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MathGroup Archive 1996

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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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