quo_rem in the polynomial rings does not use canonical coercion #383
Description
I'm looking at the polynomial function quo_rem and I see that it does it's own
coercion manually. This feels a little wrong to me. I think it should go
through the standard coercion routines. Here's a "bug" that results:
sage: x=ZZ['x'].0
sage: y=QQ['x'].0
sage: (y+1).quo_rem(1/2*x)
(2, 1)
sage: (x+1).quo_rem(1/2*y)
...
<type 'exceptions.TypeError'>: no coercion of this rational to integer
The bug is that I don't see why these two things are treated substantially
differently. The reason I found this is because the simple "TypeError"
exception did not provide the usual message about parents being
mis-matched -- I think this is a bug in itself
The fix for all that is to make the quo_rem stuff use canonical coercion model.
All of the quo_rem instances in sage/rings/polynomial/polynomial_element_generic.py suffer from some sort of coercion impropriety.
Component: basic arithmetic
Author: Robert Bradshaw
Reviewer: William Stein
Merged: sage-4.3.1.rc2
Issue created by migration from https://trac.sagemath.org/ticket/383