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Find link is a tool written by Edward Betts.Longer titles found: Exponentiation by squaring (view), Modular exponentiation (view), Base (exponentiation) (view), Addition-chain exponentiation (view)

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if μ ≤ π. It will be unique (and equal to π) if and only if μ < π. Exponentiation is given by | X | | Y | = | X Y | , {\displaystyle |X|^{|Y|}=\left|X^{Y}\right|Matrix exponential (9,099 words) [view diff] exact match in snippet view article find links to article

multiplication, hence also exponentiation, of diagonal matrices is equivalent to element-wise addition and multiplication, and hence exponentiation; in particularPrincipal branch (482 words) [view diff] no match in snippet view article find links to article

In mathematics, a principal branch is a function which selects one branch ("slice") of a multi-valued function. Most often, this applies to functions definedGimel function (399 words) [view diff] exact match in snippet view article find links to article

function is used for studying the continuum function and the cardinal exponentiation function. The symbol ℷ {\displaystyle \gimel } is a serif form of theSchanuel's conjecture (1,102 words) [view diff] exact match in snippet view article find links to article

Wilkie, for example, proved that the theory of the real field with exponentiation, ℝexp, is decidable provided Schanuel's conjecture is true. In factPR (complexity) (220 words) [view diff] exact match in snippet view article

decided by such a function. This includes addition, multiplication, exponentiation, tetration, etc. The Ackermann function is an example of a functionRational number (2,595 words) [view diff] no match in snippet view article find links to article

In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominatorCompound Poisson process (810 words) [view diff] no match in snippet view article find links to article

A compound Poisson process is a continuous-time (random) stochastic process with jumps. The jumps arrive randomly according to a Poisson process and theSI derived unit (342 words) [view diff] exact match in snippet view article find links to article

more of the base units, possibly scaled by an appropriate power of exponentiation. The SI has special names for 22 of these derived units (for exampleContinuum hypothesis (3,721 words) [view diff] exact match in snippet view article find links to article

directly only to cardinal exponentiation with 2 as the base, one can deduce from it the values of cardinal exponentiation ℵ α ℵ β {\displaystyle \alephConvergent matrix (1,010 words) [view diff] exact match in snippet view article find links to article

convergent matrix is a matrix that converges to the zero matrix under matrix exponentiation. When successive powers of a matrix T become small (that is, when allItoh–Tsujii inversion algorithm (208 words) [view diff] exact match in snippet view article find links to article

2, the first exponentiation. This is one reason why this algorithm is well-suited for the normal basis, since squaring and exponentiation are relativelyContinuum function (57 words) [view diff] exact match in snippet view article find links to article

\mapsto 2^{\kappa }} , i.e. raising 2 to the power of κ using cardinal exponentiation. Given a cardinal number, it is the cardinality of the power set ofEpsilon numbers (mathematics) (2,163 words) [view diff] exact match in snippet view article

exponentiation starting from ε α + 1 {\displaystyle \varepsilon _{\alpha }+1} (or by base ε α {\displaystyle \varepsilon _{\alpha }} exponentiation startingLebedev–Milin inequality (427 words) [view diff] exact match in snippet view article find links to article

_{k=1}^{n}(k|\alpha _{k}|^{2}-1/k)\right).} See also exponential formula (on exponentiation of power series). Conway, John B. (1995), Functions of One Complex VariableConstant term (497 words) [view diff] exact match in snippet view article find links to article

instead of each variable; thus, eliminating each variable. The concept of exponentiation to 0 can be extended to power series and other types of series, forTrapdoor function (1,064 words) [view diff] exact match in snippet view article find links to article

candidates are the RSA and Rabin families of functions. Both are written as exponentiation modulo a composite number, and both are related to the problem of primeStephen Pohlig (219 words) [view diff] exact match in snippet view article find links to article

concepts of Diffie-Hellman key exchange, including the Pohlig–Hellman exponentiation cipher and the Pohlig–Hellman algorithm for computing discrete logarithmsPhiten (771 words) [view diff] exact match in snippet view article find links to article

represent the golden ratio in the natural world while "Ten" (10) used as an exponentiation base signifies the infinite possibilities at both the micro and macroCantor–Zassenhaus algorithm (1,328 words) [view diff] exact match in snippet view article find links to article

fields (also called Galois fields). The algorithm consists mainly of exponentiation and polynomial GCD computations. It was invented by David G. CantorMatrix analysis (1,119 words) [view diff] exact match in snippet view article find links to article

operations derived from these), functions of matrices (such as matrix exponentiation and matrix logarithm, and even sines and cosines etc. of matrices),Constructive set theory (1,845 words) [view diff] exact match in snippet view article find links to article

} is assumed. The Axiom of Fullness implies CST's Axiom of Exponentiation: Exponentiation: Given two sets, the collection of all total functions fromSpeedcoding (364 words) [view diff] exact match in snippet view article find links to article

pseudo-instructions for common mathematical functions: logarithms, exponentiation, and trigonometric operations. The resident software analyzed pseudo-instructionsLimit ordinal (878 words) [view diff] exact match in snippet view article find links to article

all of these recursive definitions via multiplication, exponentiation, repeated exponentiation, etc. yield limit ordinals. All of the ordinals discussedOrdinal analysis (1,178 words) [view diff] exact match in snippet view article find links to article

arithmetic with induction on Δ0-predicates without any axiom asserting that exponentiation is total. EFA, elementary function arithmetic. IΔ0 + exp, arithmeticSuperfunction (2,647 words) [view diff] exact match in snippet view article find links to article

the function a d d c {\displaystyle ~\mathrm {add_{c}} ~} on C. Exponentiation exp c {\displaystyle \exp _{c}} is superfunction (from 1 to c {\displaystyleExponential map (discrete dynamical systems) (212 words) [view diff] exact match in snippet view article

