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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 .
Successor to Derive. Based on Derive's engine used in TI-89/Voyage 200 and TI-Nspire handheld. Wolfram Alpha. Wolfram Research. 2009. 2013. Pro version: $4.99 / month, Pro version for students: $2.99 / month, ioRegular version: free. Proprietary. Online computer algebra system with step-by step solutions.
In algebra, the free product ( coproduct) of a family of associative algebras over a commutative ring R is the associative algebra over R that is, roughly, defined by the generators and the relations of the 's. The free product of two algebras A, B is denoted by A ∗ B. The notion is a ring-theoretic analog of a free product of groups .
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Xcas. Xcas/Giac is an open-source project developed at the Joseph Fourier University of Grenoble since 2000. Written in C++, maintained by Bernard Parisse's [ fr] et al. and available for Windows, Mac, Linux and many others platforms. It has a compatibility mode with Maple, Derive and MuPAD software and TI-89, TI-92 and Voyage 200 calculators.
In this construction, A is an algebra with involution, meaning: A is an abelian group under + A has a product that is left and right distributive over + A has an involution *, with (x*)* = x, (x + y)* = x* + y*, (xy)* = y*x*. The algebra B = A ⊕ A produced by the Cayley–Dickson construction is also an algebra with involution.
Free objects are the direct generalization to categories of the notion of basis in a vector space. A linear function u : E1 → E2 between vector spaces is entirely determined by its values on a basis of the vector space E1. The following definition translates this to any category. A concrete category is a category that is equipped with a ...