poly

A Python package for polynomials.

>>> from poly import polyval
>>> from fractions import Fraction
>>> p = (Fraction(1, 2), Fraction(3, 4))
>>> x = Fraction(5, 6)
>>> polyval(p, x)
Fraction(9, 8)

Installation

pip install git+https://github.com/goessl/poly.git

Usage

This package heavily depends on and is the natural extension of goessl/vector.

Operation	poly	sparse
Creation
\(0\)	`polyzero`	`polyszero`
\(1\)	`polyone`	`polysone`
\(x\)	`polyx`	`polysx`
\(x^n\)	`polymono`	`polymono`
\((x^n)_{n\in\mathbb{N}_0}\)	`polymonos`	`polysmonos`
Uniform random	`polyrand`	`polysrand`
Normal random	`polyrandn`	`polysrandn`
From roots	`polyfromroots`	`polysfromroots`
Utility
Degree	`polydeg`	`polysdeg`
Comparison	`polyeq`	`polyseq`
Trimming	`polytrim`	`polystrim`
Conversion
		`polystod`
		`polydtos`
	`polysympify`	`polyssympify`
	`polyunsympify`	`polysunsympify`
Evaluation
Evaluation	`polyval`	`polysval`
	`polyval_naive`
	`polyval_iterative`
Evaluation of basis	`polyvals`
Evaluation at \(x=0\)	`polyvalzero`	`polysvalzero`
Composition	`polycom`	`polyscom`
	`polycom_naive`
	`polycom_iterative`
	`polycom_horner`
Shift	`polyshift`	`polysshift`
Scale	`polyscale`	`polysscale`
Arithmetic
Positive	`polypos`	`polyspos`
Negation	`polyneg`	`polysneg`
Addition	`polyadd`	`polysadd`
Basis addition	`polyaddc`	`polysaddc`
Subtraction	`polysub`	`polyssub`
Scalar multiplication	`polyscalarmul`	`polysscalarmul`
Scalar true division	`polyscalartruediv`	`polysscalartruediv`
Scalar floor division	`polyscalarfloordiv`	`polysscalarfloordiv`
Scalar mod	`polyscalarmod`	`polysscalarmod`
Scalar divmod	`polyscalardivmod`	`polysscalardivmod`
Multiplication	`polymul`	`polysmul`
	`polymul_naive`	`polysmul_naive`
	`polymul_karatsuba`
Multiplication by \(x\)	`polymulx`	`polysmulx`
Exponentiation	`polypow`	`polyspow`
	`polypow_naive`	`polyspow_naive`
	`polypow_binary`	`polyspow_binary`
Powers of polynomials	`polypows`	`polyspows`
Calculus
Differentiation	`polyder`	`polysder`
Integration	`polyantider`	`polysantider`

Design

Coefficient order

Coefficients are stored in ascending order like every sane person would do.

This ways the coefficient indices correspond to the monomial exponent (or the basis index incase of Hermite polynomials).

The newer numpy.polynomial does it this way, the older numpy.poly1d does it in reverse. sympy also does it the wrong way.

Roadmap

License (MIT)

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.