Real Function Period Computation 

The new function FunctionPeriod can compute the period of a large class of functions, including trigonometric, engineering, exponential, hyperbolic, and special functions.

Trigonometric functions.

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X FunctionPeriod[Sin[2 x] + Cos[3 x], x]

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Engineering functions.

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X FunctionPeriod[TriangleWave[(2 x + 3)/13], x]

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Special functions.

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X FunctionPeriod[Mod[x, 2] + Mod[x, 3], x]

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In[4]:=

X FunctionPeriod[EllipticTheta[1, x, q], x]

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The graph of each function consists of repeating blocks.

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In[5]:=

X Grid[Partition[ MapThread[ Function[{f, p}, Plot[f, {x, 0, 3 p}, MeshFunctions -> {#1/p &}, Mesh -> {Range[3]}, MeshStyle -> None, MeshShading -> {Red, Black}, PlotLabel -> f, ImageSize -> Automatic -> {250, 250/GoldenRatio}]], {{Sin[2 x] + Cos[3 x], TriangleWave[(2 x + 3)/5], Mod[x, 2] + Mod[x, 3], EllipticTheta[1, 5 x/4, 1/3]}, {2 Pi, 13/2, 6, 8 Pi/5}}], 2], Alignment -> Bottom, Spacings -> {Automatic, 2}]

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