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Что (кто) такое quadratic residue technique - определение

IN NUMBER THEORY CONCERNING PRIMES

Euler criterion; Euler's quadratic residue theorem; Euler quadratic residue theorem; Euler's Criterion

Найдено результатов: 1031

Quadratic residue

INTEGER THAT IS A PERFECT SQUARE MODULO SOME INTEGER

Quadratic residues; Quadratic non-residue; Quadratic congruences; Quadratic congruence; Modular square root; Square root modulo n; Square root mod n; Quadratic residuosity; Quadratic nonresidue; Least quadratic non-residue; Quadratic excess

In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e.

https://en.wikipedia.org/wiki/Quadratic_residue

Quadratic irrational number

MATHEMATICAL CONCEPT

Quadratic surd; Quadratic irrationality; Quadratic Irrational Number; Quadratic irrationalities; Quadratic irrational; Quadratic irrational numbers

In mathematics, a quadratic irrational number (also known as a quadratic irrational, a quadratic irrationality or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients which is irreducible over the rational numbers.Jörn Steuding, Diophantine Analysis, (2005), Chapman & Hall, p.

https://en.wikipedia.org/wiki/Quadratic_irrational_number

Residue (complex analysis)

COEFFICIENT OF THE TERM OF ORDER −1 IN THE LAURENT EXPANSION OF A FUNCTION HOLOMORPHIC OUTSIDE A POINT, WHOSE VALUE CAN BE EXTRACTED BY A CONTOUR INTEGRAL

Residue of an analytic function; Residue at a pole; Complex residue; Residue (mathematics)

In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities. (More generally, residues can be calculated for any function f\colon \mathbb{C} \setminus \{a_k\}_k \rightarrow \mathbb{C} that is holomorphic except at the discrete points {ak}k, even if some of them are essential singularities.

https://en.wikipedia.org/wiki/Residue_(complex_analysis)

Residue theorem

THE THEOREM THAT COMPLEX CONTOUR INTEGRALS ARE SIMPLY THE SUMS OF RESIDUES OF SINGULARITIES CONTAINED WITHIN THE CONTOUR

Cauchy residue theorem; Cauchy residue formula; Residue theory; Residue Theorem; Cauchy's Residue Theorem; Cauchys Residue Theorem; Cauchy Residue Theorem; Residue formula; Residue theorem of Cauchy; Cauchy's residue theorem

In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals and infinite series as well. It generalizes the Cauchy integral theorem and Cauchy's integral formula.

https://en.wikipedia.org/wiki/Residue_theorem

Quadratic reciprocity

THEOREM

Law of quadratic reciprocity; Quadratic reciprocity rule; Aureum Theorema; Law of Quadratic Reciprocity; Quadratic reciprocity law; Quadratic reciprocity theorem; Quadratic Reciprocity; Qr theorem

In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Due to its subtlety, it has many formulations, but the most standard statement is:

https://en.wikipedia.org/wiki/Quadratic_reciprocity

Linear–quadratic regulator

LINEAR OPTIMAL CONTROL TECHNIQUE

Linear-quadratic control; Dynamic Riccati equation; Linear-quadratic regulator; Quadratic quadratic regulator; Quadratic–quadratic regulator; Quadratic-quadratic regulator; Polynomial quadratic regulator; Polynomial–quadratic regulator; Polynomial-quadratic regulator; Linear quadratic regulator

The theory of optimal control is concerned with operating a dynamic system at minimum cost. The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is called the LQ problem.

https://en.wikipedia.org/wiki/Linear–quadratic_regulator

Poincaré residue

GENERALIZATION OF THE CONCEPT OF RESIDUE OF A HOLOMORPHIC FUNCTION TO HIGHER DIMENSIONS

Poincare residue; Draft:Residue in several complex variables; Residue (complex geometry); Draft:Residue (Complex Geometry); Draft:Residue (complex geometry)

In mathematics, the Poincaré residue is a generalization, to several complex variables and complex manifold theory, of the residue at a pole of complex function theory. It is just one of a number of such possible extensions.

https://en.wikipedia.org/wiki/Poincaré_residue

Quadratic sieve

INTEGER FACTORIZATION ALGORITHM

Multiple Polynomial Quadratic Sieve; Mpqs; Quadratic Sieve; Multipolynomial quadratic sieve; SIQS; MPQS

The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second fastest method known (after the general number field sieve). It is still the fastest for integers under 100 decimal digits or so, and is considerably simpler than the number field sieve.

https://en.wikipedia.org/wiki/Quadratic_sieve

Quadratic programming

SOLVING AN OPTIMIZATION PROBLEM WITH A QUADRATIC OBJECTIVE FUNCTION

Quadratic program; List of solvers for quadratic programming problems

Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constraints on the variables.

https://en.wikipedia.org/wiki/Quadratic_programming

Musical technique

GROUP OF TECHNIQUES RELATING TO THE COMPOSING, PRODUCTION OR PERFORMANCE OF MUSIC

Technique (music); General Instrumental technique; Performance technique; Instrumental technique; Brass technique; String instrument technique; String technique; Brass instrument technique; Stringed instrument technique; Woodwind technique; Woodwind instrument technique; Percussion technique; Percussion instrument technique; Percussion instrumental technique; Woodwind instrumental technique; Brass instrumental technique; String instrumental technique; Stringed instrumental technique

Musical technique is the ability of instrumental and vocal musicians to exert optimal control of their instruments or vocal cords in order to produce the precise musical effects they desire. Improving one's technique generally entails practicing exercises that improve one's muscular sensitivity and agility.

https://en.wikipedia.org/wiki/Musical_technique

Википедия

Euler's criterion

In number theory, Euler's criterion is a formula for determining whether an integer is a quadratic residue modulo a prime. Precisely,

Let p be an odd prime and a be an integer coprime to p. Then

a^{\tfrac {p-1}{2}}\equiv {\begin{cases}\;\;\,1{\pmod {p}}&{\text{ if there is an integer }}x{\text{ such that }}a\equiv x^{2}{\pmod {p}},\\-1{\pmod {p}}&{\text{ if there is no such integer.}}\end{cases}}

Euler's criterion can be concisely reformulated using the Legendre symbol:

\left({\frac {a}{p}}\right)\equiv a^{\tfrac {p-1}{2}}{\pmod {p}}.

The criterion first appeared in a 1748 paper by Leonhard Euler.

https://en.wikipedia.org/wiki/Euler's criterion