Algorithms in Real Algebraic GeometrySpringer Science & Business Media, 9. mar. 2013 - 602 sider The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, or deciding whether two points belong in the same connected component of a semi-algebraic set occur in many contexts. In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects, and researchers in computer science and engineering will find the required mathematical background. Being self-contained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. |
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Resultater 1-5 af 92
... exists Q € K [ X ] with P = ( X − x ) " Q ( X ) and Q ( x ) 0 . Exercise 1.9 . Prove that if C is algebraically ... exist by using euclidean division repeatedly . Given P , Q € K [ X ] , not both 0 , we define the signed remainder ...
... exists one and only one ( G , C ) € Posgcd ( P ) such that y Є R ( C ) . Moreover , y Є R ( C ) implies that Gy is a greatest common divisors of Py . The set of possible greatest common divisors of a family 20 1 Algebraically Closed Fields.
... exists x Є ( a , b ) such that P ( x ) = 0 . Real closed fields are characterized as follows . Theorem 2.14 . If R is a field then the following properties are equivalent : ( i ) R is real closed . ( ii ) R [ i ] = R [ X ] / ( X2 + 1 ) ...
... exists € R ( T1 , ... , Tp ) Є K [ T1 , ... , Tp ] such that Q ( X1 , . . . , Xp ) = R ( E1 , ... , Ep ) . Thus Q ... exist λ and μ with xx + xμ + hxxxμ Є R [ i ] . Since there are infinitely many integers and only a finite number of ...
... exists Q € K [ X ] with P = ( X - x ) " Q and Q ( x ) 0. Note that if x is not a root of P , the multiplicity of x as a root of P is equal to 0 . Lemma 2.26 . Let K be a field of characteristic zero . The element x € K is a root of PЄ K ...
Indhold
1 | |
Algebra | 91 |
པ Decomposition of SemiAlgebraic Sets | 137 |
Elements of Topology | 173 |
Quantitative Semialgebraic Geometry | 201 |
Complexity of Basic Algorithms | 241 |
Cauchy Index and Applications | 283 |
Real Roots 321 | 320 |
Cylindrical Decomposition Algorithm 421 | 420 |
Existential Theory of the Reals | 465 |
Quantifier Elimination | 493 |
Computing Roadmaps and Connected Components | 522 |
Computing Roadmaps and Connected Components | 549 |
References 587 | 586 |
Index | 595 |
Polynomial System Solving | 365 |
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Algorithms in Real Algebraic Geometry Saugata Basu,Richard Pollack,Marie-Françoise Coste-Roy Begrænset visning - 2007 |
Algorithms in Real Algebraic Geometry Saugata Basu,Richard Pollack,Marie-Françoise Roy Begrænset visning - 2003 |
Algorithms in Real Algebraic Geometry Saugata Basu,Richard Pollack,Marie-Françoise Roy Begrænset visning - 2006 |