ALGORITHMS IN REAL ALGEBRAIC GEOMETRY

By C. BEZIN

1 ALGEBRAICALLY CLOSED FIELDS 1 2 REAL CLOSED FIELDS 18 3 SEMI ALGEBRAIC SETS 72 4 ALGEBRA 89 5 DECOMPOSITION OF SEMI ALGEBRAIC SETS 146 6 ELEMENTS OF TOPOLOGY 182 7 QUANTITATIVE SEMI ALGEBRAIC GEOMETRY 224 8 COMPLEXITY OF BASIC ALGORITHMS 268 9 CAUCHY INDEX AND APPLICATIONS 310 10 REAL ROOTS 338 11 CYLINDRICAL DECOMPOSITION ALGORITHM 389 12 POLYNOMIAL SYSTEM SOLVING 431 13 EXISTENTIAL THEORY OF THE REALS 490 14 QUANTIFIER ELIMINATION 518 15 COMPUTING ROADMAPS AND CONNECTED COMPONENTS OF ALGEBRAIC SETS 548 16 COMPUTING ROADMAPS AND CONNECTED COMPONENTS OF SEMI ALGEBRAIC SETS 578