Polynomial¶

This file contains the Polynomial class, created to quick and easy access to polynomials.

class fft.polynomial.Polynomial(_list: list)¶

This class represents polynomials as a list of coefficients.

Example

import fft.Polynomial as Poly

# f(x) = 1 + 2x + xx
f = Poly([1, 2, 1])

# The f is callable and will evaluate the polynomial at the input value.
f(3) -> 16.

degreeint: The largest power the variable is raised to in the polynomial.

add(polynomial_1list, polynomial_2list)list: Adds two polynomials and returns the result.
adjust(polynomial_1list, polynomial_2list)list: Adds a buffer so that the two lists representing the polynomials are the same size.
are_equal(polynomial_1list, polynomial_2list)bool: Compares the two input polynomials to check if they are the same.

static add(polynomial_1: list, polynomial_2: list) → list¶

Adds together two input polynomials and returns the result.

Example

# (1 + 2x) + (3 + 2x + 5xx) = 4 + 4x + 5xx
Poly.add([1, 2], [3, 2, 5]) -> [4, 4, 5]

Returns: The sum of the two polynomials.

static adjust(polynomial_1: list, polynomial_2: list) → tuple¶

Insures that polynomials are the same size by adding zeros as buffer.

This function is useful for the add method.

Returns: The two polynomials adjusted to have the same size.

static are_equal(polynomial_1: list, polynomial_2: list) → bool¶

Checks if two polynomials are equal.

Returns: Returns true if the polynomials are equal and false otherwise.

evens()¶: This returns a polynomial whose coefficients correspond to the even powers of x of the polynomial it is run on.

horners_rule(x: complex) → complex¶

Evaluates this polynomial using Horner’s Rule.

Horner’s Rule allows polynomials to be evaluated in linear time, whereas evaluating term by term would have a polynomial time complexity.

Parameters: x – Input to the polynomial.
Returns: The polynomial evaluated at the input.

odds()¶: This returns a polynomial whose coefficients correspond to the run powers of x of the polynomial it is run on.

strip_zeros() → list¶

Removes any terms with coefficient zero from the end of the polynomial.

Returns: The polynomial as a list without trailing zeros.

static strip_zeros_l(polynomials: list) → list¶

Strips zeros from a list of polynomials.

Parameters: polynomials – A list of polynomials.
Returns: The same polynomials with trailing terms with trailing zeros removed.