To compute the roots of a polynomials, use the polynomial.polyroots() method in Python Numpy. The method returns an array of the roots of the polynomial. If all the roots are real, then out is also real, otherwise it is complex. The parameter, c is a 1-D array of polynomial coefficients.The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the power series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value ... Read More

To compute the roots of a polynomials, use the polynomial.polyroots() method in Python Numpy. The method returns an array of the roots of the polynomial. If all the roots are real, then out is also real, otherwise it is complex. The parameter, c is a 1-D array of polynomial coefficients.The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the power series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value ... Read More

To generate a monic polynomial with given complex roots, use the polynomial.polyfromroots() method in Python Numpy. The method returns the 1-D array of the polynomial’s coefficients If all the roots are real, then out is also real, otherwise it is complex. The parameter roots are the sequence containing the roots.StepsAt first, import the required libraries -from numpy.polynomial import polynomial as PGiven complex roots −j = complex(0, 1) print("Result...", P.polyfromroots((-j, j)))Get the datatype −print("Type...", P.polyfromroots((-j, j)).dtype) Get the shape −print("Shape...", P.polyfromroots((-j, j)).shape)Examplefrom numpy.polynomial import polynomial as P # To generate a monic polynomial with given roots, use the polynomial.polyfromroots() method ... Read More

To evaluate a 3-D Chebyshev series at points (x, y, z), use the polynomial.chebval3d() method in Python Numpy. The method returns the values of the multidimensional polynomial on points formed with triples of corresponding values from x, y, and z.The parameters are x, y, z. The three dimensional series is evaluated at the points (x, y, z), where x, y, and z must have the same shape. If any of x, y, or z is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn’t an ndarray it is treated ... Read More

To evaluate a Evaluate a 3-D Chebyshev series at points (x, y, z), use the polynomial.chebval3d() method in Python Numpy. The method returns the values of the multidimensional polynomial on points formed with triples of corresponding values from x, y, and z.The parameters are x, y, z. The three dimensional series is evaluated at the points (x, y, z), where x, y, and z must have the same shape. If any of x, y, or z is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn’t an ndarray it ... Read More

To evaluate a 2-D Chebyshev series at points (x, y), use the polynomial.chebval2d() method in Python Numpy. The method returns the values of the two dimensional Chebyshev series at points formed from pairs of corresponding values from x and y i.e. Parameters, x, y. The two dimensional series is evaluated at the points (x, y), where x and y must have the same shape. If x or y is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.The parameter, c is ... Read More

To evaluate a Chebyshev series at points x, use the chebyshev.chebval(() method in Python Numpy. The 1st parameter, x, if x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x or its elements must support addition and multiplication with themselves and with the elements of c. The 2nd parameter, C, an array of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If c is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the ... Read More

To evaluate a Chebyshev series at points x, use the chebyshev.chebval(() method in Python Numpy. The 1st parameter, x, if x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x or its elements must support addition and multiplication with themselves and with the elements of c.The 2nd parameter, C, an array of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If c is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the coefficients ... Read More

To raise a Chebyshev series to a power, use the chebyshev.chebpow() method in Python Numpy. Returns the Chebyshev series c raised to the power pow. The argument c is a sequence of coefficients ordered from low to high. i.e., [1, 2, 3] is the series T_0 + 2*T_1 + 3*T_2. The method returns the Chebyshev series of power.The parameter, c is a 1-D array of Chebyshev series coefficients ordered from low to high. The parameter, power is a power to which the series will be raised. The parameter, maxpower is the maximum power allowed. This is mainly to limit growth ... Read More

To divide one Chebyshev series by another, use the polynomial.chebyshev.chebdiv() method in Python Numpy. The method returns arrays of Chebyshev series coefficients representing the quotient and remainder.Returns the quotient-with-remainder of two Chebyshev series c1 / c2. The arguments are sequences of coefficients from lowest order “term” to highest, e.g., [1, 2, 3] represents the series T_0 + 2*T_1 + 3*T_2. The parameters c1 and c2 are 1-D arrays of Chebyshev series coefficients ordered from low to high.StepsAt first, import the required libraries -import numpy as np from numpy.polynomial import chebyshev as CCreate 1-D arrays of Chebyshev series coefficients −c1 = ... Read More