Part of algebraic geometry devoted to the elimination of variables between polynomials
In commutative algebra and algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating some variables between polynomials of several variables, in order to solve systems of polynomial equations.
Classical elimination theory culminated with the work of Francis Macaulay on multivariate resultants, as described in the chapter on Elimination theory in the first editions (1930) of Bartel van der Waerden's Moderne Algebra. After that, elimination theory was ignored by most algebraic geometers for almost thirty years, until the introduction of new methods for solving polynomial equations, such as Gröbner bases, which were needed for computer algebra.
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commutative algebra and algebraic geometry, eliminationtheory is the classical name for algorithmic approaches to eliminating some variables between polynomials...
Look up elimination in Wiktionary, the free dictionary. Elimination may refer to: Elimination reaction, an organic reaction in which two functional groups...
way. They concentrated on the study of elimination of variables. In 1683, Seki pushed ahead with eliminationtheory, based on resultants, in the Kaifukudai...
theorem of eliminationtheory states that every projective scheme is proper. A version of this theorem predates the existence of scheme theory. It can be...
theory Dempster-Shafer theory Dimension theory Distribution theory Dynamical systems theoryEliminationtheory Ergodic theory Extremal graph theory Field...
Quantifier elimination is a concept of simplification used in mathematical logic, model theory, and theoretical computer science. Informally, a quantified...
polynomials could be carried over directly. Traditionally, eliminationtheory is concerned with eliminating one or more variables from a system of polynomial equations...
echelon form is sometimes called Gauss–Jordan elimination. In this case, the term Gaussian elimination refers to the process until it has reached its...
The theory for varieties is older, with roots in Bézout's theorem on curves and eliminationtheory. On the other hand, the topological theory more quickly...
proceed through an "internal" elimination mechanism, the Ei mechanism. The E2 mechanism, where E2 stands for bimolecular elimination, involves a one-step mechanism...
The Elimination Chamber is a professional wrestling elimination-based match held in the WWE. The match was created by Triple H, and introduced by Eric...
was eliminated by AJ Styles. On the January 31 episode of Raw, Theory defeated Kevin Owens in a Elimination Chamber qualifying match. At Elimination Chamber...
usual resultant. It is, with Gröbner bases, one of the main tools of eliminationtheory. The resultant of two univariate polynomials A and B is commonly denoted...
if it has a perfect elimination ordering. Rose, Lueker & Tarjan (1976) (see also Habib et al. 2000) show that a perfect elimination ordering of a chordal...
basis of eliminationtheory. Probably because of the size of the computation which is implied by multivariate resultants, eliminationtheory was forgotten...
theory — Galois theory — Game theory — Gauge theory — Graph theory — Group theory — Hodge theory — Homology theory — Homotopy theory — Ideal theory —...
built (in part). In the second epoch, Noether turned her attention to the theory of rings. With her paper Moduln in nichtkommutativen Bereichen, insbesondere...
of Langlands and Shelstad Fundamental lemma of sieve theory Main theorem of eliminationtheory List of theorems Toy theorem Apostol, Tom M. (1967), Calculus...
reductive elimination. Additionally, wide ligand bite angles generally accelerate reductive elimination because the sterics force the eliminating groups...
studied by Seki Kōwa in 1683. Eliminationtheory In 1683 (Kai-Fukudai-no-Hō), Seki Kōwa came up with eliminationtheory, based on resultant. To express...
In compiler theory, common subexpression elimination (CSE) is a compiler optimization that searches for instances of identical expressions (i.e., they...
Feyerabend often confused two different notions of the sort of elimination that the term "eliminative materialism" entailed. On the one hand, they claimed, the...
determinants of the second and third order and applied it to questions of eliminationtheory; he proved many special cases of general identities. Gauss (1801)...
curve is said to be a complete intersection. By eliminating variables (by any tool of eliminationtheory), an algebraic curve may be projected onto a plane...
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