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MathGroup Archive 2006

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Assuming non-integer values in Mathematica simplifications

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71032] [mg71002] Assuming non-integer values in Mathematica simplifications
  • From: vladimir <gpwr9k95 at yahoo.com>
  • Date: Mon, 6 Nov 2006 02:52:30 -0500 (EST)

I just started using Mathematica. I need to simplify the following expressions assuming that w/Pi is not integer (see below). I used the command Element(w/Pi,Rationals] and Element[w/Pi,Reals], but I still get the answer containing If(w/Pi is Integers ...) in many places, making it difficult to extract the answer for non-integer w/Pi. It seems that the simplification commands in Mathematica do not listen to the assumption statements even when such a statement is given within the simplification command. Does anybody know how to tell Mathematice to stop evaluating the integer cases? Thanks in advance.

Here is my expression:

FullSimplify[(Sum[1, {k, 0, n - 1}]*Sum[
            Cos[w*k]*Sin[w*k], {k, 0, n - 1}]*Sum[Sin[w*k]*x[k], {k, 
              0, n - 1}] - Sum[1, {k, 0, n - 1}]*Sum[Cos[w*k]*x[
          k], {k, 0, n - 1}]*Sum[Sin[w*k]^2, {k, 
            0, n - 1}] - Sum[Cos[w*k], {k, 0, 
        n - 1}]*Sum[Sin[w*k], {k, 0, n - 1}]*Sum[Sin[w*k]*x[
            k], {k, 0, n - 1}] - Sum[Cos[w*k]*Sin[w*k], {k, 0, n - 1}]*
          Sum[Sin[w*k], {k, 0, n - 1}]*Sum[x[k], {k, 0, n - 1}] + Sum[Cos[w*
        k], {k, 0, n - 1}]*Sum[x[k], {k, 0, n - 1}]*Sum[Sin[w*k]^2, {k, 0, 
            n - 1}] + Sum[Cos[w*
            k]*x[k], {k, 
              0, n - 1}]*Sum[Sin[w*k], {k, 0, n - 1}]^2)/(-2*Sum[Cos[
            w*k], {k, 0, n - 1}]*Sum[Sin[w*
        k], {k, 0, n - 1}]*Sum[Cos[w*k]*Sin[w*k], {k, 0, 
            n - 1}] + Sum[Sin[w*k], {k, 0,
           n - 1}]^2*Sum[Cos[w*k]^2, {k, 0, n - 1}] + Sum[Cos[w*k]*
          Sin[w*k], {k, 0, n - 1}]^2*Sum[1, {k, 0, n - 1}] + Sum[
        Cos[w*k], {k, 0, n - 1}]^2*
            Sum[Sin[w*k]^2, {k, 0, n - 1}] - Sum[1, {k, 0, n - 
            1}]*Sum[Cos[w*k]^2, {k, 0, n - 1}]*Sum[Sin[w*k]^2, {k, 0, n - 
            1}]), w/Ï? â?? Rationals]


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