Simplifying Problems

• To: mathgroup at smc.vnet.net
• Subject: [mg22392] Simplifying Problems
• From: "Jordan Rosenthal" <jr at ece.gatech.edu>
• Date: Sun, 27 Feb 2000 18:55:32 -0500 (EST)
• Organization: Georgia Institute of Technology, Atlanta GA, USA
• Sender: owner-wri-mathgroup at wolfram.com

```Hi all,

Two questions:

------------------------
First question:
------------------------
I have an expression which has a sum of a number of sinc-like terms.  For
example,

f[k] = Sin[k Pi] / k

If I try using simplify with the assumption that k is an integer I get

In[2]:=
Simplify[f[k], k \[Element] Integers]

Out[2]=
0

Although this is true for most integers, it is incorrect for the integer
k==0 since f[0] = Pi.  So why is this happening?  I would have expected it
to either leave the expression untouched or to give me an If expression.

What I would like is to be able to convert the expression to

If[ k==0, Pi, 0]

What is the best way to do this?  I can setup a rule like:

f[k] /. Sin[k_*Pi]/k_ -> If[k == 0, Pi, 0]

but my problem is that this does not account for the fact that the pattern
k_ must be an integer.  How do I include that information?  (See my second
question for why I can't just use k_?IntegerQ).

------------------------
Second question:
------------------------
Let's say I declare a variable to be an Integer with

j \[Element] Integers

Now I set up a function which should only work on integers

f[x_?IntegerQ] = x+2

This, however, does not recognize that the variable j has been declared an
integer:

In[3]:=
f[2]

Out[3]=
4

In[4]:=
f[j]

Out[4]=
f[j]

Is there a way I can get the function to work for variables declared as
integers with the Element function?

Any help is appreciated.  Thanks,

Jordan

```

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