)} . The only difference is that, due to multi-valued properties of exponentiation, there may be a few select cases that can only be found in one versionBirthday problem (6,459 words) [view diff] no match in snippet view article find links to article

In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of themAngus Macintyre (845 words) [view diff] exact match in snippet view article find links to article

Macintyre has proved many results on the model theory of real and complex exponentiation. With Alex Wilkie he proved the decidability of real exponential fieldsPerplexity (983 words) [view diff] exact match in snippet view article find links to article

perplexity is independent of the base, provided that the entropy and the exponentiation use the same base.) This measure is also known in some domains as theStrength reduction (3,035 words) [view diff] exact match in snippet view article find links to article

replacing a multiplication within a loop with an addition replacing an exponentiation within a loop with a multiplication Most of a program's execution timeLog semiring (1,020 words) [view diff] exact match in snippet view article find links to article

on real numbers, and then take the logarithm to reverse the initial exponentiation. As usual in tropical analysis, the operations are denoted by ⊕ andQuantum Computation Language (445 words) [view diff] exact match in snippet view article find links to article

controlled phase. Quantum algorithms for addition, multiplication and exponentiation (all modulus n) The quantum fourier transform Data types Quantum - quregSuccessor ordinal (259 words) [view diff] exact match in snippet view article find links to article

}(\alpha +\beta )} In particular, S(α) = α + 1. Multiplication and exponentiation are defined similarly. The successor points and zero are the isolatedOrdinal collapsing function (10,038 words) [view diff] exact match in snippet view article find links to article

applying the following functions: ordinal addition, multiplication and exponentiation and the function ψ ↾ α {\displaystyle \psi \upharpoonright _{\alphaAPL (programming language) (8,857 words) [view diff] exact match in snippet view article

assignment, function parameter). Another example of this theme is that exponentiation in APL is written as "2⋆3", which indicates raising 2 to the power 3Elementary function arithmetic (666 words) [view diff] exact match in snippet view article find links to article

The axioms of Robinson arithmetic for 0, 1, +, ×, < The axioms for exponentiation: x0 = 1, xy+1 = xy × x. Induction for formulas all of whose quantifiersCartesian product (2,491 words) [view diff] exact match in snippet view article find links to article

frequently denoted XI. This case is important in the study of cardinal exponentiation. An important special case is when the index set is N {\displaystylePfaffian function (1,501 words) [view diff] exact match in snippet view article find links to article

adds the exponential function to R to get the ordered real field with exponentiation, Rexp, a result known as Wilkie's theorem. Wilkie then tackled the questionConformable matrix (206 words) [view diff] exact match in snippet view article find links to article

have this requirement. Only a square matrix is conformable for matrix exponentiation. Linear algebra Cullen, Charles G. (1990). Matrices and linear transformations239 (number) (487 words) [view diff] exact match in snippet view article

prime with no imaginary part and real part of the form 3n − 1 (with no exponentiation implied). 239 is also a happy number. 239 is the smallest positive integerGraham's number (2,856 words) [view diff] exact match in snippet view article find links to article

enormous size of Graham's number, it may be helpful to express—in terms of exponentiation alone—just the first term (g1) of the rapidly growing 64-term sequenceEuler measure (79 words) [view diff] exact match in snippet view article find links to article

(-1)^{d}} . Measure theory Weisstein, Eric W. "Euler Measure". Euler Measure. Wolfram MathWorld. Retrieved 7 July 2018. Exponentiation and Euler measureTranscendental number theory (2,629 words) [view diff] exact match in snippet view article find links to article

numbers equipped with the operations of addition, multiplication, and exponentiation. Moreover, in this abstract structure Schanuel's conjecture does indeedBachmann–Howard ordinal (310 words) [view diff] exact match in snippet view article find links to article

and Ω, and repeatedly applying ordinal addition, multiplication and exponentiation, and ψ to previously constructed ordinals (except that ψ can only beProVerif (1,226 words) [view diff] exact match in snippet view article find links to article

equivalence. Kusters & Truderung examine protocols with Diffie-Hellman exponentiation and XOR. Smyth, Ryan, Kremer & Kourjieh formalise and analyse verifiabilitySpecial functions (1,360 words) [view diff] exact match in snippet view article find links to article

ambiguity and may lead to confusion. Superscripts may indicate not only exponentiation, but modification of a function. Examples (particularly with trigonometricComplex conjugate (1,731 words) [view diff] exact match in snippet view article find links to article

0\end{aligned}}} Conjugation is commutative under composition with exponentiation to integer powers, with the exponential function, and with the naturalEXPSPACE (593 words) [view diff] exact match in snippet view article find links to article

