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Longer titles found: Exponentiation by squaring (view), Modular exponentiation (view), Base (exponentiation) (view), Addition-chain exponentiation (view)

searching for Exponentiation 195 found (497 total)

alternate case: exponentiation

Cardinal number (3,436 words) [view diff] exact match in snippet view article find links to article

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 particular
Principal 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 defined
Gimel 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 the
Schanuel'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 fact
PR (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 function
Rational 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 denominator
Compound 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 the
SI 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 example
Continuum 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 \aleph
Convergent 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 all
Itoh–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 relatively
Continuum 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 of
Epsilon 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 starting
Lebedev–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 Variable
Constant 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, for
Trapdoor 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 prime
Stephen 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 logarithms
Phiten (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 macro
Cantor–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. Cantor
Matrix 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 from
Speedcoding (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-instructions
Limit 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 discussed
Ordinal 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, arithmetic
Superfunction (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 {\displaystyle
Exponential 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 version
Birthday 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 them
Angus 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 fields
Perplexity (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 the
Strength 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 time
Log 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 ⊕ and
Quantum 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 - qureg
Successor 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 isolated
Ordinal 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 _{\alpha
APL (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 3
Elementary 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 quantifiers
Cartesian 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 {\displaystyle
Pfaffian 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 question
Conformable 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 transformations
239 (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 integer
Graham'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 sequence
Euler 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 measure
Transcendental 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 indeed
Bachmann–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 be
ProVerif (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 verifiability
Special 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 trigonometric
Complex 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 natural
EXPSPACE (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 equivalent
Transseries (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 power
Phong 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 specular
Principia 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 infinite
FinSet (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 in
Algebraic-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 other
Exponential 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 thereafter
Egorychev 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 : {\displaystyle
Calculator (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 Convert
Equinumerosity (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 functions
Mathematical 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 is
Carry-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 common
Context-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 languages
Ψ₀(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 and
Robotics 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 basis
List 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 fixed
HP-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 calculators
Schnorr 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 Juxtaposition
Computational 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, computing
Poincaré 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, the
ElGamal 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 a
Imaginary 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 following
Adder–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 operation
ECMAScript (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 programming
Atlas 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 reserved
Binary 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 operation
Cartesian 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 if
Java 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 DSA
Gell-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 properties
Antenna 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 formula
HP 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 customer
Ordinal 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-ordered
Logarithmic 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, though
Lévy 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 binary
Limit 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 condition
Paillier 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 Paillier
Bit 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 with
Arithmetic 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 operation
Elliptic 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 Resistance
ARITH-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 **: Exponentiation
Carry-select adder (667 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 operation
Operator-precedence parser (1,488 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 dynamic
Saharon 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 which
Diagnostic 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 ratio
Adder (electronics) (1,971 words) [view diff] exact match in snippet view article
Bitwise ops (0b00) Bitwise operation NOT AND OR Bit shifts Bit manipulation See also Kochanski multiplication (exponentiation) Multiply–accumulate operation
Algebra of physical space (1,551 words) [view diff] exact match in snippet view article find links to 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 . {\displaystyle
Power 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 {\displaystyle
Folded 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 constraint
E (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 than
Log 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 to
List 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. Lecture
0 (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 some
Canonical 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 relation
Versor (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(1
Polynomial 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 an
KenKen (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, such
Jim 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:math
Inverse 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 generalised
Mandelbrot 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 unknown
Gentzen'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 consistency
Julia 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 (named
Prime 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 function
De 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 Nonoverlapping
Provable 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, Lecture
Symmetric 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 and
Cryptography (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 used
Blum–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 decryption
Extended 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 than
Brent–Kung adder (1,115 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 operation
TUTOR (4,027 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, Sherwood
PHP (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 constants
Dartmouth 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). Additionally
Zipper (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, product
Leonhard 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 and
Directional 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 position
Subtractor (883 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 operation
Gluon field (1,508 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 transforms
CFScript (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 the
Lou 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 2118545
Kogge–Stone adder (870 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 operation
Carry-skip adder (1,627 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 operation
ALTRAN (790 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 {\displaystyle
Projective 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 dimension
Occurrences 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:math
Chain 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 complicated
Group 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, A
Matrix (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 eA
Dc (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, $e
Dynamic 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 the
Field (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 ) ) = exp
Wave 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}=\sum
Isaak 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 Nonoverlapping
Second-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, ISSN
List 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 a
Kronecker 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 matrix
Philosophy 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 holding
Lambda 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.λe
Charts 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 this
Canonical 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 considered
X86 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 register
List 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 class
Yang 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 from
Goodstein'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 {\mathfrak
Stirling 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 subgroups
Bispinor (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
Bitwise ops (0b00) Bitwise operation NOT AND OR Bit shifts Bit manipulation See also Kochanski multiplication (exponentiation) Multiply–accumulate operation
Seidel's algorithm (793 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 are
Large 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 be
SYmbolic 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 decimal
Loop 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 primitive
Common 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 macro
MAD (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. (bitwise
Algorithm 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 common
Calculator 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 functions
List 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 spite
Chebyshev 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 sequence
Adolph 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 Nonoverlapping
FOSD 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 functionality
Polylogarithm (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 ) ) {\displaystyle
PL/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, either
List 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, expositor
Glossary 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 of
Principalization (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 \mathbb
Grunsky 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 Nonoverlapping
Didier 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 them
RETRIEVE (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 AND
TheFormTool (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 almost
Light-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 is
History 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 / n
ACE 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)