Comment #1 on issue 2031 by mattpap: Add field option to Poly.operation()
functions
http://code.google.com/p/sympy/issues/detail?id=2031
It does not make much sens to add field option to Poly's method, because
the same thing can be achieved with to_field() method, e.g.:
In [1]: Poly(x, x).quo(Poly(2, x))
(...)
ExactQuotientFailed: 2 does not divide x
In [2]: Poly(x, x).to_field().quo(Poly(2, x))
Out[2]: Poly(1/2*x, x, domain='QQ')
(you don't have to use to_field() on both polynomials, because auto
unification of polynomials will do the job).
If the domain is already a field, then to_field() is noop, so no cost is
associated.
What we can do is to add auto flag to div() and friends, as it was done to
gcdex(), invert(), sturm() etc., to automatically choose the best domain
for the particular operation. This makes sense because would have field for
Euclidean division (div()) and ring for primitive division (pdiv()) (no
auto flag in this case).
If we add auto flag, then another issue is: if the input polynomials are
divisible over a ring (the initial domain was a ring) and auto=True (which
means we are going to convert to a field), then should we convert the
result back to a ring or leave it as is?
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