Exponential space completeness, pp. 313–317. Demonstrates that determining equivalence of regular expressions with exponentiation is EXPSPACE-complete.Stack overflow (899 words) [view diff] exact match in snippet view article find links to article

in these languages. Consider the example below of two simple integer exponentiation functions. Both pow(base, exp) functions above compute an equivalentTransseries (5,720 words) [view diff] exact match in snippet view article find links to article

be convenient for representing functions. Through their inclusion of exponentiation and logarithms, transseries are a strong generalization of the powerPhong reflection model (2,201 words) [view diff] exact match in snippet view article find links to article

infinity. Another approximation that addresses the calculation of the exponentiation in the specular term is the following: Considering that the specularPrincipia Mathematica (9,158 words) [view diff] exact match in snippet view article find links to article

cardinals of different types. PM define addition, multiplication and exponentiation of cardinals, and compare different definitions of finite and infiniteFinSet (283 words) [view diff] exact match in snippet view article find links to article

ordinal sum n + m, and the exponential object is given by the ordinal exponentiation nm. The subobject classifier in FinSet and FinOrd is the same as inAlgebraic-group factorisation algorithm (672 words) [view diff] exact match in snippet view article find links to article

implementation of the PRAC group-exponentiation algorithm which is rather more efficient than the standard binary exponentiation approach. The use of otherExponential backoff (770 words) [view diff] exact match in snippet view article find links to article

'truncated' simply means that after a certain number of increases, the exponentiation stops; i.e. the retransmission timeout reaches a ceiling, and thereafterEgorychev method (1,647 words) [view diff] exact match in snippet view article find links to article

i}}\int _{|z|=\varepsilon }{\frac {1}{(1-z)^{k+1}z^{n-k+1}}}\;dz.} Exponentiation integral n k = k ! 2 π i ∫ | z | = ε exp ( n z ) z k + 1 d z : {\displaystyleCalculator (macOS) (452 words) [view diff] exact match in snippet view article

addition, subtraction, multiplication, and division operations, with exponentiation and the use of the percent sign to denote percentage. "How to ConvertEquinumerosity (1,719 words) [view diff] exact match in snippet view article find links to article

× C) These properties are used to justify cardinal multiplication. Exponentiation: If A ~ B and C ~ D then AC ~ BD. (Here XY denotes the set of all functionsMathematical software (831 words) [view diff] exact match in snippet view article find links to article

perform simple mathematical operations, like addition, multiplication, exponentiation and trigonometry. Data input is typically manual, and the output isCarry-save adder (1,356 words) [view diff] exact match in snippet view article find links to article

Montgomery multiplications saves time but a single one does not. Fortunately exponentiation, which is effectively a sequence of multiplications, is the most commonContext-sensitive language (1,352 words) [view diff] exact match in snippet view article find links to article

problem, say, the set of pairs of equivalent regular expressions with exponentiation. The union, intersection, concatenation of two context-sensitive languagesΨ₀(Ωω) (218 words) [view diff] exact match in snippet view article

{\displaystyle \Omega _{i}} , and is closed under ordinal addition and exponentiation, and contains Ψ j ( ξ ) {\displaystyle \Psi _{j}(\xi )} if j ≥ i andRobotics Toolbox for MATLAB (455 words) [view diff] exact match in snippet view article find links to article

lines, and provides support for Lie group operations such as logarithm, exponentiation, and conversions to and from skew-symmetric matrix form. As the basisList of things named after Leonhard Euler (1,395 words) [view diff] exact match in snippet view article find links to article

derivatives Euler's infinite tetration theorem – About the limit of iterated exponentiation Euler's rotation theorem – In 3D-space, a displacement with a fixedHP-65 (851 words) [view diff] exact match in snippet view article find links to article

inverse, trigonometric (sine, cosine, tangent and their inverses), exponentiation, logarithms and factorial. The HP-65 was one of the first calculatorsSchnorr signature (1,177 words) [view diff] exact match in snippet view article find links to article

{\displaystyle H:\{0,1\}^{*}\rightarrow \mathbb {Z} _{q}} . In the following, Exponentiation stands for repeated application of the group operation JuxtapositionComputational Diffie–Hellman assumption (799 words) [view diff] exact match in snippet view article find links to article

base g {\displaystyle g} ; compute g a b {\displaystyle g^{ab}} by exponentiation: g a b = ( g b ) a {\displaystyle g^{ab}=(g^{b})^{a}} ; So far, computingPoincaré group (2,077 words) [view diff] exact match in snippet view article find links to article

SO+(1, 3), is connected to the identity and is thus provided by the exponentiation exp(iaμPμ) exp(iωμνMμν/2) of this Lie algebra. In component form, theElGamal signature scheme (1,207 words) [view diff] exact match in snippet view article find links to article

digital signature scheme based on the algebraic properties of modular exponentiation, together with the discrete logarithm problem. The algorithm uses aImaginary unit (2,667 words) [view diff] exact match in snippet view article find links to article

carried out with real numbers can also be carried out with i, such as exponentiation, roots, logarithms, and trigonometric functions. All of the followingAdder–subtractor (594 words) [view diff] exact match in snippet view article find links to article

Bitwise ops (0b00) Bitwise operation NOT AND OR Bit shifts Bit manipulation See also Kochanski multiplication (exponentiation) Multiply–accumulate operationECMAScript (2,614 words) [view diff] exact match in snippet view article find links to article

functions, destructuring patterns (of variables), proper tail calls, exponentiation operator ** for numbers, await, async keywords for asynchronous programmingAtlas Autocode (899 words) [view diff] exact match in snippet view article find links to article

a single symbol. For example, the character set had no ↑ symbol, so exponentiation was an overstrike of | and *. The aforementioned underlining of reservedBinary multiplier (2,121 words) [view diff] exact match in snippet view article find links to article

