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Diffie–Hellman key exchange
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supercomputers. The simplest and the original implementation, later formalized as Finite Field Diffie-Hellman in RFC 7919, of the protocol uses the multiplicative groupBateman–Horn conjecture (1,047 words) [view diff] exact match in snippet view article find links to article
x)^{2}}}.} When the integers are replaced by the polynomial ring F[u] for a finite field F, one can ask how often a finite set of polynomials fi(x) in F[u][x]Wedderburn's little theorem (1,293 words) [view diff] exact match in snippet view article find links to article
group of a finite field is trivial. In fact, this characterization immediately yields a proof of the theorem as follows: let k be a finite field. Since the57-cell (334 words) [view diff] exact match in snippet view article find links to article
projective special linear group of the 2-dimensional vector space over the finite field of 19 elements, L2(19). It has Schläfli type {5,3,5} with 5 hemi-dodecahedral11-cell (330 words) [view diff] exact match in snippet view article find links to article
projective special linear group of the 2-dimensional vector space over the finite field with 11 elements L2(11). It was discovered in 1977 by Branko GrünbaumArithmetic zeta function (1,561 words) [view diff] exact match in snippet view article find links to article
spectrum of a finite field with q elements, then ζX(s)=11−q−s.{\displaystyle \zeta _{X}(s)={\frac {1}{1-q^{-s}}}.} For a variety X over a finite field, it isBehrend's trace formula (1,001 words) [view diff] exact match in snippet view article find links to article
Grothendieck–Lefschetz trace formula to a smooth algebraic stack over a finite field conjectured in 1993 and proven in 2003 by Kai Behrend. Unlike the classicalLanglands dual group (936 words) [view diff] exact match in snippet view article find links to article
absolute Galois group of the finite field. The dual group G* is then the reductive algebraic group over the finite field associated to the dual root datumWeil group (983 words) [view diff] no match in snippet view article find links to article
In mathematics, a Weil group, introduced by Weil (1951), is a modification of the absolute Galois group of a local or global field, used in class fieldWeil group (983 words) [view diff] no match in snippet view article find links to article
In mathematics, a Weil group, introduced by Weil (1951), is a modification of the absolute Galois group of a local or global field, used in class fieldModuli stack of principal bundles (800 words) [view diff] exact match in snippet view article find links to article
In algebraic geometry, given a smooth projective curve X over a finite field Fq{\displaystyle \mathbf {F} _{q}} and a smooth affine group scheme G overFeit–Thompson theorem (2,851 words) [view diff] exact match in snippet view article find links to article
underlying set of the finite field of order pq of the form x→axσ+b where a has norm 1 and σ is an automorphism of the finite field, where p and q are distinctEichler–Shimura congruence relation (274 words) [view diff] exact match in snippet view article find links to article
endomorphisms of the Jacobian J0(N)Fp of the modular curve X0N over the finite field Fp. The Eichler–Shimura congruence relation and its generalizations toNilcurve (133 words) [view diff] exact match in snippet view article find links to article
In mathematics, a nilcurve is a pointed stable curve over a finite field with an indigenous bundle whose p-curvature is square nilpotent. Nilcurves wereCipolla's algorithm (2,737 words) [view diff] exact match in snippet view article find links to article
is an odd prime. Here Fp{\displaystyle \mathbf {F} _{p}} denotes the finite field with p{\displaystyle p} elements; {0,1,…,p−1}{\displaystyle \{0,1,\dotsEisenstein sum (292 words) [view diff] exact match in snippet view article find links to article
In mathematics, an Eisenstein sum is a finite sum depending on a finite field and related to a Gauss sum. Eisenstein sums were introduced by EisensteinSquare-free polynomial (1,343 words) [view diff] exact match in snippet view article find links to article
the square-free factorization (see square-free factorization over a finite field). In characteristic zero, a better algorithm is known, Yun's algorithmHermite–Minkowski theorem (141 words) [view diff] exact match in snippet view article find links to article
