Comment #15 on issue 2308 by smi...@gmail.com: Should we rename
primitive()? (and Expr.primitive() should call primitive())
http://code.google.com/p/sympy/issues/detail?id=2308
Also is this the lack of unity between the function and method that is the
source of the ending lines of comment 9?
h[11] >>> primitive(3/S(2)+3*x/4)
(1, 3/2 + 3*x/4)
h[12] >>> (2*x/3 + 4*y/9).primitive()
(2/9, 2*y + 3*x)
Why don't we just stick with the terms_gcd idea. That pulls out all
gcds...the primitive just pulls out Rational so how about rat_gcd:
>>> eq = 3*x*y+3*x
>>> terms_gcd(eq)
3*x*(1 + y)
>> rat_gcd(eq)
3*(x + x*y)
>> rat_gcd(S(3)/2 + 3*x)
3*(1 + 2*x)/2
>> rat_gcd(S(3)/2 + 15*x/4)
3*(2 + 5*x)/4
>> rat_gcd(3 + (3 + 6*x)*y)
3*(1 + (1 + 2*x)*y)
I prefer the last expression to either of these:
h[15] >>> primitive(3 + (3 + 6*x)*y)
(3, 1 + y + 2*x*y)
h[16] >>> (3 + (3 + 6*x)*y).primitive()
(1, 3 + y*(3 + 6*x))
And don't expose primitive.
Finally, if we do this, rat_gcd could take the place of as_coeff_Mul. I
wonder if there is a case where you wouldn't want the additional work of
rat_gcd where you would be using as_coeff_Mul. e.g. in _pi_coeff if the
coeff of pi were (2*x + 4*y)*pi then I would want the (2, (x + 2*y)) not
the (1, 2*x + 4*y) that as_coeff_Mul gives.
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