
	Where results make sense

Topic: Algebraic element

Related Topics

abstract algebra

algebraic geometry

linear algebra

algebraic topology

Boolean algebra

Lie algebra

algebraic varieties

basis linear algebra

ring algebra

associative algebra

algebraic notation

homological algebra

In the News (Wed 23 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Mathbus: Algebra and Analysis
		Elements of the rational integers are represented by LongIntegers.
		The computer algebra approach minimizes the number of operations that need to be considered by algorithms, but limits the ability to distinguish certain classes of expressions that one might want in documentation or educational materials.
		The coefficients are elements of Z as are the exponents.
	www.cs.cornell.edu /Simlab/papers/mathbus/algebra/algebra.htm (3080 words)

	Algebraic element - Wikipedia, the free encyclopedia
		In mathematics, the roots of polynomials are in abstract algebra called algebraic elements.
		These notions generalize the algebraic numbers and the transcendental numbers (where the field extension is C/Q, C being the field of complex numbers and Q being the field of rational numbers).
		The set of all elements of L which are algebraic over K is a field that sits in between L and K.
	en.wikipedia.org /wiki/Algebraic_element (378 words)

	Element Operations
		Given an element a from an algebraic field or order L, returns the characteristic polynomial of the element over R if given or the subfield or suborder F otherwise where F is the field or order over which L is defined as an extension.
		Given an element a from an algebraic field or order L, returns the minimal polynomial of the element over R if given otherwise the subfield or suborder F where F is the field or order over which L is defined as an extension.
		For an element a of an algebraic field F, a sequence of coefficients of length degree of F with respect to the basis is returned.
	www.umich.edu /~gpcc/scs/magma/text634.htm (1704 words)

	PlanetMath: non-constant element of rational function field
		"non-constant element of rational function field" is owned by pahio.
		Cross-references: relatively prime, factors, irreducible, constant, mean, power, ring, equation, satisfies, algebraic, base field, transcendental, denominator, numerator, degrees, lowest terms, reduced, polynomials, rational functions, indeterminate, polynomial ring, field of fractions, extension, field extension, field
		This is version 14 of non-constant element of rational function field, born on 2005-02-16, modified 2005-08-26.
	planetmath.org /encyclopedia/FieldOfRationalFunctions.html (193 words)

	Algebraic number - Wikipedia, the free encyclopedia
		The concept of algebraic numbers can be generalized to arbitrary field extensions; elements in such extensions that satisfy polynomial equations are called algebraic elements.
		In fact, it is the smallest algebraically closed field containing the rationals, and is therefore called the algebraic closure of the rationals.
		The name algebraic integer comes from the fact that the only rational numbers which are algebraic integers are the integers, and because the algebraic integers in any number field are in many ways analogous to the integers.
	en.wikipedia.org /wiki/Algebraic_number (579 words)

	GAP Manual: 16.4 Algebraic Extension Elements (Site not responding. Last check: 2007-11-06)
		According to Kronecker's construction, the elements of an algebraic extension are considered to be polynomials in the primitive element.
		Unless they are already in the defining field (in which case they are represented as elements of this field), they are represented by records in sf GAP (see Extension Element Records).
		The extension corresponding to this primitive element is the default field for the algebraic element.
	www-groups.dcs.st-and.ac.uk /~gap/Gap3/Manual3/C016S004.htm (85 words)

	ABSTRACT ALGEBRA ON LINE: Fields
		F be an element algebraic over K. If the minimal polynomial of u over K has degree n, then K(u) is an n-dimensional vector space over K. Definition.
		Let F be an extension field of K. The set of all elements of F that are algebraic over K forms a subfield of F. Definition.
		G is an element of maximal order in G, then the order of every element of G is a divisor of the order of a.
	www.math.niu.edu /~beachy/aaol/fields.html (1525 words)

	Algebraic Hoop Construction
		Two elements are abcd and adcb, and others are constructed as other letter sequences.
		Each triplet of elements is a 'hooplet' which obeys rule 3, and also an identity function due to rule 4.
		The set of elements in the original list is sometimes called a basis for the generated hoop.
	c2.com /cgi/wiki?AlgebraicHoopConstruction (3393 words)

	c7s4p5df1rk (Site not responding. Last check: 2007-11-06)
		An algebraic number is characterised by the fact that it generates a subfield of C that is finite-dimensional, when viewed as a vector space over Q.
		If a is algebraic, then there is a polynomial of minimal degree of which a is a zero.
		The notion of algebraic element exists for any field K with a subfield L: an element of K is called algebraic over L if it is a zero of a nonzero polynomial in K[X].
	www.win.tue.nl /~ida/alge/c7s4p5df1rk.html (126 words)