for any integer N there are only finitely many number fields, i.e., finite field extensions K of the rational numbers Q, such that the discriminant ofSchönhage–Strassen algorithm (4,601 words) [view diff] exact match in snippet view article find links to article
generate numbers in a finite field (for example G F ( 2 n + 1 ) {\displaystyle \mathrm {GF} (2^{n}+1)} ). A root of unity under a finite field GF(r), is an elementMichael O'Nan (313 words) [view diff] case mismatch in snippet view article find links to article
Characterization of the Three-Dimensional Projective Unitary Group over a Finite Field. He was a professor at Rutgers University. In 1976 he found strong evidenceSplitting of prime ideals in Galois extensions (2,515 words) [view diff] exact match in snippet view article find links to article
corresponds to the Frobenius automorphism in the Galois group of the finite field extension Fj /F. In the unramified case the order of DPj is f and IPjConjugacy-closed subgroup (223 words) [view diff] exact match in snippet view article find links to article
also termed as being conjugacy stable. It is a known result that for finite field extensions, the general linear group of the base field is a conjugacy-closedList of irreducible Tits indices (1,109 words) [view diff] exact match in snippet view article find links to article
where D is a central division algebra over k. Special fields: Over a finite field, d = 1; over the reals, d = 1 or 2; over a p-adic field or a number fieldIngleton's inequality (857 words) [view diff] exact match in snippet view article find links to article
it is a necessary condition for representability of a matroid over a finite field. Let M be a matroid and let ρ be its rank function, Ingleton's inequalityK-groups of a field (405 words) [view diff] exact match in snippet view article find links to article
K-theory, the algebraic K-group of a field is important to compute. For a finite field, the complete calculation was given by Daniel Quillen. The map sendingSchwartz–Zippel lemma (2,113 words) [view diff] exact match in snippet view article find links to article
version was shown a year prior to Schwartz and Zippel's result. The finite field version of this bound was proved by Øystein Ore in 1922. Theorem 1 (SchwartzSmooth completion (656 words) [view diff] exact match in snippet view article find links to article
of Dirichlet's unit theorem) Let X be a smooth connected curve over a finite field. Then the units of the ring of regular functions O(X) on X is a finitelyClass formation (2,670 words) [view diff] exact match in snippet view article find links to article
integers (with trivial G-action), and G is the absolute Galois group of a finite field, which is isomorphic to the profinite completion of the integers. LocalZariski's lemma (1,212 words) [view diff] exact match in snippet view article find links to article
generated as an associative algebra over another field k, then K is a finite field extension of k (that is, it is also finitely generated as a vector space)Commuting matrices (1,305 words) [view diff] exact match in snippet view article find links to article
matrices under multiplication is the subgroup of scalar matrices. Fix a finite field Fq{\displaystyle \mathbb {F} _{q}}, let P(n){\displaystyle P(n)} denoteNick Katz (638 words) [view diff] no match in snippet view article find links to article
ISBN 0691123306. Convolution and equidistribution: Sato-Tate theorems for finite-field Mellin transforms. Annals of Mathematical Studies, Princeton 2012. WithAlgebraic Eraser (1,622 words) [view diff] exact match in snippet view article find links to article
number of strands in the braid, q {\displaystyle q} , the size of the finite field F q {\displaystyle \mathbb {F} _{q}} , M ∗ {\displaystyle M_{*}} , theLanczos algorithm (7,580 words) [view diff] no match in snippet view article find links to article
The Lanczos algorithm is an iterative method devised by Cornelius Lanczos that is an adaptation of power methods to find the m{\displaystyle m} "most useful"Jacobian variety (796 words) [view diff] exact match in snippet view article find links to article
