Can Computer Algebra be Liberated from its Algebraic Yoke ?

Algorithms of numeric (in exact arithmetic) deduction of analytical expressions, proposed and described by Shevchenko and Vasiliev (1993), are developed and implemented in a computer algebra code. This code is built as a superstructure for the computer algebra package by Shevchenko and Sokolsky (1993a) for normalization of Hamiltonian systems of ordinary differential equations, in order that high complexity problems of normalization could be solved. As an example, a resonant ...

Symbolic computation is the science of computing with symbolic objects (terms, formulae, programs, algebraic objects, geometrical objects, etc). Powerful symbolic algorithms have been developed during the past decades and have played an influential role in theorem proving, automated reasoning, software verification, model checking, rewriting, formalisation of mathematics, network security, Groebner bases, characteristic sets, etc. The international Symposium on "Symbolic Co...

This volume contains papers presented at the Ninth International Symposium on Symbolic Computation in Software Science, SCSS 2021. Symbolic Computation is the science of computing with symbolic objects (terms, formulae, programs, representations of algebraic objects, etc.). Powerful algorithms have been developed during the past decades for the major subareas of symbolic computation: computer algebra and computational logic. These algorithms and methods are successfully app...

We present a complete algorithm for finding an exact minimal polynomial from its approximate value by using an improved parameterized integer relation construction method. Our result is superior to the existence of error controlling on obtaining an exact rational number from its approximation. The algorithm is applicable for finding exact minimal polynomial of an algebraic number by its approximate root. This also enables us to provide an efficient method of converting the ra...

The purpose of this paper is to introduce the concept of the automatic integration and present a new way of approximating definite integrals using the automatic integration based on an associative algebra with zero divisors.

In computer algebra there are different ways of approaching the mathematical concept of functions, one of which is by defining them as solutions of differential equations. We compare different such approaches and discuss the occurring problems. The main focus is on the question of determining possible branch cuts. We explore the extent to which the treatment of branch cuts can be rendered (more) algorithmic, by adapting Kahan's rules to the differential equation setting.

This paper provides some reflections on the field of mathematical software on the occasion of John Rice's 65th birthday. I describe some of the common themes of research in this field and recall some significant events in its evolution. Finally, I raise a number of issues that are of concern to future developments.

Systems biology focuses on the study of entire biological systems rather than on their individual components. With the emergence of high-throughput data generation technologies for molecular biology and the development of advanced mathematical modeling techniques, this field promises to provide important new insights. At the same time, with the availability of increasingly powerful computers, computer algebra has developed into a useful tool for many applications. This articl...

Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of error autocorrection is considered. This effect occurs in efficient methods of rational approximation (e.g., Pade approximations, linear and nonlinear Pade-Chebyshev approximations) where very significant errors in the coefficients do not ...

Computer algebra in Java is a promising field of development. It has not yet reached an industrial strength, in part because of a lack of good user interfaces. Using a general purpose scripting language can bring a natural mathematical notation, akin to the one of specialized interfaces included in most computer algebra systems. We present such an interface for Java computer algebra libraries, using scripts available in the JSR 223 framework. We introduce the concept of `symb...