It is possible to use the taylor() function, but i think that better
solution is a function, that can collect terms with negative
powers(something like facsum). I found the function that can collect
terms with negative powers in Sage algebra system:
sage: var("A,B,C,D,E")
(A, B, C, D, E)
sage: expr=1/(A*B)+1/(A*C)+1/(A^2*E)+1/(A^2*D)
sage: expr.collect(A)
(1/B + 1/C)/A + (1/D + 1/E)/A^2
sage:
I think, that it is good idea to implement such collect() function into
Maxima(if it still does not exist). Sage is open source, it uses Maxima
for symbol manipulations. So, one just need to look into Sage sources,
found collect() function there and implement it into Maxima.
> taylor(1/(A*B)+1/(AC)+1/(A^2*E)+1/(A^2*D), A, 0, 3);
> gives the exact result
> (E+D)/(D*E*A^2)+1/(B*A)+1/AC+...,
> after which you can probably manually or programmatically isolate the
> coefficients of the powers of A, then expand those coefficients into
> partial fractions or whatever you want.
> -- best regards, david stoutemyer
>
> ----- Original Message -----
> From: Dmitry Shkirmanov <piminusmeson at bk.ru>
> Date: Wednesday, December 14, 2011 6:49 am
> Subject: Re: [Maxima] fraction manipulations
> To: maxima at math.utexas.edu
>
> > On 14.12.2011 17:45, Rupert Swarbrick wrote:
> > > Dmitry Shkirmanov<piminusmeson at bk.ru> writes:
> > >
> > >> Hello, list. Is there any function in maxima, that can
> > >> 1/(A*B)+1/(AC)+1/(A^2*E)+1/(A^2*D) rewrite into
> > >> 1/A*(1/B+1/C)+1/A^2*(1/D+1/E) ?
> > >>
> > > Frankly, I don't see the point though: after
> > > all, what are you going to do with the result? As soon as you
> > touch it
> > > with any other computation, it'll get re-simplified in a way
> > you don't
> > > recognise...
> > >
> > >
> > Thanks for help.
> >
> > I will try to explain why i need this. I have an expression,
> > that contains different powers of "A". The simplest example of
> > such expression is:
> >
> > 1/(A*B)+1/(AC)+1/(A^2*E)+1/(A^2*D) (But
> > it can contain terms like 1/A^3, 1/A^4 and so on)
> >
> > in my case, "B","C","E","D" is some complicated expressions.
> >
> > . I know, that "A" is big, so i want to get power series
> > expansion, like 1/A*(some_expression) + 1/A^2*(other_expression)+...
> > After this, i want to study "some_expression", "other
> > expression" separately.
> >
> > P.S. Sorry for my rough english