The Dixon elliptic functions cm, sm applied to a real-valued argument x. Both functions are periodic with real period π3 ≈ 5.29991625
In mathematics, the Dixon elliptic functions sm and cm are two elliptic functions (doubly periodic meromorphic functions on the complex plane) that map from each regular hexagon in a hexagonal tiling to the whole complex plane. Because these functions satisfy the identity , as real functions they parametrize the cubic Fermat curve , just as the trigonometric functions sine and cosine parametrize the unit circle .
They were named sm and cm by Alfred Dixon in 1890, by analogy to the trigonometric functions sine and cosine and the Jacobi elliptic functions sn and cn; Göran Dillner described them earlier in 1873.[1]
^Dixon (1890), Dillner (1873). Dillner uses the symbols
and 26 Related for: Dixon elliptic functions information
In mathematics, the Dixonellipticfunctions sm and cm are two ellipticfunctions (doubly periodic meromorphic functions on the complex plane) that map...
In mathematics, the Jacobi ellipticfunctions are a set of basic ellipticfunctions. They are found in the description of the motion of a pendulum (see...
automorphic functions, and functional equations. In 1894 Dixon wrote The Elementary Properties of the EllipticFunctions. Certain ellipticfunctions (meromorphic...
{\displaystyle w=x+yi} and sm and cm are Dixonellipticfunctions. Since there is no elementary expression for these functions, Lee suggests using the 28th degree...
functions Weierstrass elliptic functions Lemniscate elliptic functionsDixonellipticfunctions Fundamental pair of periods Period mapping Jacobi, C. G. J...
Discrete sine transform Dixonellipticfunctions Euler's formula Generalized trigonometry Hyperbolic function Lemniscate ellipticfunctions Law of sines List...
Loewner's torus inequality Hurwitz quaternion Quadratic integer Dixonellipticfunctions Both Surányi, László (1997). Algebra. TYPOTEX. p. 73. and Szalay...
focused on algebra and its application to geometry, ellipticfunctions and hyperelliptic functions. From 1908 onwards he published a series of papers on...
In mathematics, elliptic curve primality testing techniques, or elliptic curve primality proving (ECPP), are among the quickest and most widely used methods...
in turn have many particular special functions as special cases, such as elementary functions, Bessel functions, and the classical orthogonal polynomials...
Computational number theory has applications to cryptography, including RSA, elliptic curve cryptography and post-quantum cryptography, and is used to investigate...
Digital Signature Algorithm) and cyclic subgroups of elliptic curves over finite fields (see Elliptic curve cryptography). While there is no publicly known...
and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing. Not all numbers...
exponent e when given b, c, and m – is believed to be difficult. This one-way function behavior makes modular exponentiation a candidate for use in cryptographic...
family of algorithms adapted to finite fields and to some families of elliptic curves. The algorithm collects relations among the discrete logarithms...
unexpected connection between the monster group M and modular functions, in particular, the j function. The initial numerical observation was made by John McKay...
function (one of the Jacobi ellipticfunctions) and δ {\textstyle \delta } is a constant of integration reflecting the initial position. The elliptic...
ISBN 978-3-7643-9893-4. (Graves 1845) Cayley, Arthur (1845), "On Jacobi's Ellipticfunctions, in reply to the Rev. Brice Bronwin; and on Quaternions", Philosophical...
Huang presented an errorless (but expected polynomial-time) variant of the elliptic curve primality test. Unlike the other probabilistic tests, this algorithm...
generalized by elliptic hypergeometric series. A series xn is called hypergeometric if the ratio of successive terms xn+1/xn is a rational function of n. If...
and John Brillhart in 1975. The continued fraction method is based on Dixon's factorization method. It uses convergents in the regular continued fraction...
data collection phase. Another method that has some acceptance is the elliptic curve method (ECM). In practice, a process called sieving is typically...
smooth number and such functions are useful because their decomposition can be found relatively fast. The set of those functions S = { g ( x ) ∈ F p [...
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