(1948) as part of his proof of the Riemann hypothesis for curves over a finite field. The Abel–Jacobi theorem states that the torus thus built is a varietyHitchin's equations (1,350 words) [view diff] exact match in snippet view article find links to article
a completely integrable system whose twisted generalization over a finite field was used by Ngô Bảo Châu in his proof of the fundamental lemma in theSupersingular elliptic curve (2,170 words) [view diff] exact match in snippet view article find links to article
of the curve lies in a quadratic extension of the prime field of K, a finite field of order p2. Suppose E is in Legendre form, defined by the equationArf invariant (3,247 words) [view diff] exact match in snippet view article find links to article
This fact was essentially known to Leonard Dickson (1901), even for any finite field of characteristic 2, and Arf proved it for an arbitrary perfect fieldForney algorithm (721 words) [view diff] exact match in snippet view article find links to article
would be an element of the finite field. The operator · represents ordinary multiplication (repeated addition in the finite field) which is the same as theKey exchange (1,394 words) [view diff] case mismatch in snippet view article find links to article
encryption J. H. Ellis, January 1970. Non-Secret Encryption Using a Finite Field MJ Williamson, January 21, 1974. Thoughts on Cheaper Non-Secret EncryptionDivision polynomials (1,034 words) [view diff] exact match in snippet view article find links to article
E:y2=x3+Ax+B{\displaystyle E:y^{2}=x^{3}+Ax+B} be an elliptic curve over the finite field Fp{\displaystyle \mathbb {F} _{p}}, i.e., A,B∈Fp{\displaystyle A,B\inWronskian (1,446 words) [view diff] exact match in snippet view article find links to article
Wrońskian with differentiation replaced by the Frobenius endomorphism over a finite field. Alternant matrix Vandermonde matrix Peano published his example twicePolynomial method in combinatorics (1,327 words) [view diff] exact match in snippet view article find links to article
Finite Field Kakeya Conjecture using the polynomial method. Finite Field Kakeya Conjecture: Let Fq{\displaystyle \mathbb {F} _{q}} be a finite field withTorsion group (638 words) [view diff] exact match in snippet view article find links to article
groups include the additive group of the ring of polynomials over a finite field, and the quotient group of the rationals by the integers, as well asHigher local field (1,382 words) [view diff] exact match in snippet view article find links to article
the second residue field, and the pattern continues until we reach a finite field. Two-dimensional local fields are divided into the following classes:Conway's Game of Life (6,208 words) [view diff] exact match in snippet view article find links to article
creating ever-larger arrays to hold growing patterns. The Game of Life on a finite field is sometimes explicitly studied; some implementations, such as GollySemistable reduction theorem (547 words) [view diff] exact match in snippet view article find links to article
discrete valuation ring O{\displaystyle {\mathcal {O}}}, then there is a finite field extension L/K{\displaystyle L/K} such that A(L)=A⊗KL{\displaystyle A_{(L)}=A\otimesParity-check matrix (612 words) [view diff] exact match in snippet view article find links to article
GH⊤=P−P=0{\displaystyle GH^{\top }=P-P=0}. Negation is performed in the finite field Fq. Note that if the characteristic of the underlying field is 2 (i.eQUAD (cipher) (868 words) [view diff] exact match in snippet view article
quadratic system S=(Q1, ..., Qm) of m=kn equations in n unknowns over a finite field GF(q). The keystream generation process simply consists in iteratingHilbert's Nullstellensatz (3,811 words) [view diff] exact match in snippet view article find links to article
finitely generated as an associative algebra over a field k, then it is a finite field extension of k (that is, it is also finitely generated as a vector space)Real hyperelliptic curve (2,571 words) [view diff] exact match in snippet view article find links to article
{\displaystyle g\geq 1} . The general formula of Hyperelliptic curve over a finite field K {\displaystyle K} is given by C : y 2 + h ( x ) y = f ( x ) ∈ K [ xSecure multi-party computation (5,864 words) [view diff] exact match in snippet view article find links to article
