pypoly - Python Polynomial Module

David John Wilson

This module is intended to implement basic polynomials in python. They will be entirely symbolic computations wherever possible.

Note, this module will be fairly basic and is intended mainly as a learning exercise. If you wish to do true symbolic computation in Python you should check out SymPy (and think of contributing to the project!).

I am currently working on building this out into a full library. The latest stable version will be in the development branch and the aim will be for full documentation and test coverage (the travis-ci status of this branch will be shown in the badge above). The original code (which was in a sort of pseudo-package) will be kept in the master branch for now.

Description of Package

The package currently defines two classes: DensePoly and SparsePoly. These classes both define polynomials, simply in different representations.

To define a DensePoly you provide an array of coefficients, increasing from the constant coefficient, followed by $$x$$, then $$x^2$$ etc. So to define the polynomial $$5x^2+2x+3$$ you would call DensePoly([3,2,5])

To define a SparsePoly you provide an array of arrays: each inner array provides the degree and coefficient of a term in the polynomial. So to define the polynomial $$7x^6+5x+3$$ you would call SparsePoly([[0,3],[1,5],[6,7]]).

Why is it important to provide two representations? Often some operations for polynomials are easier or more intuitive in a dense representation. However, dense polynomials can quickly become very memory-intensive and inefficient. For example consider the polynomial $$x^1000000-1$$. In sparse format this is straightforward to define: SparsePoly([[0,-1],[1000000,1]]). To define it as a dense polynomial DensePoly(a) the array a would have to have length 1000001 and only the first and last entries would be non-zero.

Available Methods

Currently the following methods are defined for an instance of DensePoly:

• degree()
• printpoly()
• evalpoly(x)
• to_sparse_poly()

The following methods are defined for an instance of SparsePoly:

• degree()
• printpoly()
• evalpoly(x)
• to_dense_poly()
• simplify_poly()
• simplify_poly_inplace()
• equal_poly()
• not_equal_poly()
• copy_poly()
• add_poly()
• negate_poly()
• subtract_poly()
• multiply_poly()
• divide_poly()
• differentiate_poly()
• integrate_poly()
• definite_integral(a, b)
• numeric_solve_poly()
• symbolic_solve_poly()

More information

If you would like more information regarding this package, please visit my website davidjw.co.uk or email me developer [at] davidjw.co.uk.