Scientific area at the interface between computer science and mathematics
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Symbolic integration of the algebraic function f(x) = x/√x4 + 10x2 − 96x − 71 using the computer algebra system Axiom
In mathematics and computer science,[1]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 mathematical objects. Although computer algebra could be considered a subfield of scientific computing, they are generally considered as distinct fields because scientific computing is usually based on numerical computation with approximate floating point numbers, while symbolic computation emphasizes exact computation with expressions containing variables that have no given value and are manipulated as symbols.
Software applications that perform symbolic calculations are called computer algebra systems, with the term system alluding to the complexity of the main applications that include, at least, a method to represent mathematical data in a computer, a user programming language (usually different from the language used for the implementation), a dedicated memory manager, a user interface for the input/output of mathematical expressions, a large set of routines to perform usual operations, like simplification of expressions, differentiation using the chain rule, polynomial factorization, indefinite integration, etc.
Computer algebra is widely used to experiment in mathematics and to design the formulas that are used in numerical programs. It is also used for complete scientific computations, when purely numerical methods fail, as in public key cryptography, or for some non-linear problems.
In mathematics and computer science, computeralgebra, also called symbolic computation or algebraic computation, is a scientific area that refers to...
A computeralgebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions...
comparison of computeralgebra systems (CAS). A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects,...
mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables...
for Algebra and Geometry Experimentation") is a computeralgebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics...
mathematical suites are computeralgebra systems that use symbolic mathematics. They are designed to solve classical algebra equations and problems in...
Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which...
complexity, numerical methods and computeralgebra. Computational mathematics refers also to the use of computers for mathematics itself. This includes...
the mathematics of computation (for example, theoretical computer science, computeralgebra, numerical analysis). Statistics is probably the most widespread...
The Casio Algebra FX series was a line of graphing calculators manufactured by Casio Computer Co., Ltd from 1999 to 2003. They were the successor models...
interaction or decay (computeralgebra) and event generators (stochastic methods). Computeralgebra: Many of the computeralgebra languages were developed...
mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure...
include: Computeralgebra, including symbolic computation in fields such as statistics, equation solving, algebra, calculus, geometry, linear algebra, tensor...
the context of differential algebra. A differential algebra is an algebra with the extra operation of derivation (algebraic version of differentiation)...
complexity, probability, algebra and number theory to invent and break codes, and analyze the security of cryptographic protocols. Computer architecture – The...
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...
mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings...
have a computeralgebra system (CAS), which means that they are capable of producing symbolic results. These calculators can manipulate algebraic expressions...
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