Re: simply simplify this, a sin-ful expression
- From: rjf <fateman@xxxxxxxxx>
- Date: Sat, 14 Feb 2009 07:49:34 -0800 (PST)
oops. my finger slipped... rest of answer..
On Feb 14, 3:26 am, cliclic...@xxxxxxxxxx wrote:quite far along toward the solution. Ordinarily you have no idea
... There must be efficient algorithms
for this task.
If you have a correct hypothesis about the form of the answer, and all
you need to do is find the undetermined coefficients, you are already
what the form is going to be, a priori, and finding the form should be
part of the "algorithm". [Note that there is a proof that there is
no general algorithm even for testing for zero, so we are nibbling on
special cases.]
Note that the Risch integration algorithm operates in somewhat
analogous
fashion.
Essentially guess at the form of the integral, differentiate it and
match
coefficients. If the coefficients can't be matched up, the integral
doesn't
exist in terms of your choice of elementary functions.
Unfortunately, the guess can be hard to make; in particular you are
guessing
at the degree of certain polynomials in elements of the (differential)
field.
RJF
.
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