a quadratic field is an algebraic number field of degree two over Q {\displaystyle \mathbf {Q} } , the rational numbers. Every such quadratic field is...
11 KB (1,288 words) - 16:20, 27 September 2023
only if the two fields are equal. In this case, the extension is a trivial extension. Extensions of degree 2 and 3 are called quadratic extensions and...
19 KB (3,227 words) - 12:13, 23 July 2024
{\displaystyle 4x^{2}+2xy-3y^{2}} is a quadratic form in the variables x and y. The coefficients usually belong to a fixed field K, such as the real or complex...
33 KB (4,554 words) - 17:42, 31 May 2024
variable (x) Quadratic field, an algebraic number field of degree two over the field of rational numbers Quadratic irrational or "quadratic surd", an irrational...
3 KB (431 words) - 11:46, 3 April 2024
Discriminant (redirect from Discriminant of a quadratic form)
called discriminant: the discriminant of an algebraic number field; the discriminant of a quadratic form; and more generally, the discriminant of a form, of...
41 KB (6,702 words) - 15:11, 22 August 2024
quadratic irrational number (also known as a quadratic irrational or quadratic surd) is an irrational number that is the solution to some quadratic equation...
11 KB (1,627 words) - 22:45, 17 March 2024
theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime...
111 KB (8,553 words) - 16:55, 24 June 2024
In mathematics, a quadratic equation (from Latin quadratus 'square') is an equation that can be rearranged in standard form as a x 2 + b x + c = 0 , {\displaystyle...
52 KB (6,541 words) - 07:12, 1 September 2024
In number theory, quadratic integers are a generalization of the usual integers to quadratic fields. Quadratic integers are algebraic integers of degree...
21 KB (2,684 words) - 13:59, 18 March 2024
be greater than 1). One of the basic examples of norms comes from quadratic field extensions Q ( a ) / Q {\displaystyle \mathbb {Q} ({\sqrt {a}})/\mathbb...
11 KB (1,901 words) - 02:30, 11 April 2024