Groups > comp.soft-sys.math.mathematica > #2824

Even and Odd functions

From	yitzhakbg <yitzhakbg@gmail.com>
Newsgroups	comp.soft-sys.math.mathematica
Subject	Even and Odd functions
Date	2011-05-31 11:48 +0000
Organization	Steven M. Christensen and Associates, Inc and MathTensor, Inc.
Message-ID	<is2ki5$qqa$1@smc.vnet.net> (permalink)

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Applying makeper makes the piecewise functions x and y periodic, yet they don't appear as even and odd functions whereas the Sin and Cos functions do show as odd and even.
xx and yy are the functions which fail the even/odd test yet show as even and odd according to the plots.
I couldn't determine why. Help appreciated.


ClearAll[x, y, xx, yy, makeper]

x[t_] := Piecewise[{{-1, -1/2 <= t < 0}, {1, 0 <= t < 1/2}}]
y[t_] := Piecewise[{{-t - 1/4, -1/2 <= t < 0}, {t - 1/4, 0 <= t < 1/2}}]

makeper[f_, p_, d_][t_] := f[Mod[t, p, d]]
(* Plot[x@t,{t,-5,5},PlotRange->{-1,1}] *)

xx[t_] := makeper[x, 1, -1/2]@t
yy[t_] := makeper[y, 1, -1/2]@t
Plot[xx[t], {t, -5, 5}, PlotRange -> {-1, 1}]
Plot[yy[t], {t, -5, 5}, PlotRange -> {-1, 1}]
OddFunctionQ[f_] := Module[{x}, f[x] + f[-x] === 0]
EvenFunctionQ[f_] := Module[{x}, f[x] - f[-x] === 0]
fs = {# &, #^3 &, Sin, Cos, xx, yy}
OddFunctionQ /@ fs
{True, True, True, False, False, False}
EvenFunctionQ /@ fs
{False, False, False, True, False, False}

Best,
Yitzhak

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Even and Odd functions yitzhakbg <yitzhakbg@gmail.com> - 2011-05-31 11:48 +0000

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