Updates:
Summary: expand(power_base=True) is too aggressive
Comment #2 on issue 1766 by smichr: expand(power_base=True) is too
aggressive
http://code.google.com/p/sympy/issues/detail?id=1766
This behavior is comes from expand_pow_base upon which separatevars
depends, so it's
not intrinsic to separatevars.
Regarding the previous comment, is there a reason that they should not just
initialize all their variables as
x,y,z=symbols('xyz',positive=True)
I would prefer that they get the education by a failed attempt at solving
an equation
than to have to defend why sympy gave an expression in symbols that was not
correct
when you put numbers in their place. (I searched a bit for a FAQ or
tutorial that I
saw where Ondrej explains why expand or something wouldn't make something
like
sqrt(x*y) into sqrt(x)*sqrt(y) without giving symbols assumptions but can't
find it
now.) Is there an ODE for which this would happen, i.e. give variables
separated out
from under a radical that should not be separated?
Here's the equation you cite (and no doubt know will fail without
assumptions):
>>> dsolve(f(x).diff(x) - sqrt(f(x)*(1 + x)), f(x))
Traceback (most recent call last):
File "<interactive input>", line 1, in <module>
File "C:\Documents and Settings\chris\sympy\sympy\solvers\ode.py", line
366, in dsolve
raise NotImplementedError("dsolve: Cannot solve " + str(eq))
NotImplementedError: dsolve: Cannot solve D(f(x), x) - ((1 +z
x)*f(x))**(1/2)
But just doing this,
>>> x=Symbol('x', positive=True)
makes it work just fine.
>>> dsolve(f(x).diff(x) - sqrt(f(x)*(1 + x)), f(x))
f(x) == C1 + x/3 + x**2/3 + x**3/9 + C2*(1 + x)**(3/2)
The "just work" principal can be applied to some situations and we can call
it
"batteries included"; but to make something work with a hidden assumption
and not do
anything to make sure that that assumption is satisfied is a "bombs
included"
approach ;-)
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