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MathGroup Archive 1993

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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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