To remove in the future –– numpy.polynomial.chebyshev
This module provides a number of objects (mostly functions) useful for dealing with Chebyshev series, including a Chebyshev
class that encapsulates the usual arithmetic operations. (General information on how this module represents and works with such polynomials is in the docstring for its "parent" sub-package, numpy.polynomial
).
.. autosummary::
:toctree:generated/
Chebyshev
.. autosummary::
:toctree:generated/
chebdomain
chebzero
chebone
chebx
.. autosummary::
:toctree:generated/
chebadd
chebsub
chebmulx
chebmul
chebdiv
chebpow
chebval
chebval2d
chebval3d
chebgrid2d
chebgrid3d
.. autosummary::
:toctree:generated/
chebder
chebint
.. autosummary::
:toctree:generated/
chebfromroots
chebroots
chebvander
chebvander2d
chebvander3d
chebgauss
chebweight
chebcompanion
chebfit
chebpts1
chebpts2
chebtrim
chebline
cheb2poly
poly2cheb
chebinterpolate
The implementations of multiplication, division, integration, and differentiation use the algebraic identities :
$$T_n(x) = \frac{z^n + z^{-n}}{2} \\ z\frac{dx}{dz} = \frac{z - z^{-1}}{2}.$$where
$$x = \frac{z + z^{-1}}{2}.$$These identities allow a Chebyshev series to be expressed as a finite, symmetric Laurent series. In this module, this sort of Laurent series is referred to as a "z-series."
<Unimplemented 'footnote' '.. [1] A. T. Benjamin, et al., "Combinatorial Trigonometry with Chebyshev\n Polynomials," *Journal of Statistical Planning and Inference 14*, 2008\n (https://web.archive.org/web/20080221202153/https://www.math.hmc.edu/~benjamin/papers/CombTrig.pdf, pg. 4)'>
The following pages refer to to this document either explicitly or contain code examples using this.
numpy.polynomial.polyutils
numpy.polynomial
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