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Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Integer
Determine the spectral decomposition of an integer in a modular number system
Contributed by:
Nikolay Murzin
ResourceFunction["IntegerSpectralDecomposition"][c,h] gives coefficients of the integer c in the spectral basis of ℤh. |
Details and Options
Examples
Basic Examples (2)
The spectral decomposition of 7 in ℤ12:
| In[1]:= | ![ResourceFunction["IntegerSpectralDecomposition"][7, 12]](https://www.wolframcloud.com/obj/resourcesystem/images/b9c/b9c6b338-29aa-4359-b87c-87d56826aa49/69386fcd2db1f2c5.png){kind=small} |
| Out[1]= |  |
The spectral decomposition of -7 in ℤ15:
| In[2]:= | ![ResourceFunction["IntegerSpectralDecomposition"][-7, 15]](https://www.wolframcloud.com/obj/resourcesystem/images/b9c/b9c6b338-29aa-4359-b87c-87d56826aa49/213555b8678e665f.png){kind=small} |
| Out[2]= |  |
Properties and Relations (2)
Reconstruct an integer modulo another integer from its spectral decomposition using ChineseRemainder:
| In[3]:= | ![Mod[ChineseRemainder[
ResourceFunction["IntegerSpectralDecomposition"][11, 1337], Power @@@ FactorInteger[1337]], 1337]](https://www.wolframcloud.com/obj/resourcesystem/images/b9c/b9c6b338-29aa-4359-b87c-87d56826aa49/6306efbdf8271c7e.png) |
| Out[3]= |  |
Reconstruct an integer modulo another integer from its spectral decomposition and spectral basis, the latter of which is computed by the resource function IntegerSpectralBasis:
| In[4]:= | ![Mod[ResourceFunction["IntegerSpectralDecomposition"][11, 1337] . ResourceFunction["IntegerSpectralBasis"][1337], 1337]](https://www.wolframcloud.com/obj/resourcesystem/images/b9c/b9c6b338-29aa-4359-b87c-87d56826aa49/3748bc051b81edc7.png) |
| Out[4]= |  |
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Version History
- 1.0.0 – 18 March 2020
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License Information
This work is licensed under a Creative Commons Attribution 4.0 International License