Comment #30 on issue 1598 by smichr: New polynomials manipulation module
http://code.google.com/p/sympy/issues/detail?id=1598
The functionality for gcdfactor is there, but a simple wrapper for someone
who
doesn't want to get into Polys is not there. Compare
expr = gcdfactor(expr)
with
if (expr.is_Add or expr.is_Mul):
expo, poly = Poly(expr, expand=False).terms_gcd()
if not all(i is S.Zero for i in expo):
terms = [x**expo[i] for i,x in enumerate(poly.gens)]
terms.append(poly.as_basic())
expr = Mul(*terms)
That's a lot of overhead for someone that just wants to factor out the gcd
from an
expression. gcdfactor isn't duplicating terms_gcd, it is just putting a
non-Poly
wrapper on it. I put it in the simplify module since separatevars should be
using
gcdfactor (and not pure factor).
As for fraction and magic...it's a little underwhelming. You have to do
as_numer_denom() to get an expression to have a numer and denom or else
fraction
doesn't do anything for you...and even then, a simple removal of a gcd is
not done.
>>> eq = 1/x + 1/x**2
>>> fraction(eq)
(1/x + x**(-2), 1)
>>> n,d=(1/x**2+1/x).as_numer_denom()
>>> fraction(n/d)
(x + x**2, x**3)
I (and root finders) would really like to see
(1 + x, x**2)
come back from eq.as_numer_denom(). Whether this slows things down too
much, that's
an issue to consider. If it is, then having gcdfactor in simplify is a nice
tool
since before doing as_numer_denom() one can pull out a gcd and run
as_numer_denom on
the residual and build the result on their own:
### simulated output
>> eq = 1/x+1/x**2
>> gcdfactor(eq)
1/x*(1+1/x)
>> Mul(*[m.as_numer_denom() for m in make_list(_, Mul)]) #existing
>> as_numer_denom()
(1+x)/x**2
###
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