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