75. plugins.polynomial
— Polynomials¶
This module defines the class Polynomial, representing a polynomial in n variables.
75.1. Classes defined in module plugins.polynomial¶
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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.]
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degrees
()[source]¶ Return the degree of the polynomial in each of the dimensions.
The degree is the maximal exponent for each of the dimensions.
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degree
()[source]¶ Return the total degree of the polynomial.
The degree is the sum of the degrees for all dimensions.
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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.
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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.
75.2. 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'