different moduli).
BTW: Dont be surprised that Axiom/FriCAS misses some functionality.
Axiom/FriCAS provides a comprehensive framework in which useres
can add functionality. However, what cames in "ready" form
looks somewhat random, simply when somebody developed a domain
and in worked/looked nice it got included. When nobody worked
on given area (or made no effort to push his/her code to
distributed version) then there is no code.
--
Waldek Hebisch
[email protected]
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