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» Arithmetic as a Theory Modulo
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ICA3PP
2010
Springer
14 years 1 months ago
Modular Resultant Algorithm for Graphics Processors
Abstract. In this paper we report on the recent progress in computing bivariate polynomial resultants on Graphics Processing Units (GPU). Given two polynomials in Z[x, y], our algo...
Pavel Emeliyanenko
ISSAC
2007
Springer
142views Mathematics» more  ISSAC 2007»
14 years 2 months ago
Fast arithmetic for triangular sets: from theory to practice
We study arithmetic operations for triangular families of polynomials, concentrating on multiplication in dimension zero. By a suitable extension of fast univariate Euclidean divi...
Xin Li, Marc Moreno Maza, Éric Schost
AML
2002
69views more  AML 2002»
13 years 8 months ago
Transfer principles in nonstandard intuitionistic arithmetic
Using a slight generalization, due to Palmgren, of sheaf semantics, we present a term-model construction that assigns a model to any first-order intuitionistic theory. A modificat...
J. Avigad, Jeremy Helzner
TPHOL
1999
IEEE
14 years 1 months ago
A Machine-Checked Theory of Floating Point Arithmetic
Abstract. Intel is applying formal verification to various pieces of mathematical software used in Merced, the first implementation of the new IA-64 architecture. This paper discus...
John Harrison
TCS
2008
13 years 8 months ago
Verification of qualitative Z constraints
We introduce an LTL-like logic with atomic formulae built over a constraint language interpreting variables in Z. The constraint language includes periodicity constraints, comparis...
Stéphane Demri, Régis Gascon