Bitwise ops (0b00) Bitwise operation NOT AND OR Bit shifts Bit manipulation See also Kochanski multiplication (exponentiation) Multiply–accumulate operationCartesian product of graphs (1,102 words) [view diff] exact match in snippet view article find links to article

where the plus sign denotes disjoint union and the superscripts denote exponentiation over Cartesian products. A Cartesian product is vertex transitive ifJava Card (1,734 words) [view diff] exact match in snippet view article find links to article

Development Kit 3.0.5u1 (03.06.2015) Added support for Diffie-Hellman modular exponentiation, Domain Data Conservation for Diffie-Hellman, Elliptic Curve and DSAGell-Mann matrices (1,336 words) [view diff] exact match in snippet view article find links to article

Hermitian (so they can generate unitary matrix group elements through exponentiation), and obey the extra trace orthonormality relation. These propertiesAntenna equivalent radius (849 words) [view diff] exact match in snippet view article find links to article

_{\ell }\ln \vert {\boldsymbol {x}}-{\boldsymbol {y}}\vert \;dx\;dy.} Exponentiation of both side leads to the formula for the equivalent radius. The formulaHP calculators (541 words) [view diff] exact match in snippet view article find links to article

handle floating-point numbers, trigonometric functions, logarithms, exponentiation, and square roots. This new calculator was well received by the customerOrdinal number (6,671 words) [view diff] exact match in snippet view article find links to article

values) are called continuous. Ordinal addition, multiplication and exponentiation are continuous as functions of their second argument. Any well-orderedLogarithmic differentiation (1,589 words) [view diff] exact match in snippet view article find links to article

{\displaystyle f(x)=g(x)^{h(x)}\,\!} The natural logarithm transforms the exponentiation into a product ln ( f ( x ) ) = ln ( g ( x ) h ( x ) ) = h ( x )Station-to-Station protocol (1,189 words) [view diff] exact match in snippet view article find links to article

impact of the session's establishment. In the following explanations, exponentiation (Diffie–Hellman) operations provide the basis for key agreement, thoughLévy hierarchy (715 words) [view diff] exact match in snippet view article find links to article

well-founded relation on y x is finite Ordinal addition and multiplication and exponentiation The rank of a set The transitive closure of a set x is countable |X|≤|Y|Bit numbering (1,652 words) [view diff] exact match in snippet view article find links to article

unsigned number the value of the number can be calculated by using exponentiation with the bit number and a base of 2. The value of an unsigned binaryLimit of a function (6,517 words) [view diff] exact match in snippet view article find links to article

under certain conditions compatible with the algebraic operations and exponentiation. This fact is often called the algebraic limit theorem. The main conditionPaillier cryptosystem (1,677 words) [view diff] exact match in snippet view article find links to article

{n}}} As the original paper points out, decryption is "essentially one exponentiation modulo n 2 {\displaystyle n^{2}} ." A notable feature of the PaillierBit field (1,337 words) [view diff] exact match in snippet view article find links to article

performing power-of-two ((1 << n) evaluates to 2 n {\displaystyle 2^{n}} ) exponentiation, also support the use of the shift operator (<<) in combination withArithmetic logic unit (2,646 words) [view diff] exact match in snippet view article find links to article

Bitwise ops (0b00) Bitwise operation NOT AND OR Bit shifts Bit manipulation See also Kochanski multiplication (exponentiation) Multiply–accumulate operationElliptic Curve Digital Signature Algorithm (3,042 words) [view diff] exact match in snippet view article find links to article

State University of Campinas, 2000. Daniel J. Bernstein, Pippenger's exponentiation algorithm, 2002. Daniel R. L. Brown, Generic Groups, Collision ResistanceARITH-MATIC (164 words) [view diff] exact match in snippet view article find links to article

The T in the middle of 'TT0' stands for Tan h General Mathematical SQR(A)OOO(B) Sqrt(A)=B General Mathematical APN(A)(N)(B) A**N=B **: ExponentiationCarry-select adder (667 words) [view diff] exact match in snippet view article find links to article

"negative" operator in the above code has a higher precedence than exponentiation. Running the program with this input - a ^ 2 produces this output ((((-a)^(2))))Betza's funny notation (2,645 words) [view diff] exact match in snippet view article find links to article

serves the same purpose. The range indicator gets the character of exponentiation w.r.t. the - operator (i.e. repeated continuation in the same direction)FLOPS (2,901 words) [view diff] exact match in snippet view article find links to article

ability to represent very small numbers and very large numbers. The exponentiation inherent in floating-point computation assures a much larger dynamicSaharon Shelah (1,322 words) [view diff] exact match in snippet view article find links to article

hypothesis), there are still highly nontrivial ZFC theorems about cardinal exponentiation. Shelah constructed a Jónsson group, an uncountable group for whichDiagnostic odds ratio (1,165 words) [view diff] exact match in snippet view article find links to article

{\text{DOR}}\pm 1.96\times \mathrm {SE} \left(\ln {\text{DOR}}\right)} Exponentiation of the approximate confidence interval for the log diagnostic odds ratioAdder (electronics) (1,971 words) [view diff] exact match in snippet view article

direction of time and include rotations and boosts can be performed by an exponentiation of the spacetime rotation biparavector W L = e 1 2 W . {\displaystylePower rule (2,667 words) [view diff] exact match in snippet view article find links to article

expression 0 0 {\displaystyle 0^{0}} (the case x = 0) from our scheme of exponentiation is due to the fact that the function f ( x , y ) = x y {\displaystyleFolded normal distribution (3,141 words) [view diff] exact match in snippet view article find links to article

distribution. In order to avoid any trouble with negative variances, the exponentiation of the parameter is suggested. Alternatively, you can add a constraintE (mathematical constant) (5,059 words) [view diff] exact match in snippet view article

