Wolfram Language Paclet Repository

Community-contributed installable additions to the Wolfram Language

DanieleGregori/ GeneralizedRange

Create generalized number ranges

Contributed by: Daniele Gregori

This paclet aims to provide various functions for systematically producing numbers with generic features.

Installation Instructions

To install this paclet in your Wolfram Language environment, evaluate this code:
PacletInstall["DanieleGregori/GeneralizedRange"]


To load the code after installation, evaluate this code:
Needs["DanieleGregori`GeneralizedRange`"]

Details

This paclet aims to provide various functions for systematically producing numbers with generic features:

members of rationals, algebraics, transcendentals or complexes;
expressed in terms of constants, special functions or equations;
constrained by bounds, steps or complexity.

Currently hosted functions:

FareyRange
AlgebraicRange
TranscendentalRange
ComplexRange
FormulaComplexity

All the functions provided can be particularly useful as options for the resource function FindClosedForm, enabling it to exhaustively search generic closed forms in terms of arbitrary mathematical functions evaluated on the given ranges.

Paclet Guide

Examples

Basic Examples (2) 

Generate a range of square roots:

In[1]:=
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Out[1]=
In[2]:=
NumberLinePlot[%]
Out[2]=

Generate a range of exponentials:

In[3]:=
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Out[3]=
In[4]:=
NumberLinePlot[%]
Out[4]=

Scope (3) 

Generate a square root range with non-unit step:

In[5]:=
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Out[5]=

An algebraic range with up to 5th-roots:

In[6]:=
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Out[6]=

A transcendental range in terms of logarithms:

In[7]:=
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Out[7]=

A range in terms of E, Pi and ArcCot:

In[8]:=
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Out[8]=

Create a range made of generic algebraic numbers with a nearly uniform numeric values distribution:

In[9]:=
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Out[9]=
In[10]:=
NumberLinePlot[%]
Out[10]=

Applications (1) 

AlgebraicRange and TranscendentalRange are naturally suited for searching possible closed forms through resource function FindClosedForm:

In[11]:=
ResourceFunction["FindClosedForm"][1.05592, BarnesG, "SearchRange" -> Function[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`], 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Out[11]=
In[12]:=
N[%]
Out[12]=
In[13]:=
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Out[13]=
In[14]:=
N[%, 10]
Out[14]=

Publisher

Daniele Gregori

Version History

  • 2.0.0 – 02 June 2026
  • 1.1.0 – 02 March 2026
  • 1.0.1 – 02 March 2026
  • 1.0.0 – 22 October 2025

License Information

MIT License

Paclet Source

See Also