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Difficulties in patterns matching
*To*: mathgroup at smc.vnet.net
*Subject*: [mg3675] Difficulties in patterns matching
*From*: nader at math.chalmers.se (Nader Tajvidi)
*Date*: Fri, 5 Apr 1996 02:51:52 -0500
*Organization*: Dept. of Mathematics, Chalmers, Sweden
*Sender*: owner-wri-mathgroup at wolfram.com
Hi,
I spent some time to get a grip on the following patterns
matching problem but to no avail.
Consider the following expression.
test = (2*Sum[(gamma*x[i])/(sigma^2*(1 - (gamma*x[i])/sigma)), {i, 1, n}])/
gamma^3 + (-1 + gamma^(-1))*
Sum[(2*gamma*x[i]^3)/(sigma^4*(1 - (gamma*x[i])/sigma)^3) +
(2*x[i]^2)/(sigma^3*(1 - (gamma*x[i])/sigma)^2), {i, 1, n}] -
(2*Sum[(gamma*x[i]^2)/(sigma^3*(1 - (gamma*x[i])/sigma)^2) +
x[i]/(sigma^2*(1 - (gamma*x[i])/sigma)), {i, 1, n}])/gamma^2
I would like to apply the following transformation rules to
the above expression.
1) Sum[x[i]/(1-gamma x[i]/sigma),{i,1,n}]-> n f1[gamma,sigma]
2) Sum[x[i]^2/(1-gamma x[i]/sigma)^2,{i,1,n}]-> n f2[gamma,sigma]
3) And generally for different m's:
Sum[x[i]^m/(1-gamma x[i]/sigma)^m,{i,1,n}]-> n fm[gamma,sigma]
There are lots of such expressions and the main problem is
that I can't define a general transformation rule which can handle for
example rule no 1 for all different coefficients of x[i] in the numerator of
expressions and also for different coefficients of (1-gamma
x[i]/sigma) in the denominator of expressions. This means that the
first sum in "test" should be transformed to
n gamma f1[gamma,sigma] /sigma^2
These rules should also handle sums like
Sum[x[i]+y[i],{i,n}]=Sum[x[i],{i,n}]+Sum[y[i],{i,n}].
Thanks in advance for any advice you can give.
Regards, Nader Tajvidi
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