To compute the roots of a polynomials, use the chebyshev.chebroots() method in Python Numpy. The method returns an array of the roots of the series. If all the roots are real, then out is also real, otherwise it is complex. The parameter, c is a 1-D array of 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 series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the ... Read More

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.StepsAt first, import the required library −from numpy.polynomial import chebyshev as CGiven complex roots −j = complex(0, 1)Generate the series −print("Result...", C.chebfromroots((-j, j)))Get the datatype −print("Type...", C.chebfromroots((-j, j)).dtype) Get the shape −print("Shape...", C.chebfromroots((-j, j)).shape)Examplefrom numpy.polynomial import chebyshev as ... Read More

To evaluate a 2-D Hermite series on the Cartesian product of x and y, use the hermite.hermgrid2d(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

Suppose, we are given a grid of dimensions x * y that contains two types of cells, blocked and unblocked. Blocked cells mean that the cells aren't accessible and unblocked means that the cells are accessible. We represent the grid in a 2D array where the blocked cells are given as '#' and the unblocked cells are given as '.'. Now, we have to reach from the cell (0, 0) to cell (x, y). We can perform only two moves, we can either go right of a cell or go down from a cell. We have to keep in mind ... Read More

To evaluate a 2-D Hermite series on the Cartesian product of x and y, use the hermite.hermgrid2d(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 add one Laguerre series to another, use the polynomial.laguerre.lagadd() method in Python Numpy. The method returns an array representing the Laguerre series of their sum.Returns the sum of two Laguerre 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 Laguerre 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 Laguerre series coefficients −c1 = ... Read More

Suppose, a telecom operator has introduced a service called "all-in-one" which provides access to n OTT content providers at a fixed price of k dollars. Now, if we have to subscribe to the OTT platforms directly, we have to pay an individual amount of fee to each of the platforms. We do not need subscriptions to every platform at all months, so we have to find a way to cost-effectively use their services. The starting month in which we need the service of platform i is given in the array start_month and the ending month is given in the array ... Read More

To convert a polynomial to a Hermite series, use the hermite.poly2herm() 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 Hermite series, ordered from lowest to highest degree. The method returns a 1-D array containing the coefficients of the equivalent Hermite 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 hermite as HCreate an array using the numpy.array() method −c = np.array([1, 2, 3, 4, 5]) ... Read More

To convert a Hermite series to a polynomial, use the hermite.herm2poly() method in Python Numpy. Convert an array representing the coefficients of a Hermite 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 (relative to the “standard” basis) ordered from lowest order term to highest. The parameter c, is a 1-D array containing the Hermite series coefficients, ordered from lowest order term to highest.StepsAt first, import the required library ... Read More

To remove small trailing coefficients from Hermite polynomial, use the hermite.hermtrim() 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 ... Read More