math.PolyReal

dsp-collection / math/PolyReal

math/PolyReal

Utility routines for real polynomials and fractions of real polynomials.

Polynomial coefficients are stored in arrays ordered in ascending powers.
The associated polynomial has the form:

   a[0]  +  a[1] * x  +  a[2] * x^2  +  ...  + a[n-1] * x^(n-1)  +  a[n] * x^n

An empty array is not allowed. The real number zero ist represented by [0].

For rational algebraic fractions, the coefficients are stored in nested arrays:

[top, bottom]

The associated rational fraction has the form:

( top[0]     +  top[1]    * x  +  top[2]    * x^2  +  ...  top[n-1]    * x^(n-1)  +  top[n]    * x^n ) /
( bottom[0]  +  bottom[1] * x  +  bottom[2] * x^2  +  ...  bottom[m-1] * x^(m-1)  +  bottom[m] * x^m )

Functions

Function	Description
add	Adds two real polynomials.
addFractions	Adds two fractions.
compareEqual	Returns true if two polynomials are equal.
divide	Divides two real polynomials. Returns [quotient, remainder] = [a1 / a2, a1 % a2].
evaluateComplex	Evaluates a real polynomial with a complex argument.
evaluateFractionComplex	Evaluates a rational fraction with a complex argument.
evaluateReal	Evaluates a real polynomial with a real argument.
expand	Computes the coefficients of a polynomial from it's real zeros.
gcd	Returns the monic GCD (greatest common divisor) of two polynomials.
multiply	Multiplies two real polynomials.
multiplyFractions	Multiplies two fractions.
normalizeFraction	Normalizes the coefficients of a rational fraction so that the denominator polynomial is monic.