evaluate each gate. The function is now defined as a "circuit" over a finite field, as opposed to the binary circuits used for Yao. Such a circuit is calledCategorical theory (1,151 words) [view diff] exact match in snippet view article find links to article
of given prime exponent (essentially the same as vector spaces over a finite field) and divisible torsion-free abelian groups (essentially the same as vectorAcrobits (1,229 words) [view diff] case mismatch in snippet view article find links to article
S256 (SHA-2 256-bit) Key Agreement: DH3k (Finite Field Diffie-Hellman with 3072-bit Prime) DH2k (Finite Field Diffie-Hellman with 2048-bit Prime) PrshCarus Mathematical Monographs (734 words) [view diff] case mismatch in snippet view article find links to article
by Ezra Brown and Richard K. Guy, 2020, ISBN 978-1-4704-5279-7 The Finite Field Distance Problem, by David J. Covert, 2021, ISBN 978-1-4704-6031-0 CarusElliptic divisibility sequence (1,565 words) [view diff] exact match in snippet view article find links to article
finite field Fq, or more generally over any field, is a sequence of elements of that field satisfying the EDS recursion. An EDS over a finite field isCohomology (6,691 words) [view diff] exact match in snippet view article find links to article
the degree of the polynomial alone. When considering varieties over a finite field, or a field of characteristic p {\displaystyle p} , more powerful toolsAdele ring (18,442 words) [view diff] exact match in snippet view article find links to article
Weil that G {\displaystyle G} -bundles on an algebraic curve over a finite field can be described in terms of adeles for a reductive group G {\displaystyleMonodromy (1,459 words) [view diff] exact match in snippet view article find links to article
of the polynomial ring F[x]. An element y = f(x) of F(x) determines a finite field extension [F(x) : F(y)]. This extension is generally not Galois but hasAlgebraic group (2,240 words) [view diff] exact match in snippet view article find links to article
n!} , and the number of elements of the general linear group over a finite field is (up to some factor) the q-factorial [ n ] q ! {\displaystyle [n]_{q}Probabilistically checkable proof (1,237 words) [view diff] exact match in snippet view article find links to article
Linear PCP is a PCP in which the proof is a vector of elements of a finite field π ∈ F n {\displaystyle \pi \in \mathbb {F} ^{n}} , and such that theEamonn O'Brien (mathematician) (740 words) [view diff] exact match in snippet view article
solve the following problem: given a list of invertible matrices over a finite field, determine the composition series of the group. Implementations of algorithmsFantastic Voyage II: Destination Brain (802 words) [view diff] exact match in snippet view article find links to article
miniaturization is achieved by reducing the value of the Planck constant within a finite field, which it claims is the only conceivable way to do it. However, in reducingCohomological dimension (1,000 words) [view diff] exact match in snippet view article find links to article
non-zero characteristic p has p-cohomological dimension at most 1. Every finite field has absolute Galois group isomorphic to Z^{\displaystyle \mathbf {\hatCompactness theorem (1,948 words) [view diff] exact match in snippet view article find links to article
→ F n {\displaystyle F^{n}\to F^{n}} where F {\displaystyle F} is a finite field or the algebraic closure of such a field. A second application of theSubatomic particle (3,133 words) [view diff] no match in snippet view article find links to article
331–343. doi:10.1007/978-1-4684-5386-7_18 – via Springer Link. The finite-field model of the photon is both a particle and a wave, and hence we referTheorem of Bertini (858 words) [view diff] exact match in snippet view article find links to article
and there are infinitely many smooth hyperplane sections in X. Over a finite field, the above open subset may not contain rational points and in generalJames Milne (mathematician) (463 words) [view diff] exact match in snippet view article
constant abelian varieties over function fields in one variable over a finite field. He also gave the first examples of nonzero abelian varieties with finiteAndré plane (492 words) [view diff] exact match in snippet view article find links to article
are also André planes. Let F = G F ( q ) {\displaystyle F=GF(q)} be a finite field, and let K = G F ( q n ) {\displaystyle K=GF(q^{n})} be a degree n {\displaystyleQuadratic residue code (891 words) [view diff] exact match in snippet view article find links to article
