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MathGroup Archive 1991

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Simplify bug?

  • To: mathgroup at yoda.ncsa.uiuc.edu
  • Subject: Simplify bug?
  • From: smithw at mathnx.math.byu.edu (Bill Smith)
  • Date: Wed, 13 Feb 91 11:30:06 MST

I can't remember whether this sort of bug has been noted before.
The following 4x4 matrix arises in trying to compute eigenvectors
for a certain matrix.


Mathematica (MIPS) 1.2 (November 8, 1989) [With pre-loaded data]
by S. Wolfram, D. Grayson, R. Maeder, H. Cejtin,
   S. Omohundro, D. Ballman and J. Keiper
with I. Rivin and D. Withoff
Copyright 1988,1989 Wolfram Research Inc.
 -- Terminal graphics initialized --

In[1]:= {{(2 - 5*z + 4*z^2 - z^3)/
    (2*a - b - 2*z - 5*a*z + 2*b*z + 5*z^2 + 4*a*z^2 -
      b*z^2 - 4*z^3 - a*z^3 + z^4),
   (-b + 2*b*z - b*z^2)/
    (2*a - b - 2*z - 5*a*z + 2*b*z + 5*z^2 + 4*a*z^2 -
      b*z^2 - 4*z^3 - a*z^3 + z^4),
   (3*b - 2*c - 3*b*z + 3*c*z - c*z^2)/
    (2*a - b - 2*z - 5*a*z + 2*b*z + 5*z^2 + 4*a*z^2 -
      b*z^2 - 4*z^3 - a*z^3 + z^4), 0},
  {(-1 + 2*z - z^2)/
    (2*a - b - 2*z - 5*a*z + 2*b*z + 5*z^2 + 4*a*z^2 -
      b*z^2 - 4*z^3 - a*z^3 + z^4),
   (a - z - 2*a*z + 2*z^2 + a*z^2 - z^3)/
    (2*a - b - 2*z - 5*a*z + 2*b*z + 5*z^2 + 4*a*z^2 -
      b*z^2 - 4*z^3 - a*z^3 + z^4),
   (-3*a + c + 3*z + 3*a*z - c*z - 3*z^2)/
    (2*a - b - 2*z - 5*a*z + 2*b*z + 5*z^2 + 4*a*z^2 -
      b*z^2 - 4*z^3 - a*z^3 + z^4), 0},
  {0, 0, (2*a - b - 2*z - 3*a*z + b*z + 3*z^2 + a*z^2 -
      z^3)/(2*a - b - 2*z - 5*a*z + 2*b*z + 5*z^2 +
      4*a*z^2 - b*z^2 - 4*z^3 - a*z^3 + z^4), 0},
  {0, 0, 0, (2*a - b - 2*z - 3*a*z + b*z + 3*z^2 + a*z^2 -
      z^3)/(2*a - b - 2*z - 5*a*z + 2*b*z + 5*z^2 +
      4*a*z^2 - b*z^2 - 4*z^3 - a*z^3 + z^4)}}

In[2]:= Simplify[%]

GCD::ptoomany: Tried 4792 primes, algorithm failed.
Error: iPsparseGcdcf interpolation error
Process abort

This is on a MIPS RS2030.
The same thing happens on a NeXTcube (68040):
GCD::ptoomany: Tried 4792 primes, algorithm failed.

BTW, Factor works just fine here to give:
{{-((-2 + z)/(2*a - b - 2*z - a*z + z^2)), 

   -(b/(2*a - b - 2*z - a*z + z^2)), 

   -((3*b - 2*c + c*z)/
      ((-1 + z)*(2*a - b - 2*z - a*z + z^2))), 0}, 

  {-(2*a - b - 2*z - a*z + z^2)^(-1), 

   -((-a + z)/(2*a - b - 2*z - a*z + z^2)), 

   -((-3*a + c + 3*z)/
      ((-1 + z)*(2*a - b - 2*z - a*z + z^2))), 0}, 

  {0, 0, -(-1 + z)^(-1), 0}, {0, 0, 0, -(-1 + z)^(-1)}}



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