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Generate a Chebyshev series with given complex roots in Python
To generate a Chebyshev series with given roots, use the chebyshev.chebfromroots() method in Python Numpy. The method returns 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. The parameter roots are the sequence containing the roots.
Steps
At first, import the required library −
from numpy.polynomial import chebyshev as C
Given complex roots −
j = complex(0,1)
Generate the series −
print("Result...\n",C.chebfromroots((-j, j)))
Get the datatype −
print("\nType...\n",C.chebfromroots((-j, j)).dtype)
Get the shape −
print("\nShape...\n",C.chebfromroots((-j, j)).shape)
Example
from numpy.polynomial import chebyshev as C # To generate a Chebyshev series with given roots, use the chebyshev.chebfromroots() method in Python Numpy. # The method returns 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. # The parameter roots are the sequence containing the roots. j = complex(0,1) print("Result...\n",C.chebfromroots((-j, j))) # Get the datatype print("\nType...\n",C.chebfromroots((-j, j)).dtype) # Get the shape print("\nShape...\n",C.chebfromroots((-j, j)).shape)
Output
Result... [1.5+0.j 0. +0.j 0.5+0.j] Type... complex128 Shape... (3,)
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