There is a quadratic residue code of length p {\displaystyle p} over the finite field G F ( l ) {\displaystyle GF(l)} whenever p {\displaystyle p} and l {\displaystyleVerschiebung operator (287 words) [view diff] exact match in snippet view article find links to article
abelian group scheme. If G is the discrete group with n elements over the finite field Fp of order p, then the Frobenius homomorphism F is the identity homomorphismRouché–Capelli theorem (661 words) [view diff] exact match in snippet view article find links to article
system of linear equations admits infinitively many solutions, if K is a finite field, the number of solutions is finite, namely | K | n − r a n k ( A ) {\displaystyleTate conjecture (1,172 words) [view diff] exact match in snippet view article find links to article
from a smooth projective surface onto a smooth projective curve over a finite field. Suppose that the generic fiber F of f, which is a curve over the functionRandom self-reducibility (911 words) [view diff] exact match in snippet view article find links to article
discussion below considers the case where the matrix entries are drawn from a finite field Fp for some prime p, and where all arithmetic is performed in that fieldAlgebraic matroid (700 words) [view diff] exact match in snippet view article find links to article
are not linear; indeed the non-Pappus matroid is algebraic over any finite field, but not linear and not algebraic over any field of characteristic zeroGrothendieck–Katz p-curvature conjecture (836 words) [view diff] exact match in snippet view article find links to article
modulo p should also have a full set of algebraic solutions, over the finite field with p elements. Grothendieck's conjecture is that these necessary conditionsGalois module (1,920 words) [view diff] exact match in snippet view article find links to article
with bona fide Artin representations. These are representations over a finite field of characteristic ℓ. They often arise as the reduction mod ℓ of an ℓ-adicP-group (2,753 words) [view diff] exact match in snippet view article find links to article
described in other terms as group UT(3,p) of unitriangular matrices over finite field with p elements, also called the Heisenberg group mod p. For p = 2, bothProjective orthogonal group (1,874 words) [view diff] exact match in snippet view article find links to article
replaced by the Dickson invariant. The projective orthogonal group over a finite field is used in the construction of a family of finite simple groups of LieValentiner group (523 words) [view diff] exact match in snippet view article find links to article
spanned by (001111), (111100), and (0101ωω), where the elements of the finite field F4 are 0, 1, ω, ω. The group PGL3(F4) acts on the 2-dimensional projectiveAbelian group (5,288 words) [view diff] exact match in snippet view article find links to article
comprising a vector space of dimension n {\displaystyle n} over the finite field of p {\displaystyle p} elements F p {\displaystyle \mathbb {F} _{p}}Alfred Menezes (811 words) [view diff] exact match in snippet view article find links to article
1007/3-540-49162-7_12 "Reducing elliptic curve logarithms to logarithms in a finite field" (with T. Okamoto and S. Vanstone), IEEE Transactions on InformationKey size (3,205 words) [view diff] case mismatch in snippet view article find links to article
largest RSA key publicly known to be cracked is RSA-250 with 829 bits. The Finite Field Diffie-Hellman algorithm has roughly the same key strength as RSA forRichard Lipton (1,640 words) [view diff] exact match in snippet view article find links to article
x n ) {\displaystyle f(x_{1},\dots ,x_{n})} is a polynomial over a finite field of size q with q > deg(ƒ) + 1. Then ƒ is randomly testable of order deg(ƒ)Security level (1,360 words) [view diff] case mismatch in snippet view article find links to article
Comparable Algorithm Strengths Security Bits Symmetric Key Finite Field/Discrete Logarithm (DSA, DH, MQV) Integer Factorization (RSA) Elliptic Curve (ECDSAKummer theory (1,891 words) [view diff] exact match in snippet view article find links to article
the Galois group, π is the Frobenius map minus the identity, and C the finite field of order p. Taking A to be a ring of truncated Witt vectors gives Witt'sRandomized algorithm (4,173 words) [view diff] exact match in snippet view article find links to article
