Polynomials as a numpy datatype
Project description
Numpoly is a generic library for creating, manipulating and evaluating arrays of polynomials based on numpy.ndarray objects.
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)
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