Status: Accepted
Owner: asmeurer
Labels: Type-Defect Priority-Medium Polynomial Integration
New issue 2040 by asmeurer: Better way to make a rational function out of
an expression
http://code.google.com/p/sympy/issues/detail?id=2040
In the Risch Algorithm (issue 2010), I need to convert the expression into
a rational function, which is done by first converting the non-rational
parts (exp, log) into dummy variables. My current method is along the
lines of
if expr.is_rational_function(*T):
a, d = expr.as_numer_denom()
a, d = Poly(a, t), Poly(d, t)
Where t = T[-1]. This works fine in most cases, but it fails in cases like
this one:
expr = sqrt(x**2 + y**2 + 2*x*y)
T = [x, y]
because expr.is_rational_function(*T) fails on it, but it really is a
rational function because expr == sqrt((x + y)**2) = x + y. So I think
there needs to be some function that not only is smarter about making
rational functions out expressions, but also streamlines the above process.
(P.S., I know about all the assumptions nonsense. Basically, when we work
with integration, we ignore assumptions and work with things algebraically,
and I need a function that does that.)
By the way, here's an example function that requires this functionality in
risch_integrate() to work. It is equivalent to log(x + 1) + log(x + 2) or
just log(x**2 + 3*x + 2):
sqrt(log(x**2 + 3*x + 2)*(log(x + 1) + log(x + 2)))
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