Concepts inExponential space computation of Gröbner bases
Basis (linear algebra)
Basis vector redirects here. For basis vector in the context of crystals, see crystal structure. For a more general concept in physics, see frame of reference. In linear algebra, a basis is a set of linearly independent vectors that, in a linear combination, can represent every vector in a given vector space or free module, or, more simply put, which define a "coordinate system" (as long as the basis is given a definite order).
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Euclidean space
In mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions. The term ¿Euclidean¿ distinguishes these spaces from the curved spaces of non-Euclidean geometry and Einstein's general theory of relativity, and is named for the Greek mathematician Euclid of Alexandria.
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EXPSPACE
In complexity theory, EXPSPACE is the set of all decision problems solvable by a deterministic Turing machine in O(2) space, where p(n) is a polynomial function of n. (Some authors restrict p to be a linear function, but most authors instead call the resulting class ESPACE. ) If we use a nondeterministic machine instead, we get the class NEXPSPACE, which is equal to EXPSPACE by Savitch's theorem.
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