π . {\displaystyle \ln(-1)=i\pi .} Furthermore, using the laws for exponentiation, ( cos x + i sin x ) n = ( e i x ) n = e i n x = cos ( n x ) +Verilog (4,026 words) [view diff] exact match in snippet view article find links to article

Addition - Subtraction - 2's complement * Multiplication / Division ** Exponentiation (*Verilog-2001) Relational > Greater than < Less than >= Greater thanLog amplifier (675 words) [view diff] exact match in snippet view article find links to article

To perform mathematical operations like multiplication, division and exponentiation. Multiplication is also sometimes called mixing. This is similar toList of NP-complete problems (2,316 words) [view diff] exact match in snippet view article find links to article

SIAM J. Comput., 10(3), 638–646, 1981 D. J. Bernstein, "Pippinger's exponentiation algorithm (draft) Kashiwabara & Fujisawa (1979); Ohtsuki et al. (1979);Elliptic-curve cryptography (4,426 words) [view diff] exact match in snippet view article find links to article

2006-03-27. Cohen, H.; Miyaji, A.; Ono, T. (1998). Efficient Elliptic Curve Exponentiation Using Mixed Coordinates. Advances in Cryptology – AsiaCrypt '98. Lecture0 (6,807 words) [view diff] exact match in snippet view article find links to article

number multiplied by 0 produces 1), a consequence of the previous rule. Exponentiation: x0 = x/x = 1, except that the case x = 0 may be left undefined in someCanonical commutation relation (2,628 words) [view diff] exact match in snippet view article find links to article

The group H 3 ( R ) {\displaystyle H_{3}(\mathbb {R} )} generated by exponentiation of the 3-dimensional Lie algebra determined by the commutation relationVersor (2,212 words) [view diff] exact match in snippet view article find links to article

but Lie's name has become associated with all groups generated by exponentiation. The set of versors with their multiplication has been denoted Sl(1Polynomial basis (783 words) [view diff] exact match in snippet view article find links to article

Squaring is an important operation because it can be used for general exponentiation, as well as inversion of an element. The most basic way to square anKenKen (1,621 words) [view diff] exact match in snippet view article find links to article

Other authors of puzzles include more complex operations, including exponentiation, modulus, and bit-wise operations. Ranges of values can be varied, suchJim Propp (650 words) [view diff] exact match in snippet view article find links to article

cardinality". arXiv:math.CO/0203289. Propp, James (October 2003). "Exponentiation and Euler measure". Algebra Universalis. 29 (4): 459–471. arXiv:mathInverse function (4,239 words) [view diff] exact match in snippet view article find links to article

"function" and just refer to an "inverse". Not to be confused with numerical exponentiation such as taking the multiplicative inverse of a nonzero real number.Geometric mean (4,075 words) [view diff] exact match in snippet view article find links to article

a_{i}} (i.e., the arithmetic mean on the log scale) and then using the exponentiation to return the computation to the original scale, i.e., it is the generalisedMandelbrot set (6,018 words) [view diff] exact match in snippet view article find links to article

computably enumerable. However, many simple objects (e.g., the graph of exponentiation) are also not computable in the BSS model. At present, it is unknownGentzen's consistency proof (1,754 words) [view diff] exact match in snippet view article find links to article

strong enough to describe recursively defined integer functions such as exponentiation, factorials or the Fibonacci sequence. Gentzen showed that the consistencyJulia Robinson (1,998 words) [view diff] exact match in snippet view article find links to article

RAND Corporation. Her work regarding Diophantine representation for exponentiation and her method of using Pell's equation led to the J.R. hypothesis (namedPrime zeta function (1,272 words) [view diff] exact match in snippet view article find links to article

{\displaystyle P(s)=\log \sum _{n=1}^{\infty }{\frac {a_{n}}{n^{s}}}.} (Exponentiation shows that this is equivalent to Lemma 2.7 by Li.) The prime zeta functionDe Branges's theorem (2,179 words) [view diff] exact match in snippet view article find links to article

JSTOR 2589676, MR 1682341 Grinshpan, Arcadii Z. (2002), "Logarithmic Geometry, Exponentiation, and Coefficient Bounds in the Theory of Univalent Functions and NonoverlappingProvable security (2,078 words) [view diff] exact match in snippet view article find links to article

Garray, Juan A.; Rabin, Tal (1998), "Fast batch verification for modular exponentiation and digital signatures", Advances in Cryptology -- Eurocrypt '98, LectureSymmetric level-index arithmetic (1,075 words) [view diff] exact match in snippet view article find links to article

^{e^{f}}}}}} where 0 ≤ f < 1 {\displaystyle 0\leq f<1} and the process of exponentiation is performed ℓ times, with ℓ ≥ 0 {\displaystyle \ell \geq 0} . ℓ andCryptography (9,002 words) [view diff] exact match in snippet view article find links to article

public-key algorithms involve operations such as modular multiplication and exponentiation, which are much more computationally expensive than the techniques usedBlum–Goldwasser cryptosystem (2,131 words) [view diff] exact match in snippet view article find links to article

