000 04026nam a22005535i 4500
001 978-3-540-27357-8
003 DE-He213
005 20161121230933.0
007 cr nn 008mamaa
008 100301s2005 gw | s |||| 0|eng d
020 _a9783540273578
_9978-3-540-27357-8
024 7 _a10.1007/b138957
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
082 0 4 _a512
_223
245 1 0 _aSolving Polynomial Equations
_h[electronic resource] :
_bFoundations, Algorithms, and Applications /
_cedited by Manuel Bronstein, Arjeh M. Cohen, Henri Cohen, David Eisenbud, Bernd Sturmfels, Alicia Dickenstein, Ioannis Z. Emiris.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2005.
300 _aXIV, 426 p. 44 illus., 11 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aAlgorithms and Computation in Mathematics,
_x1431-1550 ;
_v14
505 0 _ato residues and resultants -- Solving equations via algebras -- Symbolic-numeric methods for solving polynomial equations and applications -- An algebraist’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.
520 _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.
650 0 _aMathematics.
650 0 _aComputer science
_xMathematics.
650 0 _aAlgebra.
650 0 _aAlgorithms.
650 1 4 _aMathematics.
650 2 4 _aAlgebra.
650 2 4 _aAlgorithms.
650 2 4 _aSymbolic and Algebraic Manipulation.
700 1 _aBronstein, Manuel.
_eeditor.
700 1 _aCohen, Arjeh M.
_eeditor.
700 1 _aCohen, Henri.
_eeditor.
700 1 _aEisenbud, David.
_eeditor.
700 1 _aSturmfels, Bernd.
_eeditor.
700 1 _aDickenstein, Alicia.
_eeditor.
700 1 _aEmiris, Ioannis Z.
_eeditor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540243267
830 0 _aAlgorithms and Computation in Mathematics,
_x1431-1550 ;
_v14
856 4 0 _uhttp://dx.doi.org/10.1007/b138957
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c506140
_d506140