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 as ... Read More

To evaluate a 3-D Hermite_e series on the Cartesian product of x, y and z, use the hermite_e.hermegrid3d(x, y, z, c) method in Python. The method returns the values of the two dimensional polynomial at points in the Cartesian product of x, y and z.The parameters are x, y, z. The three dimensional series is evaluated at the points in the Cartesian product of x, y, and z. If 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 as ... Read More

To evaluate a 3-D Hermite_e series on the Cartesian product of x, y and z, use the hermite.hermegrid3d(x, y, z, c) method in Python. The method returns the values of the three dimensional polynomial at points in the Cartesian product of x, y and z.The parameters are x, y, z. The three dimensional series is evaluated at the points in the Cartesian product of x, y, and z. If 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 as ... Read More

To evaluate a 2-D Hermite_e series on the Cartesian product of x and y, use the hermite_e.hermegrid2d(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 parameters are x, y. The 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 parameter, c is an ... Read More

To differentiate a Hermite_e series, use the hermite_e.hermeder() method in Python. The 1st parameter, c is an array of Hermite_e series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.The 2nd parameter, m is the number of derivatives taken, must be non-negative. (Default: 1). The 3rd parameter, scl is a scalar. Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is for use in a linear change of variable. (Default: 1). The 4th parameter, axis is an Axis over which the ... Read More

To differentiate a Hermite_e series, use the hermite_e.hermeder() method in Python. The 1st parameter, c is an array of Hermite_e series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.The 2nd parameter, m is the number of derivatives taken, must be non-negative. (Default: 1). The 3rd parameter, scl is a scalar. Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is for use in a linear change of variable. (Default: 1). The 4th parameter, axis is an Axis over which the ... Read More

To multiply a Chebyshev series by an independent variable, use the polynomial.chebyshev.chebmulx() method in Python Numpy. The method returns an array representing the result of the multiplication. 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 an array −x = np.array([1, 2, 3]) Display the array −print("Our Array...", x)Check the Dimensions −print("Dimensions of our Array...", x.ndim) Get the Datatype −print("Datatype of our Array object...", x.dtype)Get the Shape −print("Shape of our Array object...", x.shape) To multiply a Chebyshev ... Read More

To subtract one Chebyshev series to another, use the polynomial.chebyshev.chebsub() method in Python Numpy. The method returns an array Of Chebyshev series coefficients representing their difference. Returns the difference of two Chebyshev series c1 - c2. The sequences of coefficients are from lowest order term to highest, i.e., [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 = np.array([1, ... Read More

To add one Chebyshev series to another, use the polynomial.chebyshev.chebadd() method in Python Numpy. The method returns an array representing the Chebyshev series of their sum. Returns the sum of two Chebyshev series c1 + c2. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [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

To remove small trailing coefficients from a polynomial, use the polynomial.polytrim() method in Python Numpy. The method returns a 1-d array with trailing zeros removed. If the resulting series would be empty, a series containing a single zero is returned.The “Small” means “small in absolute value” and is controlled by the parameter tol; “trailing” means highest order coefficient(s), e.g., in [0, 1, 1, 0, 0] (which represents 0 + x + x**2 + 0*x**3 + 0*x**4) both the 3-rd and 4-th order coefficients would be “trimmed”. The parameter c is a 1-d array of coefficients, ordered from lowest order to ... Read More