Comment #60 on issue 1598 by mattpap: New polynomials manipulation module
http://code.google.com/p/sympy/issues/detail?id=1598

> Then perhaps this should be done only to separatevars.

It depends on how useful this can be. Possibly we should finally derive  
some scheme
for implementing simplification/rewriting routines.

> Also, I wonder if you might call terms_gcd() -- the function -- simply  
> gcdfactor.
> gcd() is already taken, as I recall, in polys and terms_gcd() doesn't do  
> the same
> thing as the method by the same name.

In perfect world this would be factor_out_terms_gcd(), a bit long, but  
gcdfactor()
means nothing to me, however is shorter. Anyway, terms_gcd() is a wrong  
name at all,
because it doesn't return the GCD itself, but Poly.terms_gcd() is OK  
because it
actually returns the GCD (well, in a terms of generators' exponents and  
without
ground domain analysis, which is done in terms_gcd() version).

> since Mathematica can do this instantly (...) so, the journey will be  
> long.

No one ever said it will be short, but we already went quite far and paying  
a little
more attention to what we do and how we do it, we can go even further. For  
example a
trivial analysis of the example in c#10 shows that by being a bit more  
careful we
easily can improve factor() performance 2x..4x (for that special case). We  
could do
even better if we could implement a better multivariate GCD algorithm, like  
EEZ or
SPMOD, but this is non-trivial and requires a lot of work.

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