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	Algebraic number - Wikipedia, the free encyclopedia
		In mathematics, an algebraic number is any number that is a root of an algebraic equation, a non-zero polynomial with integer (or equivalently, rational) coefficients.
		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 (569 words)

	Polynomial - Wikipedia, the free encyclopedia
		In elementary algebra, methods are given for solving all first degree and second degree polynomial equations in one unknown.
		An equation of the form p(x)=0 is called a polynomial equation in the unknown x.
		The reduction of equations in several unknowns to equations in one unknown each is discussed in the article on the Buchberger's algorithm.
	en.wikipedia.org /wiki/Polynomial (2460 words)

	PlanetMath: algebraic equation
		By the degree of an algebraic equation is meant the degree of the polynomial.
		are algebraic equations, the degrees of which are 2 and 3.
		This is version 2 of algebraic equation, born on 2005-05-04, modified 2005-05-04.
	planetmath.org /encyclopedia/AlgebraicEquation.html (101 words)

	Algebraic equation - Wikipedia, the free encyclopedia
		In mathematics, an algebraic polynomial over a given field is a polynomial with coefficients in that field.
		Note that an algebraic equation can always be converted to one in which the coefficients are integers.
		If all the other coefficients of this form are integers, the roots of the equation are algebraic integers.
	en.wikipedia.org /wiki/Algebraic_equation (158 words)

	How do I solve systems of differential and algebraic equations?
		A set of equations that includes both differential equations and algebraic equations is called a differential-algebraic equation, or DAE.
		Differential-algebraic equations are usually solved either by first solving the algebraic equations and using the solution to construct a set of purely differential equations, or by solving the differential equations and using the solution to construct a set of purely algebraic equations.
		If neither the algebraic equations nor the differential equations can be solved symbolically, then it may be useful to consider a purely numerical solution.
	support.wolfram.com /mathematica/mathematics/equations/dae.html (383 words)

	Search Results for equation*
		He solved his operator equation in the particular cases which arise in the study of the physical problem in his thesis (and in the paper which appeared in 1900 based on that thesis) while the general case was solved by Fredholm somewhat later and not published until 1908.
		In 1799 Ruffini published a book on the theory of equations with his claim that quintics could not be solved by radicals as the title shows: General theory of equations in which it is shown that the algebraic solution of the general equation of degree greater than four is impossible.
		Although an algebraic equation of the fifth degree cannot be solved in radicals, a result which was proved by Ruffini and Abel, Hermite showed in 1858 that an algebraic equation of the fifth degree could be solved using elliptic functions.
	www-groups.dcs.st-and.ac.uk /~history/Search/historysearch.cgi?SUGGESTION=equation*&CONTEXT=1 (17342 words)

	algebraic curve (Site not responding. Last check: 2007-11-01)
		A curve is algebraic when its defining Cartesian equation is algebraic, that is a polynomial in x and y.
		An algebraic curve with degree greater than 2 is called a higher plane curve.
		An algebraic curve is called a circular algebraic curve, when the points (±1, ± i) are on the curve.
	www.2dcurves.com /algebraic.html (184 words)

	SparkNotes: Variables: Solving Algebraic Equations
		The goal in solving an equation is to get the variable by itself on one side of the equation and a number on the other side of the equation.
		Herein lies a vital role of solving algebraic equations: whatever operation is carried out on one side of the equal sign in an equation must be carried out on the other side as well.
		To solve an algebraic equation, reverse all the operations on the variable side of the equation by performing their inverse operations on both sides of the equation.
	www.sparknotes.com /math/prealgebra/variables/section3.rhtml (510 words)

	Solutions to Algebraic Equations
		There are three key ideas in an equation: an equation must involve two expressions, the expressions must be equal, and the equation must indicate that the expressions are equal.
		An identity is an equation that is true for all values of the unknown involved.
		Although this is a straightforward application of an algebraic equation to the solution of a physical problem, it illustrates the general approach that is used.
	www.tpub.com /doemathematics/mathematics40.htm (569 words)

	Visualizing solutions to n-th degree algebraic equations using right-angle geometric paths, based on Lill's Method. (Site not responding. Last check: 2007-11-01)
		In forming the right-angle path for a quadratic equation, the directions for the a, b, and c lines are individually absolute in the sense that a negative coefficient would be represented by a line in the opposite direction, without affecting the directions for the other coefficients.
		However, the algebraic solution is complicated and is usually not represented by one single equation, but rather by a sequence of equations with intermediary values, some of which are complex numbers.
		The resulting algebraic equation will be of order n + 2 and will have the same roots as the original equation of order n, and two additional roots which are: x = +/- i, where i is the square root of - 1, the unit imaginary number.
	www.concentric.net /~pvb/ALG/rightpaths.html (3794 words)

