Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 IsTranscendentalNumber

Source Notebook

Check whether a number is transcendental

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["IsTranscendentalNumber"][n]

returns True if n is a transcendental number and False if n is an algebraic number.

Details and Options

A number is transcendental if it is not a root of any univariate polynomial with integer coefficients. Otherwise, the number is algebraic.
Some numbers are not known to be algebraic or transcendental. In these cases, ResourceFunction["IsTranscendentalNumber"] returns unevaluated.

Examples

Basic Examples (2) 

Check whether 10 is transcendental:

In[1]:=
ResourceFunction["IsTranscendentalNumber"][10]
Out[1]=

Check whether π is transcendental:

In[2]:=
ResourceFunction["IsTranscendentalNumber"][\[Pi]]
Out[3]=

Possible Issues (1) 

Some numbers are not known to be algebraic or transcendental. In these cases, IsTranscendentalNumber returns unevaluated:

In[4]:=
ResourceFunction["IsTranscendentalNumber"][Pi^Pi]
Out[4]=

Publisher

Wolfram|Alpha Math Team

Version History

  • 2.0.0 – 23 March 2023
  • 1.1.0 – 12 May 2021
  • 1.0.0 – 13 March 2020

Related Resources

License Information