test for "evenness" and "oddness"

• To: mathgroup at yoda.physics.unc.edu
• Subject: test for "evenness" and "oddness"
• From: gray at cmgroup.engr.wisc.edu
• Date: Thu, 21 Jan 93 20:18:29 CST

```I have a number of expression that are functions of some
variable, say x.  I would like to be able to test each of
those functions to see whether they are odd or even in the
variable x and then eliminate (maybe set to zero) those
functions that are even.  I have not been able to find a
Mathematica function that will test for "evenness" or
"oddness" with respect to a variable or variables.  Does
such a function exist?  Is there an easy way to do this?

Thank you.

_/_/_/   _/       _/_/_/  | Gary L. Gray
_/    _/ _/       _/    _/ | Engineering Mechanics & Astronautics
_/       _/       _/        | University of Wisconsin-Madison
_/  _/_/ _/       _/  _/_/   | gray at cmgroup.engr.wisc.edu
_/    _/ _/       _/    _/    | AOL: GLGray
_/_/_/ _/_/_/_/   _/_/_/     | (608) 262-0679

I was asked what type of functions I needed to test.  Here is
an example.  I wish to test this with respect to the variable
"nu".

4      nu omega 2
kd ki omega  Cosh[--------]
2
-(-------------------------------) +
2
(6 k + ki + ki Cosh[nu omega])

4                  nu omega 2
2 ki omega  sno Cos[nu] Cosh[--------]
2
--------------------------------------- +

2
(6 k + ki + ki Cosh[nu omega])

4      nu omega 2
2 cno ki omega  Cosh[--------]  Sin[nu]
2
--------------------------------------- -

2
(6 k + ki + ki Cosh[nu omega])

5
3 cno k ki omega  Cos[nu] Sinh[nu omega]
---------------------------------------- +

3
(6 k + ki + ki Cosh[nu omega])

3
3 cno k ki omega  Cos[nu] Sinh[nu omega]
---------------------------------------- +

2
(6 k + ki + ki Cosh[nu omega])

4      nu omega
Sqrt[ki] kp omega  Csch[--------] Sinh[nu omega]
2
------------------------------------------------ -

2
2 (6 k + ki + ki Cosh[nu omega])

2      nu omega
Sqrt[ki] kp omega  Csch[--------] Sinh[nu omega]
2
------------------------------------------------ +
2 (6 k + ki + ki Cosh[nu omega])

2                  nu omega
Sqrt[ki] omega  sno Cos[nu] Csch[--------] Sinh[nu omega]
2
--------------------------------------------------------- +
6 k + ki + ki Cosh[nu omega]

5
3 k ki omega  sno Sin[nu] Sinh[nu omega]
---------------------------------------- -

3
(6 k + ki + ki Cosh[nu omega])

3
3 k ki omega  sno Sin[nu] Sinh[nu omega]
---------------------------------------- +

2
(6 k + ki + ki Cosh[nu omega])

2      nu omega
cno Sqrt[ki] omega  Csch[--------] Sin[nu] Sinh[nu omega]
2
---------------------------------------------------------
6 k + ki + ki Cosh[nu omega]

As you can see, there are many trig and hyperbolic
functions.

Thank you.

_/_/_/   _/       _/_/_/  | Gary L. Gray
_/    _/ _/       _/    _/ | Engineering Mechanics & Astronautics
_/       _/       _/        | University of Wisconsin-Madison
_/  _/_/ _/       _/  _/_/   | gray at cmgroup.engr.wisc.edu
_/    _/ _/       _/    _/    | AOL: GLGray
_/_/_/ _/_/_/_/   _/_/_/     | (608) 262-0679

```

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