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Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Integer
Obtain a spectral basis of a modular number system
Contributed by:
Nikolay Murzin
ResourceFunction["IntegerSpectralBasis"][h] gives the spectral basis of ℤh. |
Details and Options
Examples
Basic Examples (2)
The spectral basis of the integer 12:
| In[1]:= | ![ResourceFunction["IntegerSpectralBasis"][12]](https://www.wolframcloud.com/obj/resourcesystem/images/e6f/e6f75d39-55c0-4290-998f-b547c2145aaa/3c093988ff7e3811.png){kind=small} |
| Out[1]= |  |
The spectral basis of a prime is always {1}:
| In[2]:= | ![ResourceFunction["IntegerSpectralBasis"][Prime[RandomInteger[100]]]](https://www.wolframcloud.com/obj/resourcesystem/images/e6f/e6f75d39-55c0-4290-998f-b547c2145aaa/596434ffe545e66d.png){kind=small} |
| Out[2]= |  |
Properties and Relations (1)
Reconstruct any integer modulo another integer from its spectral decomposition and spectral basis, the former of which is computed by the resource function IntegerSpectralDecomposition:
| In[3]:= | ![Mod[ResourceFunction["IntegerSpectralDecomposition"][-12, 1337] . ResourceFunction["IntegerSpectralBasis"][1337], 1337] == Mod[-12, 1337]](https://www.wolframcloud.com/obj/resourcesystem/images/e6f/e6f75d39-55c0-4290-998f-b547c2145aaa/0c1e7e9cc1fa3b13.png) |
| Out[3]= |  |
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Version History
- 2.0.0 – 15 June 2020
- 1.0.0 – 23 March 2020
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This work is licensed under a Creative Commons Attribution 4.0 International License