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Topic: Bezout

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Etienne Bezout

Vandermonde

Cramer

Determinant

Adjoint

Invertible matrix

Vandermonde matrix

Determinant

	Bezout's Theorem (Site not responding. Last check: 2007-10-12)
		Bezout's Theorem is an important theorem in algebraic geometry.
		Bezout's Theorem tells us that the curves intersect in exactly 2 * 1 = 2 points.
		We now plot the solutions to the two polynomial equations in Figure 1 and observe that the intersections are as predicted by our algebra and the number of intersections are as predicted by Bezout's Theorem.
	www.geocities.com /akselsogstad/algnotes/bezout.html (316 words)

	PlanetMath: Bezout domain
		The above equation is known as the Bezout identity, or Bezout's Lemma.
		Cross-references: Bezout's lemma, equation, between, greatest common divisor, ideal generated by, gcd domain, PID, ideal, finitely generated, integral domain
		This is version 7 of Bezout domain, born on 2004-04-23, modified 2005-01-28.
	planetmath.org /encyclopedia/BezoutDomain.html (91 words)

	[No title] (Site not responding. Last check: 2007-10-12)
		Kirwan notes that the reason for associating B{\'e}zout's name to the theorem ``is not entirely clear, since although B{\'e}zout gave a proof of the theorem, it was neither correct nor the first proof to be given''.
		At least it tells something about Bezout: I have read in some place, that in fact, the lemma you mention, has been brought to the attention of mathematicians by " Bachet de Meziriac" contemporary of Fermat, Pascal....
		Bezout, French mathematician lived during the 19th century.
	www.math.niu.edu /~rusin/known-math/95/bezout (198 words)

	finalproject (Site not responding. Last check: 2007-10-12)
		And their resultant, computed by Bezout determinantal form, is a polynomial of u, r(u).
		Since ai (i=0...3) and bi (i=0...3) in the Bezout determinant are third-degree polynomials of u, the resultant is a 18th degree polynomial.
		When caculating the Bezout determinant, the terms of u have to be collected at each step of calculating each determinant inside it; otherwise, a huge number of terms results.
	www.cs.unc.edu /~yan/comp236/finalproject/finalproject.html (1407 words)

	Candidates' Seminar (Site not responding. Last check: 2007-10-12)
		Bezout's theorem answers this question by relating the degree of the polynomials with the number of the geometric intersection points in the projective plane (where intersections at infinity are counted).
		But via Bezout's theorem it turns out to apply to purely geometric problems such as the classical theorem in projective geometry known as "Pascal's Theorem".
		Later, in the second part we will be able to state Bezout's theorem and give the detailed proof of Pascal's Theorem.
	www.math.temple.edu /~renault/candidates/mohammed.html (196 words)

	The Resultant and Bezout's Theorem
		Today the proposition is known as Bezout's Theorem, named after Etienne Bezout (1730-1783), who developed the theory of determinants and resultants.
		Bezout offered a proof of this theorem in 1779, but it did not correctly account for the multiplicities of intersection points in all cases.
		Since the degrees of these polynomials are 5 and 3, Bezout's Theorem implies that there are 15 points of intersection between them.
	www.mathpages.com /home/kmath544/kmath544.htm (2714 words)

	Bezout's Theorem
		The varieties illustrated are ellipses and thus are of degree 2.
		According to Bezout's Theorem the number of intersection points should be 2x2=4.
		There are of course many more possibilities than are covered in the six Figures and many would appear to violate Bezout's Theorem, but it should be clear from the above illustrations that when intersections are considered in the complex projective plane Bezout's Theorem holds.
	www.sjsu.edu /faculty/watkins/bezout.htm (795 words)

	[No title] (Site not responding. Last check: 2007-10-12)
		Subject: Re: bezout domain Date: Fri, 11 Aug 2000 14:59:00 GMT Newsgroups: sci.math Summary: [missing] In article
		wrote: > I want an example of (non-principal) bezout domain in which every > finitely generated ideal is principal.
		Well I have no idea what a bezout domain is. An interesting example of an non-principal integral domain where every finitely generated ideal is principal would be the holomorphic functions on a connected open set in the plane.
	www.math.niu.edu /~rusin/known-math/00_incoming/domains (170 words)

	Complexity of Solving the Algebraic Bezout Equation (Site not responding. Last check: 2007-10-12)
		Sharp estimates have been made of the complexity in solving the algebraic Bezout equation for polynomials with coefficients in fields of arbitrary characteristic.
		Solving the algebraic Bezout equation is central to the problem of control of linear distributed parameter systems and related questions in Systems Theory.
		The monograph Residue currents and Bezout identities, Berenstein, Gay, Vidras and Yger, Prog.
	www.isr.umd.edu /ISR/accomplishments/002_Bezout (103 words)

