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  2. Free algebra - Wikipedia

    en.wikipedia.org/wiki/Free_algebra

    Free algebra. In mathematics, especially in the area of abstract algebra known as ring theory, a free algebra is the noncommutative analogue of a polynomial ring since its elements may be described as "polynomials" with non-commuting variables. Likewise, the polynomial ring may be regarded as a free commutative algebra.

  3. Worksheet - Wikipedia

    en.wikipedia.org/wiki/Worksheet

    In accounting, a worksheet is, or was, a sheet of ruled paper with rows and columns on which an accountant could record information or perform calculations. These are often called columnar pads, and typically green-tinted. In computing, spreadsheet software presents, on a computer monitor, a user interface that resembles one or more paper ...

  4. Free group - Wikipedia

    en.wikipedia.org/wiki/Free_group

    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 ...

  5. Free Lie algebra - Wikipedia

    en.wikipedia.org/wiki/Free_Lie_algebra

    The universal enveloping algebra of a free Lie algebra on a set X is the free associative algebra generated by X.By the Poincaré–Birkhoff–Witt theorem it is the "same size" as the symmetric algebra of the free Lie algebra (meaning that if both sides are graded by giving elements of X degree 1 then they are isomorphic as graded vector spaces).

  6. Tensor algebra - Wikipedia

    en.wikipedia.org/wiki/Tensor_algebra

    Tensor algebra. In mathematics, the tensor algebra of a vector space V, denoted T (V) or T• (V), is the algebra of tensors on V (of any rank) with multiplication being the tensor product. It is the free algebra on V, in the sense of being left adjoint to the forgetful functor from algebras to vector spaces: it is the "most general" algebra ...

  7. Maple (software) - Wikipedia

    en.wikipedia.org/wiki/Maple_(software)

    Maple (software) Maple is a symbolic and numeric computing environment as well as a multi-paradigm programming language. It covers several areas of technical computing, such as symbolic mathematics, numerical analysis, data processing, visualization, and others. A toolbox, MapleSim, adds functionality for multidomain physical modeling and code ...

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