	PS2h, Algebraic Equations and Programs
		The equation is linear in the unknown, i.e.
		To be able to do this it would be necessary for one equation to contain only one of the unknowns, it would not matter which, and the other could contain both.
		As two special cases, we have provided a simple iterative solver fo single algebraic equations and a standard solver for sets of linear equations.
	www.chemeng.ed.ac.uk /people/jack/Webware/modelling/algebraic (684 words)

	PlanetMath: equation
		See Also: algebraic equation, Diophantine equation, difference equation, differential equation, functional equation, proportion equation, finite difference, recurrence relation
		This is version 14 of equation, born on 2005-08-17, modified 2006-07-20.
		Object id is 7330, canonical name is Equation.
	planetmath.org /encyclopedia/Solution.html (213 words)

	Composite number for pi satisfies Euler's equation.
		The equation of a straight line is completely determined if the length of the perpendicular from the origin (0, 0) to the line is known, and if the angle that this perpendicular makes with the x-axis is known.
		and we note that the coefficients of this equation are in the form of a perfect square as described in the preceding paragraph.
		Algebraic irrational number — An irrational number that can be expressed as a root of an algebraic equation of the 2nd degree, for example x
	members.ispwest.com /r-logan/fullbook.html (4935 words)

	Types of Algebraic Equations
		The letters in algebraic equations are referred to as unknowns.
		The degree of an equation determines the number of roots of the equation.
		equation is the same as the degree of the equation.
	www.tpub.com /content/doe/h1014v1/css/h1014v1_119.htm (339 words)

	Math Forum Discussions (Site not responding. Last check: 2007-11-01)
		an algebraic equation and "polynomial equation with integer coefficients,"
		an algebraic number was a solution generated by an algebraic equation.
		incapable of being the root of an algebraic equation with
	mathforum.org /kb/thread.jspa?threadID=107257&messageID=552217 (986 words)

	Numerical Methods/Equation Solving - Wikibooks, collection of open-content textbooks
		While roots can be found directly for algebraic equations of fourth order or lower, and for a few special transcendental equations, in practice we need to solve equations of higher order and also arbitary transcendental equations.
		An algebraic equation can have at most as many positive roots as the number of changes of sign in f(x).
		The roots are calculated using the equation of the chord, i.e.
	en.wikibooks.org /wiki/NumericM:Equation_Solving (1396 words)

	Exploration Guide: Using Algebraic Equations Gizmo \| ExploreLearning
		Your goal is to form an English sentence that matches the algebraic equation by selecting the correct tiles and arranging them in the proper order.
		Drag tiles one by one to the bottom bin to form an algebraic equation that matches the English sentence.
		Click NEW until an algebraic equation involving addition or multiplication is displayed at the top of the Gizmo.
	www.explorelearning.com /index.cfm?method=cResource.dspExpGuide&ResourceID=123 (649 words)

	Program Files\Netscape\Communicator\Program\nshsalg\algeqn01
		This view of an equation amounts to reading an equation as an assertion that every choice of numerical values for the variables is a solution for the equation.
		The third, seventh and eighth equations are of this form.
		For an equation to be a formula in this sense it is necessary that "one side" of the equation (generally the left-side) consist of a single variable that does not occur on the other side of the equation.
	www.ii.uib.no /~wagner/hsalg/algeqn01.htm (534 words)

	Writing Algebraic Equations
		The symbols 17 + x = 68 form an algebraic equation.
		An algebraic equation is an equation that includes one or more variables.
		Directions: Select the algebraic equation that correctly represents the given sentence.
	www.mathgoodies.com /lessons/vol7/equations.html (298 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		The class implements an algebraic equations that typically extends the algebraic problem posed by the discretization of a PDE-based model.
		The constructor with integer arguments allocates the indicated number of coefficients and sets all these coefficents to be zero.
		It also initializes the global size of the matrix row correspond ing to this equation (the sum of the number of PDE unknowns and the number of extra algebraic unknowns), and sets the global equation number.
	www.phys.uu.nl /DU/diffpack/AlgebraicEquation.html (201 words)