algorithm for efficiently computing the roots of a polynomial over a finite field. In 1977, Robert M. Solovay and Volker Strassen discovered a polynomial-timeHardy space (4,171 words) [view diff] exact match in snippet view article find links to article
Gundy & Silverstein 1971). In this example, Ω = [0, 1] and Σn is the finite field generated by the dyadic partition of [0, 1] into 2n intervals of lengthOrchard-planting problem (768 words) [view diff] exact match in snippet view article find links to article
of the problem, the n points lie in a projective plane defined over a finite field.(Padmanabhan & Shukla 2020). The Handbook of Combinatorics, edited byNoel Hush (538 words) [view diff] no match in snippet view article find links to article
Nationality Australian, UK Known for Electron transfer, molecular electronics, finite-field response Awards Fellow of the Royal Society (FRS) (1988) Centenary MedalLefschetz fixed-point theorem (1,483 words) [view diff] exact match in snippet view article find links to article
fixed-point theorem. Let X {\displaystyle X} be a variety defined over the finite field k {\displaystyle k} with q {\displaystyle q} elements and let X ¯ {\displaystyleForward secrecy (2,899 words) [view diff] exact match in snippet view article find links to article
which ensures forward secrecy by leaving ephemeral Diffie–Hellman (finite field and elliptic curve variants) as the only remaining key exchange mechanismPythagorean field (1,044 words) [view diff] exact match in snippet view article find links to article
angles of a triangle is at least π. This theorem states that if E/F is a finite field extension, and E is Pythagorean, then so is F. As a consequence, no algebraicSO(8) (1,090 words) [view diff] exact match in snippet view article
S3 which may also be considered as the general linear group over the finite field with two elements, S3 ≅GL(2,2)). When one quotients Spin(8) by one centralSouth Westphalia University of Applied Sciences (475 words) [view diff] case mismatch in snippet view article find links to article
Decentralized Power Supply Digital Audio Broadcasting Digital Signal Processing Finite Field Calculations Fuzzy Technology Gerontotechnology Integrated Supply ChainElliptic curve only hash (1,753 words) [view diff] exact match in snippet view article find links to article
to be NP-hard). More formally: Let F{\displaystyle \mathbf {F} } be a finite field, E{\displaystyle E} be an elliptic curve with Weierstrass equation havingWeyl group (3,258 words) [view diff] exact match in snippet view article find links to article
is n!, and the number of elements of the general linear group over a finite field is related to the q-factorial [ n ] q ! {\displaystyle [n]_{q}!} ; thusCartan subalgebra (2,026 words) [view diff] exact match in snippet view article find links to article
construct a Cartan subalgebra is by means of a regular element. Over a finite field, the question of the existence is still open.[citation needed] For aPurely inseparable extension (1,280 words) [view diff] exact match in snippet view article find links to article
occur in the context of multiplication by p on an elliptic curve over a finite field of characteristic p. If the characteristic of a field F is a (non-zero)Principal ideal ring (1,282 words) [view diff] exact match in snippet view article find links to article
quotient of a principal ring, is itself a principal ring. 6. Let k be a finite field and put A = k [ x , y ] {\displaystyle A=k[x,y]} , m = ⟨ x , y ⟩ {\displaystylePrincipal ideal ring (1,282 words) [view diff] exact match in snippet view article find links to article
quotient of a principal ring, is itself a principal ring. 6. Let k be a finite field and put A = k [ x , y ] {\displaystyle A=k[x,y]} , m = ⟨ x , y ⟩ {\displaystyleKolakoski sequence (1,419 words) [view diff] exact match in snippet view article find links to article
"Substitution automata, functional equations and "functions algebraic over a finite field"". Papers in algebra, analysis and statistics (Hobart, 1981). ContemporaryMalcolm J. Williamson (483 words) [view diff] case mismatch in snippet view article find links to article
