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Desmos was founded by Eli Luberoff, a math and physics double major from Yale University, [3] and was launched as a startup at TechCrunch 's Disrupt New York conference in 2011. [4] As of September 2012, it had received around 1 million US dollars of funding from Kapor Capital, Learn Capital, Kindler Capital, Elm Street Ventures and Google ...
The free group F S with free generating set S can be constructed as follows. S is a set of symbols, and we suppose for every s in S there is a corresponding "inverse" symbol, s −1, in a set S −1. Let T = S ∪ S −1, and define a word in S to be any written product of elements of T. That is, a word in S is an element of the monoid ...
Cayley graph. In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, [1] is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley ), and uses a specified set of generators for the group.
Computer algebra system often include facilities for graphing equations and provide a programming language for the users' own procedures. Axiom. Axiom is a general-purpose computer algebra system. It has been in development since 1971 by IBM, and was originally named scratchpad. Richard Jenks originally headed it but over the years Barry Trager ...
A Cayley graph is a graph defined from a pair (G,S) where G is a group and S is a set of generators for the group; it has a vertex for each group element, and an edge for each product of an element with a generator. In the case of a finite cyclic group, with its single generator, the Cayley graph is a cycle graph, and for an infinite cyclic ...
t. e. In mathematics, a Lie algebra (pronounced / liː / LEE) is a vector space together with an operation called the Lie bracket, an alternating bilinear map , that satisfies the Jacobi identity. In other words, a Lie algebra is an algebra over a field for which the multiplication operation (called the Lie bracket) is alternating and satisfies ...
The 5th roots of unity in the complex plane form a group under multiplication. Each non-identity element generates the group. In abstract algebra, a generating set of a group is a subset of the group set such that every element of the group can be expressed as a combination (under the group operation) of finitely many elements of the subset and their inverses.
A Cayley graph of the symmetric group S 4 using the generators (red) a right circular shift of all four set elements, and (blue) a left circular shift of the first three set elements. Cayley table, with header omitted, of the symmetric group S 3. The elements are represented as matrices. To the left of the matrices, are their two-line form.
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