apnorton / math

My math library for programming. (In progress...)

Math Repository

This is my repository of Math-related Java code. It is a package that can be imported.

See the docs folder for JavaDoc-generated documentation that lists all current features. To use the documentation, you must have internet connection; currently, the documentation relies on connectivity to the MathJax website to render mathematical forumlae. I will fix this, it's just not on the top of my priority list right now.

Field

I am working towards a generalized linear system solver, slowly but surely. Specifically, I want to be able to row-reduce matrices over arbitrary fields; for example, row reduce over the Rational numbers, or over the Integers modulo 13, etc. Therefore, I have created a Field class; this is as close as I can (currently) reasonably get to the concept of a mathematical field from modern algebra.

Note that my Field class has a generic parameter; this is to specify a general element of the underlying set. To construct a Field object, you need two GroupOperations. A GroupOperation is an iterface that specifies an invertible binary operation that has an identity element.

I will add more documentation for these features; however, with a bit of knowledge of algebra, one can figure out the organization quite easily.

Sequences

One feature of this library with which I am quite happy is the idea of a "Sequence." Essentially, a sequence is an iterable function defined for all integral values. To create a sequence, all one needs to do is extend Sequence and override the get(long n) method. This method should compute and return the value of the sequence at n in an "iterator-friendly" way--this method should be optimized for repeated calls to incrementing values of n.

If you want your sequence to be defined on a particular range of values for n, for example 2 <= n <= 439, set the startIndex and stopIndex fields when you construct your sequence.
It is the responsibility of the your sequence's get method to ensure that no calls are made outside of this range.

As an example of a use-case, consider the following program that prints out all even Fibonacci numbers less than 1000:

public static void main(String[] args) {
  Sequence<Long> fibSeq = new FibonacciSequence();
  
  //Iterate over all Fibonacci numbers that can be represented by a Long
  for (Long f : fibSeq) {
    if (f > 1000) break; //Stop of you pass 1000
    
    //Print out the even ones
    if (f % 2 == 0) 
      System.out.println(f);
  }
}

Important sequences, such as the sequence of prime numbers, the Fibonacci sequence, etc., can be made into classes that extend Sequence, allowing intuitive iteration over all values within a certain range.

To add

• NumberTheory.java
  • phi: Euler's totient
  • fib: Returns list of Fibonacci numbers
• LinearAlgebra.java
  • Performs linear algebra over an arbitrary field
  • row reduction over a field
  • Determinant
  • Eigenvalue?
• Graph.java
• Tree.java
• Matrix.java