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In mathematics, a geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is built out of two fundamental operations, addition and the geometric product. Multiplication of vectors results in higher-dimensional objects called multivectors ...
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.
In exterior algebra and geometric algebra the exterior product of two vectors is a bivector, while the exterior product of three vectors is a trivector. A bivector is an oriented plane element and a trivector is an oriented volume element, in the same way that a vector is an oriented line element. Given vectors a, b and c, the product
Geometric algebra (GA) is an extension or completion of vector algebra (VA). [1] The reader is herein assumed to be familiar with the basic concepts and operations of VA and this article will mainly concern itself with operations in the GA of 3D space (nor is this article intended to be mathematically rigorous).
Arithmetic genus, geometric genus, irregularity; Tangent space, Zariski tangent space; Function field of an algebraic variety; Ample line bundle; Ample vector bundle; Linear system of divisors; Birational geometry. Blowing up; Resolution of singularities; Rational variety; Unirational variety; Ruled variety; Kodaira dimension; Canonical ring ...
In mathematics, geometric calculus extends geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to reproduce other mathematical theories including vector calculus , differential geometry , and differential forms .
Algebraic topology, the use in topology of algebraic methods, mainly homological algebra. Discrete geometry, the study of finite configurations in geometry. Convex geometry, the study of convex sets, which takes its importance from its applications in optimization. Complex geometry, the geometry obtained by replacing real numbers with complex ...
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.
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