numpoly 1.1.4

Polynomials as a numpy datatype

Numpoly is a generic library for creating, manipulating and evaluating arrays of polynomials based on numpy.ndarray objects.

Table of Contents:

• Feature Overview

• Installation

• Example Usage

Feature Overview

• Intuitive interface for users experienced with numpy, as the library provides a high level of compatibility with the numpy.ndarray, including fancy indexing, broadcasting, numpy.dtype, vectorized operations to name a few.

• Computationally fast evaluations of lots of functionality inherent from numpy.

• Vectorized polynomial evaluation.

• Support for arbitrary number of dimensions.

• Native support for lots of numpy.<name> functions using numpy’s compatibility layer (which also exists as numpoly.<name> equivalents).

• Support for polynomial division through the operators /, % and divmod.

• Extra polynomial specific attributes exposed on the polynomial objects like poly.exponents, poly.coefficients, poly.indeterminants etc.

• Polynomial derivation through functions like numpoly.derivative, numpoly.gradient, numpoly.hessian etc.

• Decompose polynomial sums into vector of addends using numpoly.decompose.

• Variable substitution through numpoly.call.

Installation

Installation should be straight forward:

pip install numpoly

Example Usage

Constructing polynomial is typically done using one of the available constructors:

>>> import numpoly
>>> numpoly.monomial(start=0, stop=3, dimensions=2)
polynomial([1, q0, q0**2, q1, q0*q1, q1**2])

It is also possible to construct your own from symbols together with numpy:

>>> import numpy
>>> q0, q1 = numpoly.variable(2)
>>> numpoly.polynomial([1, q0**2-1, q0*q1, q1**2-1])
polynomial([1, q0**2-1, q0*q1, q1**2-1])

Or in combination with numpy objects using various arithmetics:

>>> q0**numpy.arange(4)-q1**numpy.arange(3, -1, -1)
polynomial([-q1**3+1, -q1**2+q0, q0**2-q1, q0**3-1])

The constructed polynomials can be evaluated as needed:

>>> poly = 3*q0+2*q1+1
>>> poly(q0=q1, q1=[1, 2, 3])
polynomial([3*q1+3, 3*q1+5, 3*q1+7])

Or manipulated using various numpy functions:

>>> numpy.reshape(q0**numpy.arange(4), (2, 2))
polynomial([[1, q0],
            [q0**2, q0**3]])
>>> numpy.sum(numpoly.monomial(13)[::3])
polynomial(q0**12+q0**9+q0**6+q0**3+1)