Crate polynomen

Polynomials Library

Polynomial implementation

• builder from coefficients or roots
• degree
• extend by adding 0 coefficients to higher order terms
• transformation to monic form
• rounding to zero for small coefficients
• coefficient indexing
• zero and unit polynomials
• arithmetic operations between polynomials (addition, subtraction, multiplication, division, reminder, negation)
• arithmetic operations with floats (addition, subtraction, multiplication, division)
• multiplication using fast fourier transform
• polynomial exponentiation
• differentiation and integration
• polynomial evaluation
• evaluation of polynomial ratios that reduces overflows
• greatest common divisor between two polynomials
• polynomial norms (l1, l2, l∞)
• roots finding (real and complex) using eigenvalues of the companion matrix or iterative method

Modules

arithmetic

Arithmetic module for polynomials

Macros

poly

Macro shortcut to crate a polynomial from its coefficients.

Structs

Poly

Polynomial object

Traits

Abs

Absolute value trait

Const

Constants trait

Cos

Cosine of a number trait

Epsilon

Epsilon trait

Inv

Reciprocal of a number trait

Ln

Logarithm of a number trait

Max

Maximum of two numbers trait

NumCast

Type conversion

One

Multiplicative identity trait

Pow

Exponent of a number trait

Sign

Sign of a number trait

Sin

Sine of a number trait

Sqrt

Square root of a number trait

Zero

Additive identity trait

Functions

complex_quadratic_roots

Calculate the complex roots of the quadratic equation x^2 + b*x + c = 0.

eval_poly_ratio

Evaluate the ratio between to polynomials at the given value. This implementation avoids overflow issues when evaluating the numerator and the denominator separately.

real_quadratic_roots

Calculate the real roots of the quadratic equation x^2 + b*x + c = 0.