To generate a pseudo Vandermonde matrix of the Laguerre polynomial with x, y, z sample points, use the laguerre.lagvander3d() in Python Numpy. The parameter, x, y, z returns an 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 a list of maximum degrees of the form [x_deg, y_deg, z_deg].StepsAt first, import the required library −import numpy as np from numpy.polynomial import laguerre as LCreate arrays of point coordinates, all of the same shape using ... Read More

To generate a pseudo Vandermonde matrix of the Laguerre polynomial with x, y, z sample points, use the laguerre.lagvander3d() in Python Numpy. The parameter, x, y, z returns an 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 a list of maximum degrees of the form [x_deg, y_deg, z_deg].StepsAt first, import the required library −import numpy as np from numpy.polynomial import laguerre as LCreate arrays of point coordinates, all of the same shape using ... Read More

To divide one Legendre series by another, use the polynomial.legendre.legdiv() method in Python Numpy. The method returns quo, rem of Legendre series coefficients representing the quotient and remainder.Returns the quotient-with-remainder of two Legendre series c1 / c2. The arguments are sequences of coefficients from lowest order “term” to highest, e.g., [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. The parameters c1 and c2 are 1-D arrays of Legendre series coefficients ordered from low to high.StepsAt first, import the required library −import numpy as np from numpy.polynomial import laguerre as LCreate 1-D arrays of Legendre series coefficients −c1 ... Read More

To multiply one Legendre series from another, use the polynomial.legendre.legmul() method in Python Numpy. The method returns an array representing the Legendre series of their product. Returns the multiplication of two Legendre series c1 * c2. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. The parameters c1 and c2 are 1-D arrays of Legendre series coefficients ordered from low to high.StepsAt first, import the required library −import numpy as np from numpy.polynomial import laguerre as LCreate 1-D arrays of Legendre series coefficients −c1 ... Read More

To multiply the Legendre series c by x, where x is the independent variable, use the polynomial.laguerre.legmulx() method in Python Numpy. The method returns an array representing the result of the multiplication. Returns the difference of two Legendre series c1 - c2. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. The parameter, c is a 1-D array of Legendre series coefficients ordered from low to high.StepsAt first, import the required library −import numpy as np from numpy.polynomial import laguerre as LCreate an array ... Read More

To subtract one Legendre series from another, use the polynomial.legendre.legsub() method in Python Numpy. The method returns an array representing the Legendre series of their sum.Returns the difference of two Legendre series c1 - c2. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. The parameters c1 and c2 are 1-D arrays of Legendre series coefficients ordered from low to high.StepsAt first, import the required library −import numpy as np from numpy.polynomial import laguerre as LCreate 1-D arrays of Legendre series coefficients −c1 = ... Read More

To add one Legendre series to another, use the polynomial.legendre.legadd() method in Python Numpy. The method returns an array representing the Legendre series of their sum.Returns the sum of two Legendre series c1 + c2. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [1, 2, 3] represents the series P_0 + 2*P_1 + 3*P_2. The parameters c1 and c2 are 1-D arrays of Legendre series coefficients ordered from low to high.StepsAt first, import the required library −import numpy as np from numpy.polynomial import laguerre as LCreate 1-D arrays of Legendre series coefficients −c1 = ... Read More

To convert a polynomial to a Laguerre series, use the laguerre.poly2lag() method in Python Numpy. Convert an array representing the coefficients of a polynomial ordered from lowest degree to highest, to an array of the coefficients of the equivalent Laguerre series, ordered from lowest to highest degree.The method returns a 1-D array containing the coefficients of the equivalent Laguerre series. The parameter pol, is a 1-D array containing the polynomial coefficientsStepsAt first, import the required library −import numpy as np from numpy.polynomial import laguerre as LCreate an array using the numpy.array() method −c = np.array([1, 2, 3, 4, 5])Display the ... Read More

To convert a Laguerre series to a polynomial, use the laguerre.lag2poly() method in Python Numpy. Convert an array representing the coefficients of a Laguerre series, ordered from lowest degree to highest, to an array of the coefficients of the equivalent polynomial (relative to the “standard” basis) ordered from lowest to highest degree.The method returns a 1-D array containing the coefficients of the equivalent polynomial ordered from lowest order term to highest. The parameter c, is a 1-D array containing the Laguerre series coefficients, ordered from lowest order term to highest.StepsAt first, import the required library −import numpy as np from ... Read More

To remove small trailing coefficients from Laguerre polynomial, use the laguerre.lagtrim() 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