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In mathematics, the idea of a free object is one of the basic concepts of abstract algebra. Informally, a free object over a set A can be thought of as being a "generic" algebraic structure over A : the only equations that hold between elements of the free object are those that follow from the defining axioms of the algebraic structure.
Abstract algebra. The permutations of the Rubik's Cube form a group, a fundamental concept within abstract algebra. In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations acting on their elements. [1] Algebraic structures include groups, rings ...
Etymology. The word "algebra" is derived from the Arabic word الجبر al-jabr, and this comes from the treatise written in the year 830 by the medieval Persian mathematician, Al-Khwārizmī, whose Arabic title, Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala, can be translated as The Compendious Book on Calculation by Completion ...
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Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm ( / ˈælɡərɪðəm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
Solver. A solver is a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculates their solution. In a solver, the emphasis is on creating a program or library that can easily ...
Symbolic integration of the algebraic function f(x) = x / √ x 4 + 10x 2 − 96x − 71 using the computer algebra system Axiom. In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other ...
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