Compare Periods over Different Domains
The periodicity properties of a function may differ as it is considered over different domains. The following command compares the period of a function over the integers, reals, and complexes.
Famously, the exponential function has an imaginary period.
Out[3]= | ![](HTMLImages.en/compare-periods-over-different-domains/O_15.png) |
Functions can be periodic over the reals only or integers only as well.
Out[4]= | ![](HTMLImages.en/compare-periods-over-different-domains/O_16.png) |
Out[5]= | ![](HTMLImages.en/compare-periods-over-different-domains/O_17.png) |
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Out[6]= | ![](HTMLImages.en/compare-periods-over-different-domains/O_18.png) |
On the other hand, power functions involving roots of
are periodic over all three domains.
Out[7]= | ![](HTMLImages.en/compare-periods-over-different-domains/O_19.png) |
Out[8]= | ![](HTMLImages.en/compare-periods-over-different-domains/O_20.png) |
It is easy to compare the domains for many different functions.
Out[10]= | ![](HTMLImages.en/compare-periods-over-different-domains/O_21.png) |
Nicely format the results.
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Out[11]//TraditionalForm= |
| ![](HTMLImages.en/compare-periods-over-different-domains/O_22.png) |