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pypoly - Python Polynomial Module

David John Wilson

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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 or email me developer [at]


A Python module for manipulating polynomials symbolically and numerically.



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