Updates:
Labels: NeedsReview
Comment #45 on issue 1766 by smichr: expand(power_base=True) is too
aggressive
http://code.google.com/p/sympy/issues/detail?id=1766
I think I am seeing the light at the end of the tunnel...this has been a
pandora's
box of an issue. Here's where things stand right now as of the last 0000
commit in
branch 1766:
This
(2*f*k - f*m*w**2)/(k**2 - 3*k*m*w**2 + m**2*w**4)
simplifies to
f*(2*k - m*w**2)/(k**2 - 3*k*m*w**2 + m**2*w**4)
and these assertions do not fail
Desirable behaviors
# pretty applies to exp, too
assert fraction(exp(-x)) == (1, exp(x))
# rules of powers prohibit expansion
assert separate((x*y*z)**x) == (x*y*z)**x
# if p is positive, it can be pulled out
assert separatevars(sqrt(y*(p**2 + x*p**2))) == p*sqrt(y*(1 + x))
# a negative exponent in a power is moved to the side of the fraction
# to make the exponent positive
assert (x**n).as_numer_denom() == (1, x**-n)
# non-commutatives are not re-ordered
assert (n1*n2*n1).as_independent(n2) == (n1, n2*n1)
# exp is handled in separatevars
assert (exp(2*x)-exp(2*y))/(exp(x)-exp(y)) == exp(x) + exp(y)
One of the ode XFAILS passes now.
Questionable behaviors
# you can only extract numbers of the same sign
assert (-S(4)).extract_multiplicatively(2) == None
# shouldn't the following always be true if the base is real
# and positive (as for exp())?
assert separate((exp(x)*exp(y))**z) != exp(x*z)*exp(y*z)
# shouldn't this go to (z**y)**2 automatically?
assert powsimp(z**(2*y)) == z**(2*y)
The last commit 0000 with comments is available for review.
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