numpy.polynomial.chebyshev.
chebfromroots
Generate a Chebyshev series with given roots.
The function returns the coefficients of the polynomial
System Message: WARNING/2 (p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n), )
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in Chebyshev form, where the r_n are the roots specified in roots. If a zero has multiplicity n, then it must appear in roots n times. For instance, if 2 is a root of multiplicity three and 3 is a root of multiplicity 2, then roots looks something like [2, 2, 2, 3, 3]. The roots can appear in any order.
If the returned coefficients are c, then
System Message: WARNING/2 (p(x) = c_0 + c_1 * T_1(x) + ... + c_n * T_n(x) )
The coefficient of the last term is not generally 1 for monic polynomials in Chebyshev form.
Sequence containing the roots.
1-D array of coefficients. If all roots are real then out is a real array, if some of the roots are complex, then out is complex even if all the coefficients in the result are real (see Examples below).
See also
polyfromroots, legfromroots, lagfromroots, hermfromroots, hermefromroots
polyfromroots
legfromroots
lagfromroots
hermfromroots
hermefromroots
Examples
>>> import numpy.polynomial.chebyshev as C >>> C.chebfromroots((-1,0,1)) # x^3 - x relative to the standard basis array([ 0. , -0.25, 0. , 0.25]) >>> j = complex(0,1) >>> C.chebfromroots((-j,j)) # x^2 + 1 relative to the standard basis array([1.5+0.j, 0. +0.j, 0.5+0.j])
