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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