Le 12/02/2015 16:06, kcrisman a écrit :
As a late postscript, is #8111 related to any of this discussion? I
know this was mostly about Bezout/xgcd stuff, but that ticket looks
like it has languished and could be connected.
This is clearly the same kind of discussions. The point in #8111 is that
we rely on Flint's gcd function that returns the monic polynomial gcd.
There several possibilities that yield the desired result, and we may
even implement several of them:
- Change the `gcd` method for QQ['x'] in the same way as we changed the
`gcd` method for QQ, so that it returns a more interesting result when
the inputs actually live in ZZ['x']. Note that this change may also be
made for other methods such as `content`, which always returns 1 for
polynomials over QQ.
- Change the `reduce` method for rational functions over QQ['x'] in the
same way as above, so that it tests whether the inputs live in ZZ['x'].
- Change the `reduce` method for rational functions over QQ['x'] so that
it returns monic numerator and denominator. This last solution is
orthogonal to the previous ones, but in this case we would have the
rational functions over QQ represented in a normal form, which is not
the case to date.
The first and last solutions seem interesting to implement in any way.
Best,
Bruno
P.S.: There are other questions and conventions to take that are not
fully resolved around these questions of gcd, quo_rem, ... for
polynomials. One example is #16649 (and the pointers inside) that needs
review (shameless self plug).
- kcrisman
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