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EXSLT is a community initiative to provide extensions to XSLT, [1] [2] which are broken down into a number of modules, listed below.. The creators (Jeni Tennison, Uche Ogbuji, Jim Fuller, Dave Pawson, et al.) of EXSLT aim to encourage the implementers of XSLT processors to use these extensions, in order to increase the portability of stylesheets.
The minimal polynomial of an element, if it exists, is a member of F[x], the ring of polynomials in the variable x with coefficients in F. Given an element α of E, let J α be the set of all polynomials f(x) in F[x] such that f(α) = 0. The element α is called a root or zero of each polynomial in J α
A field extension L/K is called a simple extension if there exists an element θ in L with L = K ( θ ) . {\displaystyle L=K(\theta ).} This means that every element of L can be expressed as a rational fraction in θ , with coefficients in K ; that is, it is produced from θ and elements of K by the field operations +, −, •, / .
This is an accepted version of this page This is the latest accepted revision, reviewed on 27 January 2025. Periodic table of the elements with eight or more periods Extended periodic table Hydrogen Helium Lithium Beryllium Boron Carbon Nitrogen Oxygen Fluorine Neon Sodium Magnesium Aluminium Silicon Phosphorus Sulfur Chlorine Argon Potassium Calcium Scandium Titanium Vanadium Chromium ...
V is the symmetry group of this cross: flipping it horizontally (a) or vertically (b) or both (ab) leaves it unchanged.A quarter-turn changes it. In two dimensions, the Klein four-group is the symmetry group of a rhombus and of rectangles that are not squares, the four elements being the identity, the vertical reflection, the horizontal reflection, and a 180° rotation.
In field theory, the primitive element theorem states that every finite separable field extension is simple, i.e. generated by a single element.This theorem implies in particular that all algebraic number fields over the rational numbers, and all extensions in which both fields are finite, are simple.
An arbitrary polynomial f with coefficients in some field F is said to have distinct roots or to be square-free if it has deg f roots in some extension field.For instance, the polynomial g(X) = X 2 − 1 has precisely deg g = 2 roots in the complex plane; namely 1 and −1, and hence does have distinct roots.
An algebraic extension is a purely inseparable extension if and only if for every , the minimal polynomial of over F is not a separable polynomial. [1] If F is any field, the trivial extension is purely inseparable; for the field F to possess a non-trivial purely inseparable extension, it must be imperfect as outlined in the above section.