solving polynomial equation systems iv volume 4 buchberger theory and beyond

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Solving Polynomial Equation Systems Iv Volume 4 Buchberger Theory And Beyond

Author : Teo Mora
ISBN : 9781316381380
Genre : Mathematics
File Size : 58. 24 MB
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In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.

The Origins Of The Universe For Dummies

Author : Stephen Pincock
ISBN : 9781119998198
Genre : Science
File Size : 24. 80 MB
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Do you want to learn about the physical origin of the Universe, but don’t have the rest of eternity to read up on it? Do you want to know what scientists know about where you and your planet came from, but without the science blinding you? ‘Course you do – and who better than For Dummies to tackle the biggest, strangest and most wonderful question there is! The Origins of the Universe For Dummies covers: Early ideas about our universe Modern cosmology Big Bang theory Dark matter and gravity Galaxies and solar systems Life on earth Finding life elsewhere The Universe’s forecast

Fewnomials

Author : A. G. Khovanskiĭ
ISBN : 0821898302
Genre : Mathematics
File Size : 38. 1 MB
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The ideology of the theory of fewnomials is the following: real varieties defined by "simple", not cumbersome, systems of equations should have a "simple" topology. One of the results of the theory is a real transcendental analogue of the Bezout theorem: for a large class of systems of *k transcendental equations in *k real variables, the number of roots is finite and can be explicitly estimated from above via the "complexity" of the system. A more general result is the construction of a category of real transcendental manifolds that resemble algebraic varieties in their properties. These results give new information on level sets of elementary functions and even on algebraic equations. The topology of geometric objects given via algebraic equations (real-algebraic curves, surfaces, singularities, etc.) quickly becomes more complicated as the degree of the equations increases. It turns out that the complexity of the topology depends not on the degree of the equations but only on the number of monomials appearing in them. This book provides a number of theorems estimating the complexity of the topology of geometric objects via the cumbersomeness of the defining equations. In addition, the author presents a version of the theory of fewnomials based on the model of a dynamical system in the plane. Pfaff equations and Pfaff manifolds are also studied.

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