However, as the RSA decryption exponent is randomly distributed, modular exponentiation may require a comparable number of squarings/multiplications to BG decryptionExtended Boolean model (1,025 words) [view diff] exact match in snippet view article find links to article

P-norm model is computationally expensive because of the number of exponentiation operations that it requires but it achieves much better results thanBrent–Kung adder (1,115 words) [view diff] exact match in snippet view article find links to article

characters for subscript and superscript, and TUTOR used these for exponentiation. Consider this command (from page IV-1 of The TUTOR Language, SherwoodPHP (10,030 words) [view diff] exact match in snippet view article find links to article

Constant scalar expressions, variadic functions, argument unpacking, new exponentiation operator, extensions of the use statement for functions and constantsDartmouth BASIC (7,249 words) [view diff] exact match in snippet view article find links to article

while RESTORE was added to "rewind" the position of READ/DATA. The exponentiation problem was fixed, so -X^2 would be interpreted as -(X^2). AdditionallyZipper (data structure) (1,626 words) [view diff] exact match in snippet view article

↦ T + 1 ) {\displaystyle lfp(T\mapsto T+1)} . Here, the notation of exponentiation, multiplication, and addition correspond to function types, productLeonhard Euler (7,468 words) [view diff] exact match in snippet view article find links to article

Feynman, for its single uses of the notions of addition, multiplication, exponentiation, and equality, and the single uses of the important constants 0, 1,Generalizations of the derivative (3,620 words) [view diff] exact match in snippet view article find links to article

the limit of a ratio of differences, it deals with the limit of an exponentiation of ratios. This allows the development of the geometric derivative andDirectional derivative (3,724 words) [view diff] exact match in snippet view article find links to article

\mathbf {\theta } \times \mathbf {x} )\cdot \nabla .} Following the same exponentiation procedure as above, we arrive at the rotation operator in the positionSubtractor (883 words) [view diff] exact match in snippet view article find links to article

gauge functions dependent on spatial position r and time t. Matrix exponentiation is used in the transformation. The gauge covariant derivative transformsCFScript (576 words) [view diff] exact match in snippet view article find links to article

integer; for example, 9\4 is 2. The right operand cannot be zero ^ Exponentiation: Return the result of a number raised to a power (exponent). Use theLou van den Dries (1,027 words) [view diff] exact match in snippet view article find links to article

Marker (1994). "The elementary theory of restricted analytic fields with exponentiation". Ann. of Math. Series 2. 140 (1): 183–205. doi:10.2307/2118545. JSTOR 2118545Kogge–Stone adder (870 words) [view diff] exact match in snippet view article find links to article

+ y ) = x − y {\displaystyle (x^{2}-y^{2})\div (x+y)=x-y} Integral exponentiation D = A**K ( x + y ) 3 = x 3 + 3 x 2 y + 3 x y 2 + y 3 {\displaystyleProjective space (4,982 words) [view diff] exact match in snippet view article find links to article

denoted Pn(K) (or Pn(K), although this notation may be confused with exponentiation). The space Pn(K) is often called the projective space of dimensionOccurrences of Grandi's series (1,690 words) [view diff] exact match in snippet view article find links to article

Series. Dover. ISBN 978-0-486-66165-0. Propp, James (October 2003). "Exponentiation and Euler measure". Algebra Universalis. 29 (4): 459–471. arXiv:mathChain rule (7,575 words) [view diff] exact match in snippet view article find links to article

{d}{dx}}(g(x)h(x))=h(x){\frac {d}{dx}}g(x)+g(x){\frac {d}{dx}}h(x).} The case of exponentiation f ( u , v ) = u v {\displaystyle f(u,v)=u^{v}} is slightly more complicatedGroup structure and the axiom of choice (1,327 words) [view diff] exact match in snippet view article find links to article

math "Group structure on any set"". Karagila, Asaf (August 26, 2014). "Exponentiation and Dedekind-finite cardinals". MathOverflow. Hajnal, A.; Kertész, AMatrix (mathematics) (12,434 words) [view diff] exact match in snippet view article

powers of the diagonal entries, which is much easier than doing the exponentiation for A instead. This can be used to compute the matrix exponential eADc (computer program) (2,082 words) [view diff] exact match in snippet view article

of dc, the | command can be used to do arbitrary precision modular exponentiation without needing to write the X function. #!/usr/bin/perl my ($g, $eDynamic programming (9,627 words) [view diff] exact match in snippet view article find links to article

O ( n log n ) {\displaystyle O(n\log n)} algorithm by fast matrix exponentiation. Consider the problem of assigning values, either zero or one, to theField (mathematics) (10,329 words) [view diff] exact match in snippet view article

A widely applied cryptographic routine uses the fact that discrete exponentiation, i.e., computing an = a ⋅ a ⋅ ... ⋅ a (n factors, for an integer n ≥International System of Units (17,375 words) [view diff] exact match in snippet view article find links to article

'm' and the 's' are lowercase because neither the metre nor the second are named after people, and exponentiation is represented with a superscript '2'.3D rotation group (10,774 words) [view diff] exact match in snippet view article find links to article

because its existence would violate the hairy ball theorem; but direct exponentiation is possible, and yields exp ( ω ~ ) = exp ( θ ( u ⋅ L ) ) = expWave packet (4,760 words) [view diff] exact match in snippet view article find links to article

above time evolution of Gaussians. From the fundamental identity of exponentiation, or path integration, K z ∗ K z ′ = K z + z ′ {\displaystyle K_{z}*K_{z'}=K_{z+z'}\Substitution model (6,472 words) [view diff] exact match in snippet view article find links to article

