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MathGroup Archive 2007

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RootSum 2

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75234] RootSum 2
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Sat, 21 Apr 2007 23:11:17 -0400 (EDT)

In previous message I state that if Apart could evaluate always the root of
the denominator then we could probably avoid the generation of RootSum
(which is possibe for denomianators of degree less than five).

In fact thinking harder I came to the conclusion that it is just
suffices Apart to have been able to evaluate just the real root of the
polynomial

1 + 2*x + 3*x^2 + x^3

so that when it was called by Integrate the integrand (2*x)/((1 +
x)*(1 + 2*x + 3*x^2 + x^3))
would have been written out as

a[1]/(x+1) + a[2](x+a)+ (a[3]+a[4]*x)/(x^2+b*x+c)

where

a = - x1

b = -(x2+x3)

c = x2*x3

x1,x2,x3 roots of 1 + 2*x + 3*x^2 + x^3

and a[i] coefficients which could have been detemined during the
process of integration.

Of course how this trivial hand procedure could be implementated to a
complicated
CAS like Mathematica is another story!



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