Computing roadmaps of semi-algebraic sets on a variety
S Basu, R Pollack, MF Roy - Journal of the American Mathematical Society, 2000 - ams.org
We consider a semi-algebraic set $ S $ defined by $ s $ polynomials in $ k $ variables which
is contained in an algebraic variety $ Z (Q) $. The variety is assumed to have real dimension …
is contained in an algebraic variety $ Z (Q) $. The variety is assumed to have real dimension …
[图书][B] Fitting smooth functions to data
C Fefferman, A Israel - 2020 - books.google.com
This book is an introductory text that charts the recent developments in the area of Whitney-
type extension problems and the mathematical aspects of interpolation of data. It provides a …
type extension problems and the mathematical aspects of interpolation of data. It provides a …
[PDF][PDF] On computing a set of points meeting every cell defined by a family of polynomials on a variety
S Basu, R Pollack, MF Roy - Journal of Complexity, 1997 - core.ac.uk
On Computing a Set of Points Meeting Every Cell Defined by a Family of Polynomials on a
Variety Page 1 JOURNAL OF COMPLEXITY 13, 28–37 (1997) ARTICLE NO. CM970434 On …
Variety Page 1 JOURNAL OF COMPLEXITY 13, 28–37 (1997) ARTICLE NO. CM970434 On …
Computing real radicals and S-radicals of polynomial systems
Abstract Let f=(f 1,…, fs) be a sequence of polynomials in Q [X 1,…, X n] of maximal degree
D and V⊂ C n be the algebraic set defined by f and r be its dimension. The real radical< f> …
D and V⊂ C n be the algebraic set defined by f and r be its dimension. The real radical< f> …
Generators for the Cm-closures of ideals
C Fefferman, GK Luli - Rev. Mat. Iberoam, 2021 - ems.press
Let R denote the ring of real polynomials on Rn. Fix m≥ 0, and let A1,..., AM∈ R. The Cm-
closure of (A1,..., AM), denoted here by [A1,..., AM; Cm], is the ideal of all f∈ R expressible in …
closure of (A1,..., AM), denoted here by [A1,..., AM; Cm], is the ideal of all f∈ R expressible in …
The complexification and degree of a semi-algebraic set
MF Roy, N Vorobjov - Mathematische Zeitschrift, 2002 - Springer
The complexification and degree of a semi-algebraic set Page 1 Digital Object Identifier (DOI)
10.1007/s002090100287 Math. Z. 239, 131–142 (2002) The complexification and degree of a …
10.1007/s002090100287 Math. Z. 239, 131–142 (2002) The complexification and degree of a …
Complexity of computing the local dimension of a semialgebraic set
N Vorobjov - Journal of Symbolic Computation, 1999 - Elsevier
The paper describes several algorithms related to a problem of computing the local
dimension of a semialgebraic set. Let a semialgebraic set V be defined by a system of k …
dimension of a semialgebraic set. Let a semialgebraic set V be defined by a system of k …
Reparametrizing swung surfaces over the reals
Abstract Let K ⊆ RK⊆ R be a computable subfield of the real numbers (for instance, QQ).
We present an algorithm to decide whether a given parametrization of a rational swung …
We present an algorithm to decide whether a given parametrization of a rational swung …
Algebraic and semialgebraic proofs: Methods and paradoxes
P Conti, C Traverso - … in Geometry: Third InternationalWorkshop, ADG 2000 …, 2001 - Springer
The aim of the present paper is the following:—Examine critically some features of the usual
algebraic proof protocols, in particular the “test phase” that checks if a theorem is “true” or …
algebraic proof protocols, in particular the “test phase” that checks if a theorem is “true” or …
On the real Nullstellensatz
E Becker, J Schmid - Algorithmic Algebra and Number Theory: Selected …, 1999 - Springer
We give a survey of three implemented real quantifier elimination methods: partial cylindrical
algebraic decomposition, virtual substitution of test terms, and a combination of Grabner …
algebraic decomposition, virtual substitution of test terms, and a combination of Grabner …