numpoly: A Python repository from jonathf

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

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)

Installation

Installation should be straight forward from pip:

pip install numpoly

Alternatively, to get the most current experimental version, the code can be installed from Github as follows:

First time around, download the repository:

git clone git@github.com:jonathf/numpoly.git

Every time, move into the repository:
```
cd numpoly/
```
After the first time, you want to update the branch to the most current version of master:
```
git checkout master
git pull
```
Install the latest version of numpoly with:
```
pip install .
```

Development

Installing numpoly for development can be done from the repository root with the command:

pip install -e .[dev]

The deployment of the code is done with Python 3.10 and dependencies are then fixed using:

pip install -r requirements-dev.txt

Testing

To run test:

pytest --doctest-modules numpoly test docs/user_guide/*.rst README.rst

Documentation

To build documentation locally on your system, use make from the doc/ folder:

cd doc/
make html

Run make without argument to get a list of build targets. All targets stores output to the folder doc/.build/html.

Note that the documentation build assumes that pandoc is installed on your system and available in your path.