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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
To generate a pseudo Vandermonde matrix of the Hermite polynomial, use the hermite.hermvander2d() in Python Numpy. The method returns the pseudo-Vandermonde matrix. The parameter, x, y are an array 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 hermite as HCreate arrays of point coordinates, all of the same shape ... Read More
To generate a pseudo Vandermonde matrix of the Hermite polynomial, use the hermite.hermvander2d() in Python Numpy. The method returns the pseudo-Vandermonde matrix.The parameter, x, y is an array 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 hermite as HCreate arrays of point coordinates, all of the same shape using ... Read More
To generate a Vandermonde matrix of the Hermite polynomial, use the chebyshev.hermvander() in Python Numpy. The method returns the pseudo-Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1, ), where The last index is the degree of the corresponding Hermite polynomial. The dtype will be the same as the converted x.The parameter, x 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 the degree of the resulting ... Read More
A stream cipher is an approaches of encryption where a pseudorandom cipher digit stream is mixed with plain text digits. This pseudorandom cipher digit stream is used to each binary digit, one bit at a time. This approach of encryption uses an infinite number of pseudorandom cipher digits per key.A Stream Cipher can be used for symmetric key cryptography, or when the similar key is used to encrypt and decrypt data. A stream cipher encrypts an arbitrary length of plain text, one bit at a time, with an algorithm that needs a key.For this type of encryption to remain secure, ... Read More
Symmetric key cryptography is a type of encryption scheme in which the similar key is used both to encrypt and decrypt messages. Such an approach of encoding data has been largely used in the previous decades to facilitate secret communication between governments and militaries.Symmetric-key cryptography is called a shared-key, secret-key, single-key, one-key and eventually private-key cryptography. With this form of cryptography, it is clear that the key should be known to both the sender and the receiver that the shared. The complexity with this approach is the distribution of the key.Symmetric key cryptography schemes are usually categorized such as stream ... Read More
There are several algorithms of cryptographic which are as follows −Symmetric key Cryptography − In symmetric key cryptography, an individual key is used for both encryption and decryption. The sender needs the key (or some group of rules) to encrypt the plaintext and sends the cipher text to the receiver. The receiver uses the same key (or ruleset) to decrypt the message and restore the plaintext. Because a single key can be used for both functions, symmetric key cryptography is also known as symmetric encryption.Symmetric key cryptography schemes are frequently categorized such as stream ciphers or block ciphers. Stream ciphers ... Read More
A digital signature is a numerical technique which validates the authenticity and integrity of a message, software or digital files. It enables us to test the author name, date and time of signatures, and authenticate the message contents. The digital signature provides far more inherent security and intended to solve the issue of tampering and impersonation (Intentionally copy another person's characteristics) in digital connection.These techniques are designed to support the digital counterpart to handwritten signatures and can be implemented using cryptography. In entity a digital signature of a message is a number dependant on some secret known only to the ... Read More