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Mace4 is a program that searches for finite models of first-order formulas. For a given domain size, all instances of the formulas over the domain are constructed. The result is a set of ground clauses with equality. Then, a decision…
We give a polynomial time algorithm for computing the Igusa local zeta function $Z(s,f)$ attached to a polynomial $f(x)\in \QTR{Bbb}{Z}[x]$, in one variable, with splitting field $\QTR{Bbb}{Q}$, and a prime number $p$. We also propose a new…
We present a novel scheme to the coverage problem, introducing a quantitative way to estimate the interaction between a block and its enviroment.This is achieved by setting a discrete version of Green`s theorem, specially adapted for Model…
Fast algorithms for arithmetic on real or complex polynomials are well-known and have proven to be not only asymptotically efficient but also very practical. Based on Fast Fourier Transform (FFT), they for instance multiply two polynomials…
Inevitability properties in branching temporal logics are of the syntax forall eventually \phi, where \phi is an arbitrary (timed) CTL formula. In the sense that "good things will happen", they are parallel to the "liveness" properties in…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
A new integration technique is presented for systems of linear partial differential equations (PDEs) for which syzygies can be formulated that obey conservation laws. These syzygies come for free as a by-product of the differential Groebner…
The paper compares computational aspects of four approaches to compute conservation laws of single differential equations (DEs) or systems of them, ODEs and PDEs. The only restriction, required by two of the four corresponding computer…
The theme of symbolic computation in algebraic categories has become of utmost importance in the last decade since it enables the automatic modeling of modern algebra theories. On this theoretical background, the present paper reveals the…
This paper developed a systematic strategy establishing RBF on the wavelet analysis, which includes continuous and discrete RBF orthonormal wavelet transforms respectively in terms of singular fundamental solutions and nonsingular general…
In this note, we fill a gap in the proof of the heuristic GCD in the multivariate case made by Char, Geddes and Gonnet (JSC 1989) and give some additionnal information on this method.
GNU TeXmacs is a free wysiwyg word processor providing an excellent typesetting quality of texts and formulae. It can also be used as an interface to Computer Algebra Systems (CASs). In the present work, interfaces to three general-purpose…
These lectures give a brief introduction to the Computer Algebra systems Reduce and Maple. The aim is to provide a systematic survey of most important commands and concepts. In particular, this includes a discussion of simplification…
This thesis is devoted to the study of a calculus that describes the application of conditional rewriting rules and the obtained results at the same level of representation. We introduce the rewriting calculus, also called the rho-calculus,…
The traditional split-up into a low level language and a high level language in the design of computer algebra systems may become obsolete with the advent of more versatile computer languages. We describe GiNaC, a special-purpose system…