Steve Linton

Automated theorem proving in support of computer algebra: symbolic definite integration as a case study

We assess the current state of research in the application of computer aided formal reasoning to computer algebra, and argue that embedded verification support allows users to enjoy its benefits without wrestling with technicalities. We illustrate this claim by considering symbolic definite integration, and present a verifiable symbolic definite integral table look up: a system which matches a query comprising a definite integral with parameters and side conditions, against an entry in a verifiable table and uses a call to a library of lemmas about the reals in the theorem prover PVS to aid in the transformation of the table entry into an answer. We present the full model of such a system as well as a description of our prototype implementation showing the efficacy of such a system: for example, the prototype is able to obtain correct answers in cases where computer algebra systems [CAS] do not. We extend upon FatemanA¢Â�Â�s web-based table by including parametric limits of integration and queries with side conditions.

TORSION UNITS IN INTEGRAL GROUP RING OF THE MATHIEU SIMPLE GROUP M22, LMS

We investigate the possible character values of torsion units of the normalized unit group of the integral group ring of the Mathieu sporadic group M 22 . We confirm the Kimmerle conjecture on prime graphs for this group and specify the partial augmentations for possible counterexamples to the stronger Zassenhaus conjecture.

Lightweight formal methods for computer algebra systems

In this paper we demonstrate the use of formal methods tools to provide a semantics for the type hierarchy of the AXIOM computer algebra system, and a methodology for Aldor program analysis and veri cation. We give examples of abstract speci cations of AXIOM primitives, and provide an interface between these abstractions and Aldor code.

Constructing matrix representations of finitely presented groups

The Todd-Coxeter coset enumeration algorithm is one of the most important tools of computational group theory. It may be viewed as a means of constructing permutation representations of finitely presented groups. In this paper we present an analogous algorithm for directly constructing matrix representations over various fields. In fact the algorithm is more general than this, and can be used to construct matrix representations of finitely generated algebras. The algorithm (with some restrictions) has been implemented as a C program and some results obtained with this implementation are described.

SymGrid-Par: Designing a Framework for Executing Computational Algebra Systems on Computational Grids

SymGrid-Par is a new framework for executing large computer algebra problems on computational Grids. We present the design of SymGrid-Par , which supports multiple computer algebra packages, and hence provides the novel possibility of composing a system using components from different packages. Orchestration of the components on the Grid is provided by a Grid-enabled parallel Haskell ( GpH ). We present a prototype implementation of a core component of SymGrid-Par , together with promising measurements of two programs on a modest Grid to demonstrate the feasibility of our approach.

GROUPS AND ACTIONS IN TRANSFORMATION SEMIGROUPS

Abstract. Let

Growing at a perfect speed

S

Finding the smallest image of a set

be a transformation semigroup of degree

The GAP 4 type system: organising algebraic algorithms

n

Symbolic Computation Software Composability

. To each element