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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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