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Item Details
| Title:
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FEWNOMIALS
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| By: |
A. G. Khovanskii |
| Format: |
Hardback |
| List price:
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£75.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821845470 |
| ISBN 13: |
9780821845479 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 July, 1991 |
| Series: |
Translations of Mathematical Monographs Reprint No. 88 |
| Pages: |
139 |
| Description: |
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. This book provides a number of theorems estimating the complexity of the topology of geometric objects via the cumbersomeness of the defining equations. |
| Synopsis: |
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 given 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. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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