Re: Domain of elements in PARI

[Ilya Zakharevich <ilya@math.ohio-state.edu>]

On Fri, May 05, 2000 at 12:53:40AM +0200, Bill Allombert wrote:
> > a) a way to represent an element in a quotient by a non-principal
> >    ideal in terms of the PARI type system;
> 
> Yes, but we have to add support for rings first, and then add ideals.

I do not see a significant need to introduce rings and ideals to
PARI.  As far as we can mark that

 operations over a particular element allow the following
   primes/variables as denominators: 7, 37, y, z,

everything is OK.  And we can do it today: there are only 15 or some
mentions of t_RFRACN in the source.  Thus it should be extremly easy
to add a new type t_RFRACN_TYPED which works exactly as t_RFRACN, but
has an additional GEN.

Encode the info about allowed denominators into this GEN.  Add a gp
constructor for this type.

Now one can do calculations with such numbers as before, but one can
start to modify the source so that the relevant operations
preserve/use this info.

Ilya