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Algorithmic Algebra

Author: Bhubaneswar Mishra
Publisher: Springer Science & Business Media
ISBN: 1461243440
Size: 44.82 MB
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Algorithmic Algebra studies some of the main algorithmic tools of computer algebra, covering such topics as Gröbner bases, characteristic sets, resultants and semialgebraic sets. The main purpose of the book is to acquaint advanced undergraduate and graduate students in computer science, engineering and mathematics with the algorithmic ideas in computer algebra so that they could do research in computational algebra or understand the algorithms underlying many popular symbolic computational systems: Mathematica, Maple or Axiom, for instance. Also, researchers in robotics, solid modeling, computational geometry and automated theorem proving community may find it useful as symbolic algebraic techniques have begun to play an important role in these areas. The book, while being self-contained, is written at an advanced level and deals with the subject at an appropriate depth. The book is accessible to computer science students with no previous algebraic training. Some mathematical readers, on the other hand, may find it interesting to see how algorithmic constructions have been used to provide fresh proofs for some classical theorems. The book also contains a large number of exercises with solutions to selected exercises, thus making it ideal as a textbook or for self-study.

Computer Algebra In Science And Engineering

Author: Fleischer J
Publisher: World Scientific
ISBN: 9814549053
Size: 26.80 MB
Format: PDF, Mobi
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Systems and tools of computer algebra (Like AXIOM, Derive, FORM, Mathematica, Maple, Mupad, REDUCE, Macsyma…) let us manipulate extremely complex algebraic formulae symbolically on a computer. Contrary to numerics these computations are exact and there is no loss of accuracy. After decades of research and development, these tools are now becoming as indispensable in Science and Engineering as traditional number crunching already is.The ZiF'94 workshop is amongst the first devoted specifically to applications of computer algebra (CA) in Science and Engineering. The book documents the state of the art in this area and serves as an important reference for future work.

Computer Algebra Methods For Equivariant Dynamical Systems

Author: Karin Gatermann
Publisher: Springer
ISBN: 3540465197
Size: 66.53 MB
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This book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems. The next chapter describes algorithms in invariant theory including many examples and time tables. These techniques are applied in the chapters on symmetric bifurcation theory and equivariant dynamics. This combination of different areas of mathematics will be interesting to researchers in computational algebra and/or dynamics.

Computer Algebra In Scientific Computing

Author: Vladimir P. Gerdt
Publisher: Springer
ISBN: 3642152740
Size: 57.79 MB
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The CASC Workshops are traditionally held in turn in the Commonwealth of IndependentStates(CIS)andoutsideCIS(Germanyinparticular,but,attimes, also other countries with lively CA communities). The previous CASC Wo- shop was held in Japan, and the 12th workshop was held for the ?rst time in Armenia, which is one of the CIS republics. It should be noted that more than 35 institutes and scienti?c centers function within the National Academy of S- ences of Armenia (further details concerning the structure of the academy can be foundhttp://www. sci. am). These institutions are concerned, in particular, with problems in such branches of natural science as mathematics, informatics, physics, astronomy, biochemistry, etc. It follows from the talks presented at the previous CASC workshops that the methods and systems of computer algebra may be applied successfully in all the above-listed branches of natural sciences. Therefore, the organizers of the 12th CASC Workshop hope that the present workshop will help the Armenian scientists to become even more familiar with the capabilities of advanced computer algebra methods and systems and to get in touch with specialists in computer algebra from other countries. The 11 earlier CASC conferences, CASC 1998, CASC 1999, CASC 2000, CASC 2001, CASC 2002, CASC 2003, CASC 2004, CASC 2005, CASC 2006, CASC 2007, and CASC 2009 were held, respectively, in St. Petersburg (R- sia), Munich (Germany), Samarkand (Uzbekistan), Konstanz (Germany), Yalta (Ukraine), Passau (Germany), St.

Algorithmic Algebra And Number Theory

Author: Bernd Heinrich Matzat
Publisher: Springer Verlag
ISBN: 9783540646709
Size: 64.50 MB
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This book contains 22 lectures presented at the final conference of the German research program "Algorithmic Number Theory and Algebra 1991-1997," sponsored by the Deutsche Forschungsgemeinschaft. The purpose of this research program and the meeting was to bring together developers of computer algebra software and researchers using computational methods to gain insight into experimental problems and theoretical questions in algebra and number theory. The book gives an overview on algorithmic methods and results obtained during this period mainly in algebraic number theory, commutative algebra and algebraic geometry and group and representation theory. Some of the articles illustrate the current state of the computer algebra systems developed with support from the research program, for example KANT and LiDIA for algebraic number theory, SINGULAR, REDLOG and INVAR for commutative algebra and invariant theory respectively and GAP, SYSYPHOS and CHEVIE for group and representation theory.