03890nam a22005175i 4500001001800000003000900018005001700027007001500044008004100059020001800100024002500118050001400143072001600157072002300173082001200196245023300208264006100441300006500502336002600567337002600593338003600619347002400655490006400679505047700743520157701220650001702797650003502814650001302849650001602862650001702878650001302895650001602908650004102924700003202965700002902997700002703026700003003053700003103083700003403114700003203148710003403180773002003214776003603234830006403270856003803334978-3-540-27357-8DE-He21320180115171645.0cr nn 008mamaa100301s2005 gw | s |||| 0|eng d a97835402735787 a10.1007/b1389572doi 4aQA150-272 7aPBF2bicssc 7aMAT0020002bisacsh04a51222310aSolving Polynomial Equationsh[electronic resource] :bFoundations, Algorithms, and Applications /cedited by Manuel Bronstein, Arjeh M. Cohen, Henri Cohen, David Eisenbud, Bernd Sturmfels, Alicia Dickenstein, Ioannis Z. Emiris. 1aBerlin, Heidelberg :bSpringer Berlin Heidelberg,c2005. aXIV, 426 p. 44 illus., 11 illus. in color.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aAlgorithms and Computation in Mathematics,x1431-1550 ;v140 ato residues and resultants -- Solving equations via algebras -- Symbolic-numeric methods for solving polynomial equations and applications -- An algebraistâ€™s view on border bases -- Tools for computing primary decompositions and applications to ideals associated to Bayesian networks -- Algorithms and their complexities -- Toric resultants and applications to geometric modelling -- to numerical algebraic geometry -- Four lectures on polynomial absolute factorization. aThe subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in di?erent branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems. 0aMathematics. 0aComputer sciencexMathematics. 0aAlgebra. 0aAlgorithms.14aMathematics.24aAlgebra.24aAlgorithms.24aSymbolic and Algebraic Manipulation.1 aBronstein, Manuel.eeditor.1 aCohen, Arjeh M.eeditor.1 aCohen, Henri.eeditor.1 aEisenbud, David.eeditor.1 aSturmfels, Bernd.eeditor.1 aDickenstein, Alicia.eeditor.1 aEmiris, Ioannis Z.eeditor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9783540243267 0aAlgorithms and Computation in Mathematics,x1431-1550 ;v1440uhttp://dx.doi.org/10.1007/b138957