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PARI/GP is a computer algebra system that facilitates number-theory computation. Besides support of factoring, algebraic number theory, and analysis of elliptic curves, it works with mathematical objects like matrices, polynomials, power series, algebraic numbers, and transcendental functions. [3]
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
GeoGebra (a portmanteau of geometry and algebra) is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level.
Interactive geometry software (IGS) or dynamic geometry environments (DGEs) are computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry. In most IGS, one starts construction by putting a few points and using them to define new objects such as lines , circles or other points.
Some graphing calculators have a computer algebra system (CAS), which means that they are capable of producing symbolic results. These calculators can manipulate algebraic expressions, performing operations such as factor, expand, and simplify. In addition, they can give answers in exact form without numerical approximations. [6]
The FOIL method is a special case of a more general method for multiplying algebraic expressions using the distributive law. The word FOIL was originally intended solely as a mnemonic for high-school students learning algebra. The term appears in William Betz's 1929 text Algebra for Today, where he states: [2]
Algebraic geometry is fundamentally the study by means of algebraic methods of some geometrical shapes, called algebraic sets, and defined as common zeros of multivariate polynomials. [105] Algebraic geometry became an autonomous subfield of geometry c. 1900 , with a theorem called Hilbert's Nullstellensatz that establishes a strong ...
In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties , analytic geometry deals with complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables .