Concurrent logic languages have been used mainly for the (parallel) processing of rather irregular symbolic applications. However, since concurrent logic languages are essentially general-purpose, they should be applicable to problems with regular structures and their data-parallel processing as well. This paper studies the possibility of massively parallel processing in concurrent logic progra...

Symbolic integration deals with the evaluation of integrals in closed form. We present an overview of Risch’s algorithm including recent developments. The algorithms discussed are suited for both indefinite and definite integration. They can also be used to compute linear relations among integrals and to find identities for special functions given by parameter integrals. The aim of this present...

The success of the symbolic mathematical computation discipline is striking. The theoretical advances have been continuous and significant: Gröbner bases, the Risch integration algorithm, integer lattice basis reduction, hypergeometric summation algorithms, etc. From the beginning in the early 60s, it has been the tradition of our discipline to create software that makes our ideas readily avail...

What role should be played by symbolic mathematical computation facilities in scientific and engineering “problem solving environments”? Drawing upon standard facilities such as numerical and graphical libraries, symbolic computation should be useful for: The creation and manipulation of mathematical models; The production of custom optimized numerical software; The solution of delicate classes...

Historically the fields of numerical and symbolic methods for scientific applications have been widely separated, nearly isolated from one another. Symbolic (and algebraic) computation has used symbolic methods to obtain symbolic answers to problems. Numerical computation has used numerical methods to obtain numerical answers. The natures of the methods and answers obtained are seen by most to ...

We describe the design and implementation of the Distributed Threads System (DTS), a programming environment for the paralleliza-tion of irregular and highly data-dependent algorithms. DTS extends the support for fork/join parallel programming from shared memory threads to a distributed memory environment. It is currently implemented on top of PVM, adding an asynchronous RPC abstraction and tur...

Many problems in digital signal processing can be converted to algebraic problems over polynomial and Laurent polynomial rings, and can be solved using the existing methods of algebraic and symbolic computation. This paper aims to establish this connection in a systematic manner, and demonstrate how it can be used to solve various problems arising from multidimensional signal processing. The me...

The seminar focused on satisfiability checking for combinations of first-order logic and subclasses thereof with arithmetic theories in a very liberal sense, also covering quantifiers and parameters. It gathered members of the two communities of symbolic computation (or computer algebra) and satisfiability checking (including satisfiability modulo theories). Up-to-now, these two communities hav...

Symbolic computation in algebraic categories provides computer implementations for modern algebra theories. The present paper reveals the utility of the parameterized categorical approach by deriving a multivariate polynomial category (over various coefficient domains), which is used by our Mathematica implementation of Buchberger’s algorithms for determining the Gröbner basis. These implementa...

We investigate models of the mitogenactivated protein kinases (MAPK) network, with the aim of determining where in parameter space there exist multiple positive steady states. We build on recent progress which combines various symbolic computation methods for mixed systems of equalities and inequalities. We demonstrate that those techniques benefit tremendously from a newly implemented graph th...