	Algebraic P-adic Numbers
		This brings in lots of new, algebraic elements, like the square root of 2, but R is not algebraically closed, since there is no square root of -1.
		Its completion Q′ brings in additional elements, including quite a few algebraic elements that were not part of Q. But don't confuse the square root of 2 in the 7-adic topology with 1.4142135..., which is the square root of 2 in the linear topology.
		Q′ is not algebraically closed, nor does it contain the algebraic closure of Q. The answer to (2) is no, as we expected.
	www.mathreference.com /id-val,palg.html (1269 words)

	AlgFields Functions
		The indeterminate in each polynomial is used as the name of the new algebraic element in the field.
		Each pair of lists represents an automorphism of L over K: the first list consists of the algebraic numbers adjoined to K in defining L, and the second list gives, in order, the algebraic numbers to which the first numbers are sent under the isomorphism.
		Elements of list1 and list2 must be algebraic numbers used in defining K (resp., L) over the rationals (resp., over K)---and must be a list obtained from taking, in order, the first so many algebraic numbers used in the definition.
	www.davidson.edu /math/swallow/AlgFieldsWeb/functions.htm (2146 words)

	The Encyclopedia of Computer Languages
		Thus attributes of a group include type, elements, conjugacy classes, subgroup lattice etc. Note that generally only a subset of the attributes of a structure are defined during a computation within that structure.
		Typical of the facilities provided are: the arithmetic operations of the ring, the calculation of polynomial gcdandquot;s, the location of the zeros of a polynomial; and some operations from calculus: differentiation, integration, the calculation of limits, and the analytic solution of certain classes of differential equations.
		Bosma, Wieb; John Cannon Graham Matthews "Programming with algebraic structures: design of the MAGMA language" view detailsAbstract: MAGMA is a new software system for computational algebra, number theory and geometry whose design is centred on the concept of algebraic structure (magma).
	hopl.murdoch.edu.au /showlanguage2.prx?exp=710 (4989 words)

	GAP Manual: 16.5 Set functions for Algebraic Extensions (Site not responding. Last check: 2007-11-06)
		As algebraic extensions are fields, all set theoretic functions are applicable to algebraic elements.
		tests, whether a given object is contained in an algebraic extension.
		A random algebraic element is computed by taking a linear combination of the powers of the primitive element with random coefficients from the ground field.
	www-groups.dcs.st-and.ac.uk /gap/Gap3/Manual3/C016S005.htm (118 words)

	PlanetMath: algebraic
		This is version 4 of algebraic, born on 2002-01-05, modified 2005-03-15.
		Object id is 1297, canonical name is Algebraic.
		(Commutative rings and algebras :: Ring extensions and related topics :: Extension theory)
	planetmath.org /encyclopedia/Algebraic.html (32 words)

	FEM Books-Chung (Site not responding. Last check: 2007-11-06)
		Selected papers from the 7th International Conference on Finite Element Methods in Flow Problems, held at the University of Alabama in 1989.
		The selections are on the cutting edge of knowledge in finite element methodology and application, representing a major contribution to the field.
		In four main parts, the proceedings contains a wide range of topics concerning adaptive methods in computational fluid dynamics, the streamline diffusion finite element method, algebraic grid generation, mixed finite element methods, Navier-Stokes equations, finite element methods for 3D incompressible viscous flows and 3D turbulent incompressible flows, and analysis of reacting flows in combustion.
	ohio.ikp.liu.se /fe/chun.html (110 words)

	[No title]
		The previous section contained a defintion of an algebraic set as the locus defined by an ideal.
		(In this case, each ideal is generated by just one element.) The induction step is made more managable by introducing the following definition.
		A(X), you get two distinct algebraic sets, possibly embedded in different affine spaces, with the same coordinate ring.
	odin.mdacc.tmc.edu /~krc/agathos/hilbert.html (536 words)

	cm conference abstract: Henson & Vassilevski (Site not responding. Last check: 2007-11-06)
		The rule we propose is related to the interpolation described in [1] for AMGe, an element-based algebraic multigrid.
		Further, these element matrices must be built on all coarse levels, which is a non--trivial and expensive task [2].
		Based on the rigid body modes, we specify appropriate boundary conditions which are imposed on a local neighborhood matrix associated with a fine degree of freedom.
	www.mgnet.org /mgnet/Conferences/CMCIM00/abs/henson.html (385 words)

	Algebraic Element -- from Wolfram MathWorld
		Moreover, the sum, difference, product, and quotient of algebraic elements are again algebraic.
		The imaginary unit i is algebraic over the field
		"Algebraic Element." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.
	mathworld.wolfram.com /AlgebraicElement.html (94 words)

	Singular Manual: minpoly
		describes the coefficient field of the current basering as an algebraic extension with the minimal polynomial equal to
		The minimal polynomial has to be specified in the syntax of a polynomial.
		Its variable is not one of the ring variables, but the algebraic element which is being adjoined to the field.
	www.msri.org /about/computing/docs/singular/sing_309.htm (116 words)