The transition matrix can be computed from the rate matrix via matrix exponentiation: P ( t ) = e Q t = ∑ n = 0 ∞ Q n t n n ! , {\displaystyle P(t)=e^{Qt}=\sumIsaak Moiseevich Milin (1,092 words) [view diff] exact match in snippet view article find links to article

JSTOR 2589676, MR1682341 Grinshpan, Arcadii Z. (2002), "Logarithmic Geometry, Exponentiation, and Coefficient Bounds in the Theory of Univalent Functions and NonoverlappingSecond-order arithmetic (3,369 words) [view diff] exact match in snippet view article find links to article

longer possible) and the basic axioms by the obvious axioms defining exponentiation inductively from multiplication; then the system consists of the (enriched)Steve Vickers (computer scientist) (1,236 words) [view diff] exact match in snippet view article

1 (11), pp. 1–48, 2009. Steven Vickers, "The double powerlocale and exponentiation: a case study in geometric logic", Theoretical Computer Science, ISSNList of macOS components (6,667 words) [view diff] exact match in snippet view article find links to article

include the standard addition, subtraction, division, multiplication, exponentiation and the use of the percent sign to denote percentage. Calendar is aKronecker product (5,941 words) [view diff] exact match in snippet view article find links to article

order of B and the exponent in |B| is the order of A. Kronecker sum and exponentiation: If A is n × n, B is m × m and Ik denotes the k × k identity matrixPhilosophy of mathematics (9,518 words) [view diff] exact match in snippet view article find links to article

to somewhat similar conclusions, such as, for instance, that super-exponentiation is not a legitimate finitary function. Structuralism is a position holdingLambda calculus (10,743 words) [view diff] exact match in snippet view article find links to article

repeating the add n function m times and then applying it to zero. Exponentiation has a rather simple rendering in Church numerals, namely POW := λb.λeCharts on SO(3) (2,747 words) [view diff] exact match in snippet view article

called Euler–Rodrigues parameters; a 3 × 3 skew-symmetric matrix, via exponentiation; the 3 × 3 skew-symmetric matrices are the Lie algebra SO(3), and thisCanonical quantization (4,635 words) [view diff] exact match in snippet view article find links to article

vacuum, without affecting the time-evolution of operators via the above exponentiation operation. This subtraction of the zero-point energy may be consideredX86 assembly language (5,100 words) [view diff] exact match in snippet view article find links to article

transcendental functions, including sine, cosine, tangent, arctangent, exponentiation with the base 2 and logarithms to bases 2, 10, or e. The stack registerList of arbitrary-precision arithmetic software (1,147 words) [view diff] exact match in snippet view article find links to article

decimal has user definable precision and limited mathematical operations (exponentiation, square root, etc. but no trigonometric functions). The Fraction classYang Mi (6,232 words) [view diff] exact match in snippet view article find links to article

Beijing to a police officer and a housewife. She was given the name "幂" (exponentiation) because her parents both have the surname Yang. She graduated fromGoodstein's theorem (2,545 words) [view diff] exact match in snippet view article find links to article

P(3)(1) = f(21 + 20,2) = ω1 + ω0 = ω + 1. Addition, multiplication and exponentiation of ordinal numbers are well defined. We claim that f ( G ( m ) ( n )Representation theory of the Lorentz group (19,726 words) [view diff] exact match in snippet view article find links to article

linear) are related to the complex linear Lie algebra representations by exponentiation. The real linear representations of s l ( 2 , C ) {\displaystyle {\mathfrakStirling number (3,365 words) [view diff] exact match in snippet view article find links to article

I. (2001). "Extended Bell and Stirling Numbers From Hypergeometric Exponentiation" (PDF). Journal of Integer Sequences. 4: 01.1.4. Spivey, Michael Z.Lorentz group (7,015 words) [view diff] exact match in snippet view article find links to article

subalgebras form a lattice (see the figure), and each subalgebra generates by exponentiation a closed subgroup of the restricted Lie group. From these, all subgroupsBispinor (2,023 words) [view diff] exact match in snippet view article find links to article

representation, i.e. a bispinor representation. Now using the recipe of exponentiation of the Lie algebra representation to obtain a representation of SO(3;1)+Carry-lookahead adder (3,164 words) [view diff] exact match in snippet view article find links to article

can be any matrix class implementation supporting the multiplication, exponentiation, and indexing operators (for example numpy.matrix). def apd(A, n: int):Derivative of the exponential map (5,231 words) [view diff] exact match in snippet view article find links to article

series of the exponential map of a linear endomorphism, as in matrix exponentiation When G is a matrix Lie group, all occurrences of the exponential areLarge countable ordinal (3,060 words) [view diff] exact match in snippet view article find links to article

0, 1, ω and Ω, and repeatedly applying addition, multiplication and exponentiation, and ψ to previously constructed ordinals (except that ψ can only beSYmbolic LinK (SYLK) (2,017 words) [view diff] exact match in snippet view article

formatting codes: D default C continuous cross-cell display E scientific exponentiation F fixed decimal point G general format $ leading $ and 2 decimalLoop variant (1,567 words) [view diff] exact match in snippet view article find links to article

is usually considered tractable. Considering even the simple case of exponentiation as a primitive recursive function, and that the composition of primitiveCommon Lisp (11,904 words) [view diff] exact match in snippet view article find links to article

