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Problems with easy simplifications

  • To: mathgroup at
  • Subject: [mg54143] Problems with easy simplifications
  • From: Antonio González <gonferh2o at>
  • Date: Fri, 11 Feb 2005 03:34:47 -0500 (EST)
  • Sender: owner-wri-mathgroup at

I have found some weird behaviors of Mathematica (5.0) related to the 
simplifications of easy expressions.

Take, for instance the function

   H[x_, a_, b_] = If[x < a, a + b, a - b]

If I try now to evaluate


the result

  If[x < 0, 0 + 0, 0 - 0]

(the values of a and b are irrelevat, a similar result is obtained, for 
instance, with a=1, b= 2, or any integer, real or complex values). I 
cannot force (at least in a simple way) Mathematica to make the addition 
or the substraction. The action of Simplify or FullSimplify leaves the 
expression unchanged while a Map of Simplify

   MapAll[Simplify, H[x, 0, 0]]


   If[x < 0,
     Simplify[Simplify[0] + Simplify[0]], Simplify[Simplify[
       0] + Simplify[Simplify[-1] Simplify[0]]]]

Something even worse happens if a use values already defined. For instance

   c = 0; d = 0; H[x_] = If[x < c, c + d, c - d]


  If[x < 0, c + d, c - d]

In this case, the addition is not necessary.

   c = 0; d = 0; H[x_] = If[x < c, c, d]

leads to

  If[x < 0, c, d]

Similar problems arise using the function Which.

Any explanation or help with this malfunction would be welcome.



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