	Complexity of Bezout's theorem V: Polynomial time - Shub, Smale (ResearchIndex)
		Abstract: this paper is to show that the problem of finding approximately a zero of a polynomial system of equations can be solved in polynomial time, on the average.
		14 Complexity of Bezout's Theorem III: Condition number and pac..
		Complexity Of Bezout's Theorem IV: Probability Of Success;..
	citeseer.ist.psu.edu /shub94complexity.html (565 words)

	Coq.ZArith.Znumtheory
		Bezout_intro : forall u v:Z, u * a + v * b = d -> Bezout a b d.
		Zis_gcd_bezout : forall a b d:Z, Zis_gcd a b d -> Bezout a b d.
		bezout_rel_prime : forall a b:Z, Bezout a b 1 -> rel_prime a b.
	coq.inria.fr /library/Coq.ZArith.Znumtheory.html (1602 words)

	Discrete mathematics:Number theory - Wikibooks
		The general case is known as Bezout's identity.
		Bezout's identity above provides us with the key to solving equations in the form
		Bezout's identity on calculating gcd(a, m) will always give you the multiplicative inverse of a modulo m.
	en.wikibooks.org /wiki/Discrete_mathematics:Number_theory (4785 words)

	Bezout's Identity (Site not responding. Last check: 2007-10-12)
		In the ring of integers, gcd(a,b) can always be written as a linear combination of a and b.
		Bezout (biography) showed that the same is true in a pid, although there may not be an efficient algorithm for deriving the gcd, or the linear combination that produces the gcd.
		In a pid, let a and b generate the principle ideal c*r.
	www.mathreference.com /id,bez.html (161 words)

	Welcome to Jacques Beniot Bezout's homepage (Site not responding. Last check: 2007-10-12)
		Jacques Benoit Bezout, 76, died May 10, 2005, after battling a long illness.
		He was born January 5, 1929, to Emily (De Catalogne) and Joseph Bezout in Cap-Haitien, Haiti.
		Mwitu Ndugu) of Portland, OR, Dominique and Natalie Bezout of Cambria Heights, NY, and Christopher Jean Lubin of Ashaway, RI; and three grandchildren.
	www.jacquesbezout.com (336 words)

	MERL – Bezout Equalizer for MIMO Systems
		We have developed the Bezout equalizer to combat the both interferences through a simple array of linear FIR filters.
		We air to use this approach to enhance the receiver design and improve the performance.
		Technical Discussion: This work provides a system and method that designs an optimum Bezout space-time equalizer based on estimated MIMO channel characteristics, combines Bezout space-time equalizers with sequential detection and decoding techniques, and processes the input sequences via a layered and pipeline architecture.
	www.merl.com /projects/bezout_equalizer (353 words)

	[No title]
		( we now exhibit an algorithm that computes Bezout** coefficient: for all a b, there is u and v such that au-bv = gcd(a,b) or bv-au = gcd(a,b) ) (* the 4 lemmae gives the idea of the algorithm *) Lemma bezout_aux1 : forall (x y u v:nat),(x
		( Bezout*' theorem and relatively prime numbers ) Theorem bezout_rel_prime : forall (a b:nat),(rel_prime a b)
		elim (bezout d a b);try (unfold is_gcd;unfold is_cd;trivial).
	lamp.epfl.ch /~sbriais/coq/sqrt/sqrt.v8 (2800 words)

	HJM, Vol. 30, No. 2, 2004
		The purpose of this paper is to introduce two new classes of rings that are closely related to the classes of Prüfer domains and Bezout domains.
		If every finitely generated nonnil ideal of R is phi-invertible, then we say that R is a phi-Prüfer ring.
		Also, we say that R is a phi-Bezout ring if phi(I) is a principal ideal of phi(R) for every finitely generated nonnil ideal I of R. We show that the theories of phi-Prüfer and phi-Bezout rings resemble that of Prüfer and Bezout domains.
	www.math.uh.edu /~hjm/Vol30-2.html (1741 words)

	Fast Parallel Computation of the Polynomial Remainder Sequence Via Bezout and Hankel Matrices
		Fast Parallel Computation of the Polynomial Remainder Sequence Via Bezout and Hankel Matrices: SIAM Journal on Computing Vol.
		This result is obtained by reducing the Euclidean scheme to computing the block triangular factorization of the Bezout matrix associated with $u(x)$ and $v(x)$.
		This approach is also extended to the evaluation of polynomial gcd (greatest common divisor) over any field of constants in $O(\log^2 n)$ steps with the same number of processors.
	epubs.siam.org /sam-bin/dbq/article/20190 (167 words)

