Wolfram Language Paclet Repository

Community-contributed installable additions to the Wolfram Language

AntonAntonov/ NumberTheoryUtilities

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:

In[1]:=
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Out[1]=

Make a triangular embedding of integers up to 10 triangle rows:

In[2]:=
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Out[2]=

Sunflower embedding of integers up to 2000 with primes shown in red:

In[3]:=
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Out[3]=

Scope (3) 

Show Klauber's triangle:

In[4]:=
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PrimeQ[x]) :> 0} // Unitize, ImageSize -> Medium, Frame -> False]
Out[4]=

Show Ulam's spiral (finishing top-right):

In[5]:=
s = 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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PrimeQ[x]) :> "."} /. {(x_Integer) :> Style[x, Red]}; Grid[s2]
Out[6]=

Show primitive root chord trails plot of 509 for its primitive root 75:

In[7]:=
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Out[7]=

Publisher

Anton Antonov

Compatibility

Wolfram Language Version 14.3

Version History

  • 1.0.2 – 26 May 2025
  • 1.0.1 – 26 May 2025
  • 1.0.0 – 26 May 2025

License Information

MIT License

Paclet Source

Source Metadata

See Also