Class RationalFunction

Rational Function

Instances of this class represent rational functions in a single variable. They can be evaluated like functions.

Rational functions support addition, subtraction, multiplication, and division.

Instance Methods

__add__(self, other)

__call__(self, value)

__coerce__(self, other)

__div__(self, other)

__init__(self, numerator, denominator=[1.0])

__mul__(self, other)

__radd__(self, other)

__rdiv__(self, other)

__repr__(self)

__rmul__(self, other)

__rsub__(self, other)

__sub__(self, other)

(Scientific.Functions.Polynomial.Polynomial, RationalFunction)

divide(self, shift=0)
Returns: a polynomial and a rational function such that the sum of the two is equal to the original rational function.

Numeric.array

poles(self)
Find the poles (zeros of the denominator) by diagonalization of the associated Frobenius matrix.

Numeric.array

zeros(self)
Find the zeros (roots) of the numerator by diagonalization of the associated Frobenius matrix.

Class Variables
	is_rational_function = `1`

Method Details

init(self, numerator, denominator=`[`1.0`]`)
(Constructor)

Parameters:

numerator (Scientific.Functions.Polynomial.Polynomial or list of numbers) - polynomial in one variable, or a list of polynomial coefficients
denominator (Scientific.Functions.Polynomial.Polynomial or list of numbers) - polynomial in one variable, or a list of polynomial coefficients

divide(self, shift=0)

Parameters:

shift (int (non-negative)) - the power of the independent variable by which the numerator is multiplied prior to division

Returns: (Scientific.Functions.Polynomial.Polynomial, RationalFunction)

a polynomial and a rational function such that the sum of the two is equal to the original rational function. The returned rational function's numerator is of lower order than its denominator.

poles(self)

Find the poles (zeros of the denominator) by diagonalization of the associated Frobenius matrix.

Returns: Numeric.array: an array containing the poles

zeros(self)

Find the zeros (roots) of the numerator by diagonalization of the associated Frobenius matrix.

Returns: Numeric.array: an array containing the zeros

Class RationalFunction

__init__(self, numerator, denominator=[1.0]) (Constructor)

divide(self, shift=0)

poles(self)

zeros(self)

init(self, numerator, denominator=`[`1.0`]`)
(Constructor)