This thread is being hijacked ;-) Please keep the new polys module
discussions with Issue 1598.

Mateusz, I looked at the polys branch but don't see where terms_gcd is
being used. Are we looking at the same branch? I'm looking at the
polys version 6b6bc5b.

Here is the test case that I am working with:

f21 = (x - 1)**2 * (x + 4) / (x + a) / (x + 2)
f = f21.diff(x, 3)

I would like to see it (and any other sort of Basic expression) be
factored easily. I see that if one gives the frac=True argument then
this does factor (contrary to what I thought in comment 19 of issue
1598). But it is still taking too long, perhaps because the branch I
am looking at does not call the gcd. Again, please let me know which
is the right one. (This has me concerned because I am looking at the
one that I rebased on master.)



I did find the function terms_gcd. And as you say, making it work with
basic expressions would be trivial. Ut can also make the work simple
for a couple of other library routines:
- separatevars could benefit from using this; right now it is using
factor, but there is no need to work that hard to separate an
expression into independent factors. One would only need to try
factoring on terms which have more than one symbol in them after
removing any gcd terms.
- as_numer_denom() for an Add would benefit because the common factor
in number and denom could be removed. This also helps in rootinfinding
because the spurious roots would be thus avoided in a case like I
mentioned at 
http://groups.google.com/group/sympy/browse_thread/thread/bf20021b670fb3f1/ee73860e3e77ec00?lnk=gst&q=spurious#

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