A quantitative study of reductions in algebraic libraries

How much of existing computer algebra libraries is amenable to automatic parallelization? This is a difficult topic, yet of practical importance in the era of commodity multicore machines. This paper reports on a quantitative study of reductions in the AXIOMfamily computer algebra systems. The experiment builds on the introduction of assumptions in OpenAxiom. It identifies a variety of reductions that are candidate for implicit concurrent execution. An assumption is an axiomatic statement of an algebraic property. We hope that this study will encourage wider adoption of axioms, not just for the purpose of expression simplification and provably correct libraries, but also to enable derivation of implicit concurrency in a scalable fashion. Categories and Subject Descriptors D.3.3 [Programming Languages]: Language Constructs and Features; F.3.2 [Logics and Meanings of Programs]: Semantics of

• Type: Journal
• Year: 2010
• Where: CAP
• Authors: Yue Li, Gabriel Dos Reis
• Keywords: CAP 2010, Commodity Multicore Machines, Computer Algebra Libraries, Distributed And Parallel Computing, Implicit Concurrent Execution