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Factorise with respect to a variable

• To: mathgroup at smc.vnet.net
• Subject: [mg79584] Factorise with respect to a variable
• From: "Andrew Moylan" <andrew.j.moylan at gmail.com>
• Date: Mon, 30 Jul 2007 06:43:08 -0400 (EDT)

Here's an arbitrary expression that depends (non-polynominally) on n1 and
some other variables:

expr = (E^(I*(2*chi2 - kappa + 2*chi1*n1 - kappa*n1 - 2*chi2*n2 + 
                kappa*n2 + I*x*SuperStar[x] + I*y*SuperStar[y]))*
    Sqrt[1 + n1]*
        Sqrt[n2]*x^n1*y^n2*SuperStar[x]^(1 + n1)*
    SuperStar[y]^(-1 + n2))/
     Sqrt[n1!*(1 + n1)!*(-1 + n2)!*n2!]

Is it possible to use Mathematica to factor out the dependence of expr on
n1? That is, I would like to factorise expr into {expr1,expr2}, such that
(i) expr1 depends on n1, (ii) expr2 does not depend on n1, and such that
(given (i) and (ii)) expr1 is as simple as possible.

Here's a simpler example: When I factorise 1/(2*x*y^2) "with respect to" x,
I want the result to be {1/x, 1/(2*y^2)}.

Do you think it's possible to easily get Mathematica to do something like
this?

• Follow-Ups:
  • Re: Factorise with respect to a variable
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>