Package Scientific :: Package Functions :: Module Polynomial :: Class Polynomial

Class Polynomial

Multivariate polynomial

Instances of this class represent polynomials of any order and in any number of variables. The coefficients and thus the values can be real or complex. Polynomials can be evaluated like functions.

Instance Methods

__add__(self, other)

number

__call__(self, *args)
Returns: the value of the polynomial at the given point

__coerce__(self, other)

__div__(self, other)

__init__(self, coefficients)

__mul__(self, other)

__rdiv__(self, other)

__repr__(self)

Polynomial

derivative(self, variable=0)
Returns: a polynomial of reduced order in one variable

Polynomial

integral(self, variable=0)
Returns: a polynomial of higher order in one variable

Numeric.array

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

Class Variables
	is_polynomial = `1`

Method Details

call(self, args)
(Call operator)*

Parameters:

args (tuple of numbers) - tuple of values, one for each variable of the polynomial

Returns: number

the value of the polynomial at the given point

Raises:

TypeError - if the number of arguments is not equal to the number of variable of the polynomial

init(self, coefficients)
(Constructor)

Parameters:

coefficients (Numeric.array or nested list of numbers) - an N-dimnesional array for a polynomial in N variables. coeffcients[i, j, ...] is the coefficient of x_1^i x_2^j ...

derivative(self, variable=0)

Parameters:

variable (int) - the index of the variable with respect to which the derivative is taken

Returns: Polynomial

a polynomial of reduced order in one variable

integral(self, variable=0)

Parameters:

variable (int) - the index of the variable with respect to which the integral is computed

Returns: Polynomial

a polynomial of higher order in one variable

zeros(self)

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

Returns: Numeric.array

an array containing the zeros

Raises:

ValueError - is the polynomial has more than one variable

Note: this is defined only for polynomials in one variable

Class Polynomial

__call__(self, *args) (Call operator)

__init__(self, coefficients) (Constructor)

derivative(self, variable=0)

integral(self, variable=0)

zeros(self)

call(self, args)
(Call operator)*

init(self, coefficients)
(Constructor)