Description of algebraically constructible functions
نویسنده
چکیده
The algebraically constructible functions on a real algebraic set are the sums of signs of polynomials on this set. We prove a formula giving the minimal number of polynomials needed to write generically a given algebraically constructible function as a sum of signs. We also prove a characterization of the polynomials appearing in a generic presentation of the function with the minimal number of polynomials. Both results are e¤ective.
منابع مشابه
Topology of Real Algebraic Sets of Dimension 4: Necessary Conditions
Operators on the ring of algebraically constructible functions are used to compute local obstructions for a four-dimensional semialgebraic set to be homeomorphic to a real algebraic set. The link operator and arithmetic operators yield 2 − 43 independent characteristic numbers mod 2, which generalize the Akbulut-King numbers in dimension three. The ring of algebraically constructible functions ...
متن کاملAlgebraically Constructible Functions and Signs of Polynomials
Let W be a real algebraic set. We show that the following families of integervalued functions on W coincide: (i) the functions of the form w → χ(Xw), where Xw are the fibres of a regular morphism f : X → W of real algebraic sets, (ii) the functions of the form w → χ(Xw), where Xw are the fibres of a proper regular morphism f : X →W of real algebraic sets, (iii) the finite sums of signs of polyn...
متن کاملAlgebraically Constructible Functions
An algebraic version of Kashiwara and Schapira's calculus of constructible functions is used to describe local topological properties of real algebraic sets, including Akbulut and King's numerical conditions for a stratiied set of dimension three to be algebraic. These properties, which include generalizations of the invariants modulo 4, 8, and 16 of Coste and Kurdyka, are deened using the link...
متن کاملAlgebraically Constructible Functions: Real Algebra and Topology
Algebraically constructible functions connect real algebra with the topology of algebraic sets. In this survey we present some history, definitions, properties, and algebraic characterizations of algebraically constructible functions, and a description of local obstructions for a topological space to be homeomorphic to a real algebraic set. More than three decades ago Sullivan proved that the l...
متن کامل60 60 04 v 1 6 J un 1 99 6 ALGEBRAICALLY CONSTRUCTIBLE FUNCTIONS
An algebraic version of Kashiwara and Schapira’s calculus of constructible functions is used to describe local topological properties of real algebraic sets, including Akbulut and King’s numerical conditions for a stratified set of dimension three to be algebraic. These properties, which include generalizations of the invariants modulo 4, 8, and 16 of Coste and Kurdyka, are defined using the li...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003