Fewnomials by A. Khovanskii, Smilka Zdavkovska

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Based on the widely shared intuition that real things that can be defined by simple systems should have simple topologies, presents theorems that estimate the complexity of the topology of geometric objects by the cumbersomeness of the defining equations, and reveals that the determining factor is not the degree of the equations, but merely the number of monomials appearing in them. The results give new information on level sets of elementary functions, and even algebraic equations. First published in Russian in 1987. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Details from Seller

• ISBN: 0821845470
• Publisher: American Mathematical Society
• Pub. Date: June 1991
• Condition:

Comments from the Seller: Hardcover PLEASE NOTE: All books are promptly imported from the UK using International Priority Airmail. Delivery is typically 5-10 working days. Please do not select expedited shipping. Heavier and more expensive items have tracking number. Professional and reliable bookseller (est.1987). 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 equation...