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
• EigenConst
  Trait that defines the constants used in the Eigen solver.
• 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.