	Functions
		Algebraic module univariate polynomial, binary rational evaluation of sign.
		AFUPIIWS(M,I,A,L) Algebraic number field univariate polynomial isolating intervals weakly disjoint to strongly disjoint
		Algebraic module univariate polynomial isolating intervals weakly disjoint to strongly disjoint
	www.mcs.drexel.edu /~krandick/saclib/node69.html (599 words)

	Hypre
		Hypre contains several families of preconditioned algorithms focused on the scalable solution of very large sparse linear systems.
		These interfaces include stencil-based structured/semi-structured interfaces, finite-element based unstructured interface, and a linear algebra based interface.
		The second kind is a semi-structured grid interface named sstruct that targets applications with grids that are mostly structured, but with some unstructured features (e.g., AMR, block-structured, overset).
	acts.nersc.gov /hypre (450 words)

	Definitions of Terms (Site not responding. Last check: 2007-11-06)
		A real number that is also an algebraic number.
		A real algebraic number is represented by an integral minimal polynomial and an acceptable isolating interval.
		The integral minimal polynomial for an algebraic number
	www.mcs.drexel.edu /~krandick/saclib/node67.html (154 words)

	NSDL Metadata Record -- Algebraic Element -- from MathWorld
		NSDL Metadata Record -- Algebraic Element -- from MathWorld
		Given a field F and an extension field K\supseteq F, an element \alpha\in K is called algebraic over F if it is a root of some nonzero polynomial with coefficients in F. Obviously, every element of F is algebraic over F. Moreover, the sum, difference, product, and quotient of algebraic elements are again algebraic.
		It follows that the simple extension field F(\alpha) is an algebraic extension of F iff \alpha is algebraic over F. The imaginary unit i is algebraic over the field \mathbb{R} of...
	nsdl.org /mr/697653 (108 words)

	Subindex: element-access .. Elementary
		Construction of Elements of Structure Constant Algebras (LIE ALGEBRAS)
		Element Operations on Differential Ring Elements (DIFFERENTIAL RINGS, FIELDS AND OPERATORS)
		Element Operations on Differential Operators (DIFFERENTIAL RINGS, FIELDS AND OPERATORS)
	www.math.lsu.edu /magma/inde4.htm (212 words)

	[No title]
		StarkUnitsPolynom -> Determines the minimal polynomial of the Stark-Unit used to compute the Hilbert Class Field.
		StarkUnitsRealPolynom -> Determines a real approximation of the minimal polynomial of a primitive element generating the Hilbert class field of a totally real algebraic number field.
		The name of the Galois group is returned.
	www.ibiblio.org /pub/Linux/apps/math/symbolic/kash-2.2.CHANGES (618 words)

	Subindex: operation-element .. operations_curve-predicates
		Operations on Elements (p-ADIC RINGS AND THEIR EXTENSIONS)
		Operations on Elements of Ideals (FINITELY PRESENTED ALGEBRAS)
		Operations on Elements of Ideals (IDEAL THEORY AND GRÖBNER BASES)
	magma.maths.usyd.edu.au /magma/htmlhelp/indo2.htm (136 words)

	Multiple of an Algebraic (Site not responding. Last check: 2007-11-06)
		given an algebraic element over an integral domain r, some multiple of that element is integral.
		Let u be a root of p(x), the algebraic element.
		Build a new polynomial q(x) by multiplying a
	www.mathreference.com /id-ext,mult.html (134 words)

	Index O
		Operations on Structure Constant Algebras (STRUCTURE CONSTANT ALGEBRAS)
		Operations on Associative Algebras and their Elements (ASSOCIATIVE ALGEBRAS)
		Operations on Group Algebras and their Subalgebras (GROUP ALGEBRAS)
	www.umich.edu /~gpcc/scs/magma/indO.htm (1032 words)

	Subindex: element .. element
		Element Construction and Operations (MODULES OVER AN ALGEBRA)
		Element Constructions and Conversions (p-ADIC RINGS AND THEIR EXTENSIONS)
		Elements of a Generic Abelian Group (GENERIC ABELIAN GROUPS)
	www.math.lsu.edu /magma/inde3.htm (321 words)

	James B Von Oehsen (Site not responding. Last check: 2007-11-06)
		PhD, Algebraic Topology, Rutgers, The State University of New Jersey, 1990
		I am currently overseeing the research and development of a software package for CAEFF that numerically models viscoelastic flow occurring in polymer processing.
		Barr von Oehsen, Christopher L. Cox, Eric C. Cyr, and Brian A. Malloy, Using Design Patterns and XML to Construct an Extensible Finite Element System, Proceedings of The 2002 International Conference on Computational Science, Amsterdam, The Netherlands, April 21-24, 2002, Lecture Notes in Computer Science, Springer-Verlag.
	www.math.clemson.edu /facstaff/joehsen.htm (190 words)

Try your search on: Qwika (all wikis)