quadratic field
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Quadratic field — In algebraic number theory, a quadratic field is an algebraic number field K of degree two over Q. It is easy to show that the map d ↦ Q(√d) is a bijection from the set of all square free integers d ≠ 0, 1 to the set of… … Wikipedia
Quadratic reciprocity — The law of quadratic reciprocity is a theorem from modular arithmetic, a branch of number theory, which shows a remarkable relationship between the solvability of certain quadratic equations modulo different prime moduli.Although it allows us to… … Wikipedia
Quadratic — In mathematics, the term quadratic describes something that pertains to squares, to the operation of squaring, to terms of the second degree, or equations or formulas that involve such terms. Quadratus is Latin for square . Mathematics Algebra… … Wikipedia
Quadratic irrational — In mathematics, a quadratic irrational, also known as a quadratic irrationality or quadratic surd, is an irrational number that is the solution to some quadratic equation with rational coefficients. Since fractions can be cleared from a quadratic … Wikipedia
Quadratic programming — (QP) is a special type of mathematical optimization problem. It is the problem of optimizing (minimizing or maximizing) a quadratic function of several variables subject to linear constraints on these variables.The quadratic programming problem… … Wikipedia
Quadratic equation — This article is about quadratic equations and solutions. For more general information about quadratic functions, see Quadratic function. For more information about quadratic polynomials, see Quadratic polynomial. In mathematics, a quadratic… … Wikipedia
Quadratic form — In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example, is a quadratic form in the variables x and y. Quadratic forms occupy a central place in various branches of mathematics, including… … Wikipedia
Quadratic sieve — The quadratic sieve algorithm (QS) is a modern 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… … Wikipedia
Quadratic residue — 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., if there exists an integer x such that: Otherwise, q is called a quadratic nonresidue modulo n. Originally an abstract… … Wikipedia
Quadratic residue code — A quadratic residue code is a type of cyclic code.There is a quadratic residue code of length pover the finite field GF(l) whenever pand l are primes, p is odd andl is a quadratic residue modulo p.Its generator polynomial as a cyclic code is… … Wikipedia
Glossary of field theory — Field theory is the branch of mathematics in which fields are studied. This is a glossary of some terms of the subject. (See field theory (physics) for the unrelated field theories in physics.) Definition of a field A field is a commutative ring… … Wikipedia
