DanieleGregori/ GeneralizedRange

(1.0.1) current version: 1.1.0 »

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 • ComplexRange

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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In[2]:=

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Generate a square root range with non-unit step:

In[3]:=

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Scope (3)

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

In[5]:=

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In[6]:=

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AlgebraicRange[ord,{x,y}] is naturally suited for searching possible closed forms through resource function FindClosedForm:

In[7]:=

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In[8]:=

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The built-in function RootApproximant may have difficulty recognizing certain root combinations:

In[9]:=

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In[10]:=

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However, equipping resource function FindClosedForm with AlgebraicRange[x,y,s,options] enables its systematic recognition:

In[11]:=

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