Williamson's January 1974 internal GCHQ note "Non-Secret Encryption Using a Finite Field" (A couple of typos in this pdf: Extended Euclidean Algorithm modulusFinitely generated algebra (1,075 words) [view diff] exact match in snippet view article find links to article
is generated over K by a single element, t, as a field. If E/F is a finite field extension then it follows from the definitions that E is a finitely generatedPolar space (681 words) [view diff] exact match in snippet view article find links to article
q)} be the projective space of dimension n{\displaystyle n} over the finite field Fq{\displaystyle \mathbb {F} _{q}} and let f{\displaystyle f} be a reflexiveShor's algorithm (5,686 words) [view diff] case mismatch in snippet view article find links to article
to break public-key cryptography schemes, such as The RSA scheme The Finite Field Diffie-Hellman key exchange The Elliptic Curve Diffie-Hellman key exchangeDART radiative transfer model (1,163 words) [view diff] exact match in snippet view article find links to article
JSTARS-2014-00702.R1, in press. Simulating images of passive sensors with finite field of view by coupling 3-D radiative transfer model and sensor perspectiveWeierstrass point (1,058 words) [view diff] exact match in snippet view article find links to article
example of non-classical curves. These are projective curves defined over finite field GF(q2){\displaystyle GF(q^{2})} by equation yq+y=xq+1{\displaystyle y^{q}+y=x^{q+1}}Commitment scheme (7,696 words) [view diff] exact match in snippet view article find links to article
1 {\displaystyle \mathbb {G} _{1}} might be an elliptic curve over a finite field, as is common in elliptic-curve cryptography. Then, the division assumptionLucas–Lehmer primality test (3,222 words) [view diff] exact match in snippet view article find links to article
\end{aligned}}} where the first equality uses the Binomial Theorem in a finite field, which is (x+y)Mp≡xMp+yMp(modMp){\displaystyle (x+y)^{M_{p}}\equivSourav Pal (1,776 words) [view diff] exact match in snippet view article find links to article
above procedure, the derivative of the KS matrix is obtained using the finite field, and then the density matrix derivative is obtained by a single-stepComplex number (11,600 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \mathbb {R} ,} Q p , {\displaystyle \mathbb {Q} _{p},} and their finite field extensions, including C , {\displaystyle \mathbb {C} ,} are called localAlain M. Robert (288 words) [view diff] exact match in snippet view article find links to article
the rationality of the zeta function of an algebraic variety over a finite field and the theory of p-adic differential equations) and contains numerousHaboush's theorem (1,094 words) [view diff] exact match in snippet view article find links to article
Steinberg representation of G(Fq) of dimension qN. (Here Fq ⊂ K is the finite field of order q.) The Steinberg representation is an irreducible representationPseudorandom generator (1,842 words) [view diff] exact match in snippet view article find links to article
statistical tests consist of all multivariate linear functions over some finite field F{\displaystyle \mathbb {F} }, one speaks of epsilon-biased generatorsSeparable algebra (1,777 words) [view diff] exact match in snippet view article find links to article
is a perfect field – for example a field of characteristic zero, or a finite field, or an algebraically closed field – then every extension of K is separableCorrado de Concini (394 words) [view diff] exact match in snippet view article find links to article
George Lusztig (The mod-2 cohomology of the orthogonal groups over a finite field). In 1975 he was a lecturer (Professore Incaricato) at the UniversityMonstrous moonshine (4,480 words) [view diff] exact match in snippet view article find links to article
order of the monster, there exists a graded vertex algebra over the finite field Fp with an action of the centralizer of an order p element g, such thatJoseph A. Thas (453 words) [view diff] exact match in snippet view article find links to article
Geometries, Oxford University Press 1991 Projective geometry over a finite field and Generalized Polygons in F. Buekenhout Handbook of incidence geometryHomography (3,641 words) [view diff] exact match in snippet view article find links to article
PGL(2, 7) acts on the eight points in the projective line over the finite field GF(7), while PGL(2, 4), which is isomorphic to the alternating group