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bundles / numpy 2.4.3 / numpy / poly1d

class

numpy:poly1d

source: /numpy/__init__.py

Signature

class poly1d(c_or_r, r = False, variable = None)

Summary

A one-dimensional polynomial class.

Extended Summary

A convenience class, used to encapsulate "natural" operations on polynomials so that said operations may take on their customary form in code (see Examples).

Parameters

c_or_r : array_like

The polynomial's coefficients, in decreasing powers, or if the value of the second parameter is True, the polynomial's roots (values where the polynomial evaluates to 0). For example, poly1d([1, 2, 3]) returns an object that represents , whereas poly1d([1, 2, 3], True) returns one that represents .

r : bool, optional

If True, c_or_r specifies the polynomial's roots; the default is False.

variable : str, optional

Changes the variable used when printing p from x to variable (see Examples).

Examples

import numpy as np
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Construct the polynomial :math:`x^2 + 2x + 3`: 
import numpy as np
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p = np.poly1d([1, 2, 3])
print(np.poly1d(p))
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   2
1 x + 2 x + 3
Evaluate the polynomial at :math:`x = 0.5`: 
p(0.5)
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np.float64(4.25)
Find the roots: 
p.r
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array([-1.+1.41421356j, -1.-1.41421356j])

p(p.r)
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array([4.4408921e-16+0.j, 4.4408921e-16+0.j])
These numbers in the previous line represent (0, 0) to machine precision Show the coefficients: 
p.c
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array([1, 2, 3])
Display the order (the leading zero-coefficients are removed): 
p.order
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2
Show the coefficient of the k-th power in the polynomial (which is equivalent to ``p.c[-(i+1)]``): 
p[1]
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np.int64(2)
Polynomials can be added, subtracted, multiplied, and divided (returns quotient and remainder): 
p * p
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poly1d([ 1,  4, 10, 12,  9])

(p**3 + 4) / p
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(poly1d([ 1.,  4., 10., 12.,  9.]), poly1d([4.]))
``asarray(p)`` gives the coefficient array, so polynomials can be used in all functions that accept arrays: 
p**2 # square of polynomial
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poly1d([ 1,  4, 10, 12,  9])

np.square(p) # square of individual coefficients
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array([1, 4, 9])
The variable used in the string representation of `p` can be modified, using the `variable` parameter: 
p = np.poly1d([1,2,3], variable='z')
print(p)
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   2
1 z + 2 z + 3
Construct a polynomial from its roots: 
np.poly1d([1, 2], True)
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poly1d([ 1., -3.,  2.])
This is the same polynomial as obtained by: 
np.poly1d([1, -1]) * np.poly1d([1, -2])
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poly1d([ 1, -3,  2])

Aliases

  • numpy.poly1d

Referenced by

Other packages