How to declare Integers?

• To: mathgroup at smc.vnet.net
• Subject: [mg12966] How to declare Integers?
• From: wexler at einstein.phys.ufl.edu (Carlos Wexler)
• Date: Sun, 28 Jun 1998 02:51:54 -0400
• Organization: University of Florida, Gainesville
• Sender: owner-wri-mathgroup at wolfram.com

```How can one declare a variable to be integer in Mathematica?

Let me just give an example:

Integrate[Sin[m x]/Sin[x], {x,0,Pi}]

is well behaved if one explicitly sets m=1,2,3,... BEFORE doing the
integral:

In[1]:= Integrate[Sin[1 x]/Sin[x], {x,0,Pi}] Out[1]= Pi

In[2]:= Integrate[Sin[2 x]/Sin[x], {x,0,Pi}]  Out[2]= 0

but

In[3]:= Integrate[Sin[m x]/Sin[x], {x,0,Pi}] Out[3]= Integrate::"idiv":
Integral of Csc[x] Sin[m x] does not converge on {0,Pi}

Other examples include evaluation of Sin[m Pi], etc...

I tried the following trick stated in the manual:

In[4]:=	m/: IntegerQ[m] = True
Out[4]= True

but still Sin[m Pi] does not simplify to 0 nor does Mathematica figures
out that the integral above does converge in this case.

How can one declare m to be integer? There has to be a way! In Maple it
is rather easy and the expected behavior is obtained. I cannot believe
that it is not possible to accomplish the same in Mathematica as well.

Thanks!!

Carlos

----------------------------------------------------------------- Carlos
Wexler                     |  Dept. of Physics, Box 118440
|  University of Florida
|  Gainesville, FL 32611-8440
|  Tel: (352) 392-7334
wexler at phys.ufl.edu               |  FAX: (352) 392-0524
-----------------------------------------------------------------

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```

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