Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
AntonAntonov/
Number
Number Theory utility functions
Contributed by: Anton Antonov
Utility functions for visualizing Number theory relationships and phenomena.
Installation Instructions
To install this paclet in your Wolfram Language environment,
evaluate this code:
PacletInstall["AntonAntonov/NumberTheoryUtilities"]
To load the code after installation, evaluate this code:
Needs["AntonAntonov`NumberTheoryUtilities`"]
Details
The functions TriangleMatrixEmbedding and SpiralEmbedding give data structures for making Klauber triangles and Ulam spirals.
The function SunflowerEmbedding and SunflowerEmbeddingPlot are used to make sunflower embeddings data and visualizations.
SunflowerEmbedding can be given a function that classifies the positive integers into groups.
SunflowerEmbeddingPlot uses those groups to color the corresponding points.
Examples
Basic Examples (3)
Make a Ulam's spiral embedding within a square with 11 rows and columns:
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| Out[1]= |  |
Make a triangular embedding of integers up to 10 triangle rows:
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| Out[2]= |  |
Sunflower embedding of integers up to 2000 with primes shown in red:
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| Out[3]= |  |
Scope (3)
Show Klauber's triangle:
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40] /. {(x_Integer /; ! PrimeQ[x]) :> 0} // Unitize, ImageSize -> Medium, Frame -> False]](https://www.wolframcloud.com/obj/resourcesystem/images/cc0/cc07aad1-4efb-4e8c-aad6-7a02458a2afc/72f8d5ca6a6865a1.png) |
| Out[4]= |  |
Show Ulam's spiral (finishing top-right):
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s2 = s /. {(x_Integer /; ! PrimeQ[x]) :> "."} /. {(x_Integer) :> Style[x, Red]};
Grid[s2]](https://www.wolframcloud.com/obj/resourcesystem/images/cc0/cc07aad1-4efb-4e8c-aad6-7a02458a2afc/3bcd0d9ae47beedd.png) |
| Out[6]= |  |
Show primitive root chord trails plot of 509 for its primitive root 75:
| In[7]:= | ![InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 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| Out[7]= |  |
Publisher
Compatibility
Wolfram Language Version 14.3
External Links
- Primitive roots generation trails
- Number theory neat examples in Raku (Set 1) - YouTube
- Number theory neat examples in Raku (Set 2) - YouTube
- Number theory neat examples in Raku (Set 3) - YouTube