	Using Algebraic Equations Gizmo \| ExploreLearning
		Read the equation or sentence and select word tiles or symbol tiles to form the corresponding sentence or equation.
		If you formed an algebraic equation to model the sentence, three times a number is equal to nine, how many variables would be in the equation?
		Which algebraic equation models the English sentence, a number subtracted from 8 is equal to 4?
	www.explorelearning.com /index.cfm?method=cResource.dspView&ResourceID=123&CFID=737113&CFTOKEN=58631594 (327 words)

	Computers Support Algebraic Thinking (Site not responding. Last check: 2007-11-01)
		Try this problem: Write an equation using the variables Sand P to represent this statement: "There are six times as many students as professors at this university." Use S for the number of students and P for the number of professors.
		Equations on paper are rarely "run." Running equations on a computer allows students to work with the process--testing, debugging, and exploring.
		If we see algebra as primarily the study of functions and their representations, we might use function plotters, curve fitters, and symbolic manipulators.
	investigations.terc.edu /relevant/ComputersSupport.html (3367 words)

	algebraic equation
		Our software Algebra Buster provides step-by-step problem solutions and explanations to most problems found in reviewed algebra books (elementary to college level).
		The step-by-step lessons include hundreds of practice problems and over 50 Algebra 2 topics using animation, sound and hands-on demonstrations for math success.
		This textbook is intended for a one term sophomore/junior level course, its goal is to ease the transition from lower division calculus courses, to upper level courses in algebra, analysis, number theory and so on.
	www.algebra-online.com /algebraic-equation.html (347 words)

	Engineering and Scientific Subroutine Library for AIX Version 3 Release 3: Guide and Reference - Overview of the Linear ...
		Some of the linear algebraic equations were designed in accordance with the Level 2 BLAS, Level 3 BLAS, and LAPACK de facto standard.
		The dense linear algebraic equation subroutines provide solutions to linear systems of equations for both real and complex general matrices and their transposes, positive definite real symmetric and complex Hermitian matrices, real symmetric indefinite matrices and triangular matrices.
		The sparse linear algebraic equation subroutines provide direct and iterative solutions to linear systems of equations both for general sparse matrices and their transposes and for sparse symmetric matrices.
	www.nersc.gov /vendor_docs/ibm/essl/essl133.html (1048 words)

	how do i convert a basic algebraic equation
		This course highlights the essentials of arithmetic, algebra, and geometry.
		This course includes a review of operations with fractions and decimals, and includes operations with percent, scientific notation, unit conversions, perimeter, area, volume, basic algebra, equations and formulas, right triangles, data graphs, and descriptive statistics.
		Develop mathematic and problem solving skills that include accuracy, correct use of order of operations and procedures, use of calculator or measurement tools, use of appropriate geometric formulas, interpretation of data, and use of variables in algebraic expressions and equations.
	www.softmath.com /tutorials2/how-do-i-convert-a-basic-algebraic-equation.html (355 words)

	Control of Nonlinear Differential Algebraic Equation Systems with Applications to Chemical Processes
		The feedback control of nonlinear differential and algebraic equation systems (DAEs) is a relatively new subject.
		This book-the first of its kind-introduces the reader to the inherent characteristics of nonlinear DAE systems and the methods used to address their control, then discusses the significance of DAE systems to the modeling and control of chemical processes.
		Within a unified framework, Control of Nonlinear Differential Algebraic Equation Systems presents recent results on the stabilization, output tracking, and disturbance elimination for a large class of nonlinear DAE systems.
	www.ramex.com /ch/ch-3678.html (223 words)

	Cynthia Lanius' Lessons: Algebra - Fun with Calendars
		Your friend should tell you only the sum of the four days, and you can tell her what the four days are.
		Let's pretend that the 4 numbers that the person chose were the highlighted ones here - 18, 19, 25, and 26.
		Factor 4 from the left side of the equation:
	math.rice.edu /~lanius/Lessons/calen.html (301 words)

	algebraic and analytical thinking (Site not responding. Last check: 2007-11-01)
		The game entitled "Great Equations" found in the 3rd/4th grade section allows the students to solve open ended equations by dragging numbers into the correct place in the equation.
		This is an interactive site for 4th grade and up students to solve algebraic problems.
		Students solve algebraic equations by finding the value of x and can then submit their answer for scoring.
	www.svsu.edu /mathsci-center/eaat.htm (826 words)

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