56. plugins.polynomial
— Polynomials¶
This module defines the class Polynomial, representing a polynomial in n variables.

class
plugins.polynomial.
Polynomial
(exp, coeff=None)[source]¶ A polynomial in ndim dimensions.
Parameters:
 exp: (nterms,ndim) int array with the exponents of each of the ndim variables in the nterms terms of the polynomial.
 coeff: (nterms,) float array with the coefficients of the terms. If not specified, all coefficients are set to 1.
Example:
>>> p = Polynomial([(0,0),(1,0),(1,1),(0,2)],(2,3,1,1)) >>> print(p.atoms()) ['1', 'x', 'x*y', 'y**2'] >>> print(p.human()) 2.0 + 3.0*x 1.0*x*y 1.0*y**2 >>> print(p.evalAtoms([[1,2],[3,0],[2,1]])) [[ 1. 1. 2. 4.] [ 1. 3. 0. 0.] [ 1. 2. 2. 1.]] >>> print(p.eval([[1,2],[3,0],[2,1]])) [ 1. 11. 5.]

degrees
()[source]¶ Return the degree of the polynomial in each of the dimensions.
The degree is the maximal exponent for each of the dimensions.

degree
()[source]¶ Return the total degree of the polynomial.
The degree is the sum of the degrees for all dimensions.

evalAtoms1
(x)[source]¶ Evaluate the monomials at the given points
x is an (npoints,ndim) array of points where the polynomial is to be evaluated. The result is an (npoints,nterms) array of values.

evalAtoms
(x)[source]¶ Evaluate the monomials at the given points
x is an (npoints,ndim) array of points where the polynomial is to be evaluated. The result is an (npoints,nterms) array of values.
56.1. Functions defined in module plugins.polynomial¶

plugins.polynomial.
polynomial
(atoms, x, y=0, z=0)[source]¶ Build a matrix of functions of coords.
 atoms: a list of text strings representing a mathematical function of x, and possibly of y and z.
 x, y, z: a list of x (and optionally y, z) values at which the atoms will be evaluated. The lists should have the same length.
Returns a matrix with nvalues rows and natoms colums.

plugins.polynomial.
monomial
(exp, symbol='xyz')[source]¶ Compute the monomials for the given exponents
 exp: a tuple of integer exponents
 symbol: a string of at least the same length as exp
Returns a string representation of a monomial created by raising the symbols to the corresponding exponent.
Example:
>>> monomial((2,1)) 'x**2*y'