This book discusses the use of the real numbers in theorem proving. Typ ically, theorem
provers only support a few'discrete'datatypes such as the natural numbers. However the …

Let a semialgebraic set be given by a quantifier-free formula of the first-order theory of real
closed fields with k atomic subformulae of the type fi≥ 0 for 1≤ i≤ k, where the polynomials …

We present a fully proof-producing implementation of a quantifier elimination procedure for
real closed fields. To our knowledge, this is the first generally useful proof-producing …

This volume presents an exhaustive treatment of computation and algorithms for finite fields.
Topics covered include polynomial factorization, finding irreducible and primitive …

Let a semialgebraic set be given by a quantifier-free formula of the first-order theory of real
closed fields with atomic subformulae of type (fi≥ 0), 1≤ i≤ k where the polynomials fi ε ℤ X …

Non algebraic cylindrical decompositions are discussed. False derivatives and local Sturm
sequences are defimed as tools for computing them. The crucial fact in the algebraic case is …

The elementary numbers are the complex numbers which can be implicitly or explicitly
defined by starting with the rationals and using addition, subtraction, multiplication and …

It is shown that within a coordinate aligned rectangle in the real plane there exists a
cylindrical decomposition of the zero set of any function of two variables which can be …

Suppose the polynomials P 1…, P k∈ ℤ [X 1,…, X n, U], h∈ ℤ [X 1,…, X n] have degrees
deg (P i), deg (h)< d and the absolute value of any coefficient of P i or h is less or equal to 2 …

An algorithm is proposed for producing all components of the varieties defined by equations
which involve polynomials and exponentials of polynomials, irreducible over real algebraic …