41962092341162602522202993782792835301376 Compare with the built in exponentiation: CL-USER > (= (expt 2 200) (power 2 200)) T WITH-OPEN-FILE is a macroMAD (programming language) (2,395 words) [view diff] exact match in snippet view article

negation) + (addition) - (subtraction) * (multiplication) / (division) .P. (exponentiation) .N. (bitwise negation) .A. (bitwise and) .V. (bitwise or) .EV. (bitwiseAlgorithm characterizations (8,744 words) [view diff] exact match in snippet view article find links to article

the reader—e.g. addition, subtraction, multiplication and division, exponentiation, the CASE function, concatenation, etc., etc.; for a list see Some commonCalculator Applications (UIL) (964 words) [view diff] exact match in snippet view article

The test for Grades 9-12 covers the subjects under Grades 6-8 plus exponentiation, logarithms, trigonometric functions, inverse trigonometric functionsList of first-order theories (5,259 words) [view diff] exact match in snippet view article find links to article

apply. Complications arise when adding further function symbols (e.g., exponentiation). Second-order arithmetic can refer to a first order theory (in spiteChebyshev polynomials (9,389 words) [view diff] exact match in snippet view article find links to article

T_{n}{\big (}T_{m}(x){\big )}=T_{nm}(x);} and the expression of complex exponentiation in terms of Chebyshev polynomials: given z = a + bi, z n = | z | n (Felix Hausdorff (7,335 words) [view diff] exact match in snippet view article find links to article

introduced by Hausdorff, the basis for all further results for Aleph exponentiation. Hausdorff' excellent knowledge of the problems of this type of sequenceAdolph Winkler Goodman (888 words) [view diff] exact match in snippet view article find links to article

ISSN 0278-1077 Grinshpan, Arcadii Z. (2002), "Logarithmic Geometry, Exponentiation, and Coefficient Bounds in the Theory of Univalent Functions and NonoverlappingFOSD program cubes (1,282 words) [view diff] exact match in snippet view article find links to article

pair basic calculator functionality (base) with optional logarithmic/exponentiation (lx) and trigonometric (td) features. Rows allow one to pair core functionalityPolylogarithm (9,620 words) [view diff] exact match in snippet view article find links to article

{\displaystyle -\pi <\operatorname {Im} (\mu )\leq \pi } . Also, all exponentiation will be assumed to be single-valued: z s = exp ( s ln ( z ) ) {\displaystylePL/I preprocessor (1,638 words) [view diff] exact match in snippet view article find links to article

expression in %IF evaluates to BIT. All PL/I operators are allowed except exponentiation. %DECLARE establishes an identifier as a preprocessor variable, eitherList of Latin words with English derivatives (374 words) [view diff] exact match in snippet view article find links to article

dispositive, dispositor, entrepôt, expone, exponent, exponential, exponentiation, exponible, exposit, exposition, expositional, expositive, expositorGlossary of set theory (8,805 words) [view diff] exact match in snippet view article find links to article

ordinals α β {\displaystyle \alpha ^{\beta }} 1. Cardinal exponentiation 2. Ordinal exponentiation β α {\displaystyle {}^{\beta }\alpha } 1. The set ofPrincipalization (algebra) (8,913 words) [view diff] exact match in snippet view article

U\\E\mapsto E^{\sigma -1}:=\sigma (E)/E\end{cases}}} is the symbolic exponentiation with the difference σ − 1 ∈ Z [ G ] {\displaystyle \sigma -1\in \mathbbGrunsky matrix (6,166 words) [view diff] exact match in snippet view article find links to article

JSTOR 2589676, MR 1682341 Grinshpan, Arcadii Z. (2002), "Logarithmic Geometry, Exponentiation, and Coefficient Bounds in the Theory of Univalent Functions and NonoverlappingDidier Sornette (8,715 words) [view diff] exact match in snippet view article find links to article

fluctuations due to past earthquakes. As elastic stresses add up, the exponentiation thus makes this model nonlinear. Solving it analytically allowed themRETRIEVE (2,730 words) [view diff] exact match in snippet view article find links to article

math, including +, -, * for multiplication, / for division, and ↑ for exponentiation. These could be further combined with boolean expressions using ANDTheFormTool (996 words) [view diff] exact match in snippet view article find links to article

Logarithm, Maximum, Minimum, Months, Now, Payment, Raise to Power (Exponentiation), Remainder, Root, Round and Years, each of which can be nested almostLight-front computational methods (10,872 words) [view diff] exact match in snippet view article find links to article

Fock states are determined by the lower-state wave functions and the exponentiation of an operator T {\displaystyle T} . Specifically, the eigenstate isHistory of Lorentz transformations (67,261 words) [view diff] exact match in snippet view article find links to article

by Johann H. Lambert. Euler described some transcendental functions: exponentiation and circular functions. He used the exponential series ∑ 0 ∞ x n / nACE Encrypt (5,343 words) [view diff] exact match in snippet view article find links to article

* 10^(-5) sec 1.0 * 10^(-4) sec 4.4 * 10^(-5) sec 1.4 * 10^(-4) sec Exponentiation 1.9 * 10^(-2) sec 1.2 * 10^(-1) sec 2.6 * 10^(-2) sec 1.7 * 10^(-1)