Elimination Practice: Software Tools and Applications
With a software library included, this book provides an elementary introduction to polynomial elimination in practice. The library Epsilon, implemented in Maple and Java, contains more than 70 well-documented functions for symbolic elimination and decomposition with polynomial systems and geometric reasoning. The book presents the functionality, implementation, and performance of Epsilon and demonstrates the usefulness of the elimination tool by a number of selected applications, together with many examples and illustrations. The reader will find Epsilon an efficient tool, applicable to a wide range of problems in science, engineering, and industry, and this book an accessible exposition and a valuable reference for elimination theory, methods, and practice. Contents: Polynomial Elimination at Work; The Epsilon Library; The CharSets Package; The TriSys and SiSys Modules; The GEOTHER Environment; Relevant Elimination Tools; Solving Polynomial Systems; Automated Theorem Proving and Discovering in Geometry; Symbolic Geometric Computation; Selected Problems in Computer Mathematics. Readership: Researchers and graduate students in symbolic mathematical computation, geometric reasoning and modeling, as well as mathematical software engineers.
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The Epsilon Library
The CharSets Package
The TriSys and SiSys Modules
The GEOTHER Environment
Relevant Elimination Tools
Solving Polynomial Systems
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Elimination Practice: Software Tools and Applications (With CD-ROM)
Limited preview - 2004
1nputted a list AABC affine space algebraic curve algebraic element algebraic extension algebraic extension fields algebraic surface algebraic variety algorithms ascending sets automated bases basset bisectors characteristic set CharSets CharSets package coefficients components computer algebra systems coordinates Cpsilon decomposed denote derived differential polynomial set differential triangular equations and inequations Example factors finite functions geometric theorem GEOTHER given Grobner basis hypothesis implementation implicit equations irreducible triangular series Kukles Liapunov constants Maple medial set modules nondegeneracy conditions nonrero normaliration optional parametric parametric surface polyno polynomial equations polynomial ideal polynomial set polynomial system problem pseudo-remainder quasi-irreducible regser regular series regular systems rero decomposition respect returns Sect set of polynomial solutions solving subsidiary conditions surface system P,Q systems of polynomial theorem is true three polynomials triangle triangular sets triangular systems triser trisetc TriSys and SiSys variable ordering x1 Zariski closure Zero(P Zero(P/Q