Number Theory Libraries

When I've taught introductory number theory as part of courses on "Discrete Maths" and "Algorithms", I've not found a single library that covers the wide range of topics. As a consequence, my examples use a number of different libraries, which are listed below. They can be obtained separately from the links below or you can download my zipped collection of them all.

Libraries

• The standard Java classes: java.lang.Math, java.math.BigInteger, and java.math.BigDecimal. All the third-party libraries are built atop these classes, which means they can be readily used together.
   
  
• Apache Commons Numbers, which holds the numerical features of Apache Commons Math. I only use about half of the Numbers classes (i.e. combinatorics, core, fractions, and primes).
   
  
• The java-math-library (JML) overlaps with Apache Commons Numbers in many places, but has more support for factoring, gcd, and extra BigInteger and BigDecimal functions. Its main drawback is a lack of online documentation, although I've generated its API documentation, which you can download as a zip file.
   
  
• Big-Math has a large collection of BigDecimal functions, although I've only employed its trigonometry features.
   
  
• An important aspect of teaching number theory is being able to visualize the concepts, and I've employed three libraries in that role: StdDraw, Simple Java Plot, and Console Table. I've described the first two on other pages on this website, while Console Table is a simple (but very useful) class for generating ASCII formatted tables (e.g. see RecipsTable.java). The examples that generate images include "Screenshot" links.
   
  
• Even with all of these libraries, I've still found it necessary to include a small set of my own utilities in Nut.java (Nut is short for "NUmber Theory").
   
  

The examples are separated into several categories, but you may prefer to download all the code as a single zip file.

Special Numbers

Series

Pi

Fractions

Binomials

Modulo

Primes

Ciphers

Utilities

Other Downloads and Links

• Batch files to easily compile and run my code: compile.bat and run.bat
   
  
• All the examples in one zipped file (1.79 MB)
   
  
• My copies of the various libraries (1.92 MB). Unzip the file, and place the libs folder in the same directory as the examples and batch files.
   
  
• JML is a little lacking in online documentation, although the source code includes examples and annotations for the API. My copies of those API documents can be downloaded as a zip file (1.32 MB).
   
  
• Apache Commons Numbers has an excellent user guide, and online documentation. I only use about half of its libraries – combinatorics, core, fractions, and primes – although I'm sure its complex, field, and gamma classes would be useful for more complicated number theory tasks.
   
  
• Big-math's online documentation can be found here. I've only used the trigonometry functions from the BigDecimalMath class.
   
  
• Two great sources for number theory problems are Project Euler and Rosetta Code. Many, many Java solutions for Euler questions can be found at Project Nayuki, along with code written in Haskell, Mathematica, and Python. Rosetta Code can be easily searched; a good starting point is its Prime Numbers category.
   
  
• I'm sometimes asked for a good beginners book on number theory. I recommend Number Theory: A Lively Introduction with Proofs, Applications, and Stories by James E. Pommersheim, Tim K. Marks, and Erica L. Flapan, Wiley, 2010.