multipoly

A multivariate polynomial module.

This package provides a single class, MultiPoly, to handle multivariate polynomials of form

$$ p(\vec{x}) = \sum_{0\leq n\leq\deg(p)}a_n(\vec{x}-\vec{c})^n = \sum_{n_0=0}^{\deg_0(p)}\cdots\sum_{n_{\dim(p)-1}=0}^{\deg_{\dim(p)-1}(p)}a_{n_0\cdots n_{\dim(p)-1}}(x_0-c_0)^{n_0}\cdots(x_{\dim(p)-1}-c_{\dim(p)-1})^{n_{\dim(p)-1}} $$

where $n$ and $\deg(p)$ are multi-indices. This differs from the usual upper sum limit $|n|\leq\deg(p)$ where $n$ is a multi-index and $\deg(p)$ a natural number, because this way the degree in every variable can be controlled individually.

Installation

pip install multipoly

Usage

A polynomial can be initialized in two ways:

• With the constructor Multipoly(a, c=None), that takes the coefficients and optional offsets. The coefficients are of shape deg, that is a tuple with the degree for every variable.
• By fitting data with Multipoly.fit(X, y, deg, c=None).

MultiPoly objects have

• a dimension dim, the number of variables &
• a degree deg, the degrees in its variables.

They can

• be called on a single datapoint p(x, y, ...) or on multiple datapoints in a 2D numpy.array,
• rounded p.round(decimals=0), to round coefficients a and offsets c &
• be converted to strings with toString(symbols=None), where the symbols for its variables can be specified (__str__ defaults to x0, x1, ...).

License (MIT)

Copyright (c) 2023 Sebastian Gössl

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.