DanieleGregori/ GeneralizedRange

Create generalized number ranges

Contributed by: Daniele Gregori

This paclet aims to provide various functions for systematically producing numbers with generic features: - rational, algebraic, transcendental or complex; - expressed in terms of constants, special functions or equations; - constrained by bounds, steps or complexity.

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

***Under construction***

All the functions provided can be particularly useful as options for ResourceFunction["FindClosedForm"], permitting 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 and 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 ResourceFunction["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:

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

In[11]:=

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