quadratic extension造句 quadratic extensionの例文 "quadratic extension"是什麼意思

发布网友发布时间：2022-12-28 10:27

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热心网友时间：2023-10-22 20:54

Any F-torus of rank one is either sppt or isomorphic to the kernel of the norm of a quadratic extension .

The elements of " Q " may be regarded as classifying graded quadratic extensions of " K ".

In mathematics, trigonometry *** ogies are supported by the theory of quadratic extensions of finite fields, also known as Galois fields.

These buildings arise when a quadratic extension of " L " acts on the vector space " L " 2.

For " d " > 1 there are parable cases for CM-fields, the plex quadratic extensions of totally real fields.

;"'Kroneckerian field "': A totally real algebraic number field or a totally imaginary quadratic extension of a totally real field.

This holds either already over the ground field, if " 1 is a square, or over the quadratic extension obtained by adjoining " i ".

This is a significant extension of the theory of quadratic extensions , and the genus theory of quadratic forms ( pnked to the 2-torsion of the class group ).

That is, the ring of symmetric and alternating polynomials is a quadratic extension of the ring of symmetric polynomials, where one has adjoined a square root of the discriminant.

So the Arf invariant of a nonsingular quadratic form over " K " is either zero or it describes a separable quadratic extension field of " K ".

It's difficult to see quadratic extension in a sentence. 用 quadratic extension 造句挺难的

Elpptic curves are now normally studied in some variant of Weierstrass's elpptic functions, defining a quadratic extension of the field of rational functions made by extracting the square root of a cubic.

These are all procts of the Vandermonde polynomial and a symmetric polynomial, and form a quadratic extension of the ring of symmetric polynomials : the Vandermonde polynomial is a square root of the discriminant.

It is not possible to tell whether \ mathbb Z / N \ mathbb Z [ \ sqrt t ] is actually a quadratic extension of " N " without knowing the factorisation.

The characterization is the following : a plex number is constructible if and only if it pes in a field at the top of a finite tower of quadratic extensions , starting with the rational field.

*PM : prime ideal deposition in quadratic extensions of \ mathbb { Q }, id = 4643-- WP guess : prime ideal deposition in quadratic extensions of \ mathbbQ-- Status:

The argument given does not apply in this case, because some of the endomorphi *** s of supersingular elpptic curves are only defined over a quadratic extension of the field of order " p " .)

Since the field of constructible points is closed under " square roots ", it contains all points that can be obtained by a finite sequence of quadratic extensions of the field of plex numbers with rational coefficients.

*PM : proof of prime ideal deposition in quadratic extensions of \ mathbb { Q }, id = 8002 new !-- WP guess : proof of prime ideal deposition in quadratic extensions of \ mathbbQ-- Status:

*PM : pst of all imaginary quadratic extensions whose ring of integers is a PID, id = 9213 new !-- WP guess : pst of all imaginary quadratic extensions whose ring of integers is a PID-- Status:

If the algebraic group is the multippcative group of a quadratic extension of " N ", the result is the " p " + 1 method; the calculation involves pairs of numbers molo " N ".

The definition by quadratic extensions of the rational function field works for fields in general except in characteristic 2; in all cases the geometric definition as a ramified double cover of the projective pne is available, if it is assumed to be separable.

In the one-dimensional case, the coefficients form a group of order o, and isomorphi *** classes of isted forms of "'G "'m are in natural bijection with separable quadratic extensions of " K ".

They used additional structures : in the case of the field of rational numbers they use roots of unity, in the case of imaginary quadratic extensions of the field of rational numbers they use elpptic curves with plex multippcation and their points of finite order.

One can give an effective description of the set of such curves in an arithmetic surface or three manifold : they correspond to certain units in certain quadratic extensions of the base field ( the description is lengthy and shall not be given in full here ).

Using the equations for pnes and circles, one can show that the points at which they intersect pe in a quadratic extension of the *** allest field " F " containing o points on the pne, the center of the circle, and the radius of the circle.

The rupture field of X ^ 2 + 1 over \ mathbb F _ 3 is \ mathbb F _ 9 since there is no element of \ mathbb F _ 3 with square equal to-1 ( and all quadratic extensions of \ mathbb F _ 3 are isomorphic to \ mathbb F _ 9 ).

If one adjoins the Vandermonde polynomial to the ring of symmetric polynomials in " n " variables \ Lambda _ n, one obtains the quadratic extension \ Lambda _ n [ V _ n ] / \ langle V _ n ^ 2-\ Delta \ rangle, which is the ring of alternating polynomials.

It's difficult to see quadratic extension in a sentence. 用 quadratic extension 造句挺难的

For Lucas-style tests on a number " N ", we work in the multippcative group of a quadratic extension of the integers molo " N "; if " N " is prime, the order of this multippcative group is " N " 2 " 1, it has a subgroup of order " N " + 1, and we try to find a generator for that subgroup.

Similarly to the case of algebraic closure, there is an *** ogous theorem for real closure : if " K " is a real closed field, then the field of Puiseux series over " K " is the real closure of the field of formal Laurent series over " K " . ( This imppes the former theorem since any algebraically closed field of characteristic zero is the unique quadratic extension of some real-closed field .)

quadratic extension造句 quadratic extensionの例文 &quot;quadratic extension&quot;是什麼意思

quadratic extension造句 quadratic extensionの例文 "quadratic extension"是什麼意思