To differentiate a polynomial, use the polynomial.polyder() method in Python Numpy. Return the polynomial coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl (the scaling factor is for use in a linear change of variable). The argument c is an array of coefficients from low to high degree along each axis, e.g., [1, 2, 3] represents the polynomial 1 + 2*x + 3*x**2 while [[1, 2], [1, 2]] represents 1 + 1*x + 2*y + 2*x*y if axis=0 is x and axis=1 is y. The method returns the Polynomial coefficients of the derivative.The ... Read More

To evaluate a 2-D polynomial on the Cartesian product of x and y, use the polynomial.polygrid2d(x, y, c) method in Python. The method returns the values of the two dimensional polynomial at points in the Cartesian product of x and y.The 1st parameter, x and y, are two dimensional series is evaluated at the points in the Cartesian product of x and y. 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 2nd parameter, c ... Read More

To evaluate a 2-D polynomial on the Cartesian product of x and y, use the polynomial.polygrid2d(x, y, c) method in Python. The method returns the values of the two dimensional polynomial at points in the Cartesian product of x and y.The 1st parameter, x and y, are two dimensional series is evaluated at the points in the Cartesian product of x and y. 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 2nd parameter, c is ... Read More

To evaluate a 3-D polynomial at points (x, y, z), use the polynomial.polyval3d() 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 generate a pseudo Vandermonde matrix of the Chebyshev polynomial, use the chebyshev.chebvander() in Python Numpy. The method returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y). The parameter x, y are the arrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays. The parameter, deg is the list of maximum degrees of the form [x_deg, y_deg].StepsAt first, import the required library −import numpy as np from numpy.polynomial import chebyshev as CCreate arrays ... Read More

To evaluate a polynomial specified by its roots at points x, use the polynomial.polyvalfromroots() method in Python Numpy. The 1st parameter is 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 r.The 2nd parameter, r is an array of roots. If r is multidimensional the first index is the root index, while the remaining indices enumerate multiple polynomials. For instance, in the two dimensional case the ... Read More

To generate a monic polynomial with given 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 library −from numpy.polynomial import polynomial as PGenerating a monic polynomial −print("Result...", P.polyfromroots((-1, 0, 1))) Get the datatype −print("Type...", P.polyfromroots((-1, 0, 1)).dtype)Get the shape −print("Shape...", P.polyfromroots((-1, 0, 1)).shape) Examplefrom numpy.polynomial import polynomial as P # To generate a monic polynomial with given roots, use the polynomial.polyfromroots() method ... Read More

To Integrate a polynomial, use the polynomial.polyint() method in Python. Returns the polynomial coefficients c integrated m times from lbnd along axis. At each iteration the resulting series is multiplied by scl and an integration constant, k, is added. The scaling factor is for use in a linear change of variable. The argument c is an array of coefficients, from low to high degree along each axis, e.g., [1, 2, 3] represents the polynomial 1 + 2*x + 3*x**2 while [[1, 2], [1, 2]] represents 1 + 1*x + 2*y + 2*x*y if axis=0 is x and axis=1 is y.The ... Read More

To generate a pseudo Vandermonde matrix of the Chebyshev polynomial, use the chebyshev.chebvander() in Python Numpy. The method returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y).The parameter x, y are the arrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays. The parameter, deg is the list of maximum degrees of the form [x_deg, y_deg].StepsAt first, import the required library −import numpy as np from numpy.polynomial import chebyshev as CCreate arrays of ... Read More

To generate a Vandermonde matrix of the Chebyshev polynomial, use the chebyshev.chebvander() in Python Numpy. The method returns the Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1, ), where The last index is the degree of the corresponding Chebyshev polynomial. The dtype will be the same as the converted x.The parameter, a is Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If x is scalar it is converted to a 1-D array. The parameter, deg is the degree of the resulting matrix.StepsAt ... Read More