	Faculty Handbook Online 2005/06 : Module Description - Durham University
		Bezout's theorem: Resultants, weak form of Bezout, applications of Pascal's theorem, Cayley-Bacharach theorem, group law on a cubic.
		Bezout's theorem: applications, flexes, Hessian, configuration of flexes of a cubic.
		Reading material on a topic in the following area:parametrizing the branches of a curve by Puiseux Series.
	www.dur.ac.uk /faculty.handbook/module_description.php?module_code=MATH4011 (374 words)

	Elliptic curves and Bezout's theorem
		Bezout's Theorem (almost): It is almost true that the intersection of a curve
		To make the theorem true, some care must be taken.
		The precise version of Bezout's Theorem reads as follows:
	mathcircle.berkeley.edu /BMC4/Handouts/elliptic/node5.html (431 words)

	Citebase - Bezout's theorem and Cohen-Macaulay modules (Site not responding. Last check: 2007-10-12)
		We prove a Bezout theorem for modules which meet very properly.
		Furthermore, we show for equidimensional subschemes X and Y: If they intersect properly in an arithmetically Cohen-Macaulay subscheme of positive dimension then X and Y are arithmetically Cohen-Macaulay.
		Use the Correlation Generator to explore the correlation between download impact ("hits") and citation impact.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/9907074 (435 words)

	Atlas: Preufer and Bezout $f$-ring extensions by Digen Zhang (Site not responding. Last check: 2007-10-12)
		Atlas: Preufer and Bezout $f$-ring extensions by Digen Zhang
		Let R be a commutative f-ring with 1 (not necessary with the bounded inversion).
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # camj-03.
	atlas-conferences.com /cgi-bin/abstract/camj-03 (112 words)

	Search results for 'Struppa' (Site not responding. Last check: 2007-10-12)
		TR 86-74: Small Degree Solutions for the Polynomial Bezout Equation.
		TR 87-101: Small Degree Solutions for the Polynomial Bezout Equation.
		K.Y. Choi, A.A. Khan TR 86-74: Small Degree Solutions for the Polynomial Bezout Equation.
	www.isr.umd.edu /htdig-cgi-bin/htsearch?method=and&format=long&sort=score&config=isr&words=Struppa&restrict=TechReports (379 words)

	Elliptic curves and Bezout's theorem
		Bezout's Theorem (almost): It is almost true that the intersection of a curve f(x,y)=0 of degree mwith a curve g(x,y)=0 of degree nconsists of exactly mn points.
		Bezout's Theorem: Let X and Y be curves of degrees m and nin the projective plane over the complex numbers.
		If X and Y have no curves in common, then the number of intersection points in
	mathcircle.berkeley.edu /elliptic1/node5.html (576 words)

	Bezout
		This page computes arithmetic relations between 2 integers or polynomials: gcd, lcm, euclidean division, Bezout relation.
		It is useless for you to gather them through a robot program.
		Description: computes euclidean division, gcd, lcm, Bezout relation.
	wims.unice.fr /~wims/wims.cgi?lang=en&module=tool/arithmetic/bezout.en&cmd=new (147 words)

	Bézout Identities With Inequality Constraints (ResearchIndex) (Site not responding. Last check: 2007-10-12)
		14 Residue Currents and Bezout Identities (context) - Berenstein, Gay et al.
		2 Th'eorie g'en'erale des 'equations algebriques (context) - B'ezout
		1 Small degree solutions for the polynomial Bezout equation (context) - Berenstein, Struppa - 1988
	citeseer.ist.psu.edu /lawton98beacutezout.html (564 words)

	WWW interactive multipurpose server
		Complex shoot, locate a complex number by clicking on the complex plane.
		Bezout, computes euclidean division, gcd, lcm, Bezout relation.
		Magic rectangles, game based on a variation of magic squares.
	wims.unice.fr /~wims/wims.cgi?lang=en&module=tool/arithmetic/... (2378 words)

	Bézout's Theorem for Non-Commutative Projective Spaces - Mori, Smith (ResearchIndex) (Site not responding. Last check: 2007-10-12)
		Abstract: We prove a version of B'ezout's theorem for non-commutative analogues of the projective spaces P n.
		Mori and S.P. Smith, Bezout's theorem for non-commutative projective spaces, preprint, 1999.
		@misc{ mori99bezouts, author = "I. Mori and S. Smith", title = "Bezout's theorem for non-commutative projective spaces", text = "I. Mori and S.P. Smith, Bezout's theorem for non-commutative projective spaces, preprint, 1999.", year = "1999", url = "citeseer.ist.psu.edu/mori99beacutezouts.html" }
	citeseer.ist.psu.edu /mori99beacutezouts.html (419 words)

	Bezout - ticalc.org
		Ranked as 2316 on our top downloads list for the past seven days with 9 downloads.
		Ce programme calcule les coefficients de Bezout, le PGCD et le PPCM avec les étapes (= tableau)
		If you have downloaded and tried this program, please rate it on the scale below
	www.ticalc.org /archives/files/fileinfo/177/17799.html (190 words)

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