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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.
Examples of separable extensions are many including first separable algebras where R is a separable algebra and S = 1 times the ground field. Any ring R with elements a and b satisfying ab = 1 , but ba different from 1, is a separable extension over the subring S generated by 1 and bRa .
The conjecture is true if the Hilbert space is not separable (i.e. if it has an uncountable orthonormal basis). In fact, if x {\displaystyle x} is a non-zero vector in H {\displaystyle H} , the norm closure of the linear orbit [ x ] {\displaystyle [x]} is separable (by construction) and hence a proper subspace and also invariant.
Separable polynomials are used to define separable extensions: A field extension K ⊂ L is a separable extension if and only if for every α in L which is algebraic over K, the minimal polynomial of α over K is a separable polynomial. Inseparable extensions (that is, extensions which are not separable) may occur only in positive characteristic.
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.
Galois theory has been used to solve classic problems including showing that two problems of antiquity cannot be solved as they were stated (doubling the cube and trisecting the angle), and characterizing the regular polygons that are constructible (this characterization was previously given by Gauss but without the proof that the list of ...
In field theory, a branch of algebra, an algebraic field extension / is called a separable extension if for every , the minimal polynomial of over F is a separable polynomial (i.e., its formal derivative is not the zero polynomial, or equivalently it has no repeated roots in any extension field). [1]