2015-02-05 21:38 UTC+01:00, John Cremona <john.crem...@gmail.com>:
> If you ask for operator.mul instead of operator.div then you get the
> poly ring.  Is that it, perhaps?

Nope. I want to get rid of many hacks in rings/polynomial. In order to
do that I need the div operation to be correctly handled by the
coercion (or perhaps I missed something about the aim of coercion?).
Namely, if p is an element of GF(5)['x,y'] then (p/Integer(2)) should
be an element of GF(5)['x,y']. You can argue that this is what you get
in Sage

sage: R = GF(5)['x','y']
sage: (R.an_element() / 2).parent()
Multivariate Polynomial Ring in x, y over Finite Field of size 5

But the reason why is a bit of a hack that actually introduce many
bugs in other places:

sage: R = GF(5)['x,y']
sage: (R.one() / R.one()).parent()
Multivariate Polynomial Ring in x, y over Finite Field of size 5

the above should be an element of the fraction field! And you can
build more involved examples.

Vincent

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