Can Computer Algebra be Liberated from its Algebraic Yoke ?

Digital mathematical libraries assemble the knowledge of years of mathematical research. Numerous disciplines (e.g., physics, engineering, pure and applied mathematics) rely heavily on compendia gathered findings. Likewise, modern research applications rely more and more on computational solutions, which are often calculated and verified by computer algebra systems. Hence, the correctness, accuracy, and reliability of both digital mathematical libraries and computer algebra s...

We provide a theoretical framework for analysing and comparing different forms of organizing introductions to mathematical analysis at the secondary level, then illustrate it by two characteristic examples from certain periods of change in the 20th century, as they occurred in Denmark. We conclude by extracting from this a fundamental dilemma for the teaching of analysis at secondary level in view of the requirements and affordances provided by computer algebra systems on the...

The capability of R to do symbolic mathematics is enhanced by the caracas package. This package uses the Python computer algebra library SymPy as a back-end but caracas is tightly integrated in the R environment, thereby enabling the R user with symbolic mathematics within R. Key components of the caracas package are illustrated in this paper. Examples are taken from statistics and mathematics. The caracas package integrates well with e.g. Rmarkdown, and as such creation of s...

xloops is a program package that calculates Feynman diagrams by using computer algebra systems. In this paper it is shown which problems to be solved by computer algebra arise during such calculations, and how this problems are handled in the framework of xloops.

Many computer algebra systems have more than 1000 built-in functions, making expertise difficult. Using mock dialog boxes, this article describes a proposed interactive general-purpose wizard for organizing optional transformations and allowing easy fine grain control over the form of the result even by amateurs. This wizard integrates ideas including: * flexible subexpression selection; * complete control over the ordering of variables and commutative operands, with well...

This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we are referring to is that of symbolic methods, largely based on a formalism of umbral type which provides a tremendous simplification of the derivation of the associated properties. The strategy we will follow is that of establishing the rules...

There have been several modifications of how basic calculus has been taught, but very few of these modifications have considered the computational tools available at our disposal. Here, we present a few tools that are easy to develop and use. Doing so also addresses a different way to view calculus, and attempts to fill the gaps in students' understanding of both differentiation and integration. We will describe the basics of both these topics in a way that might be much more...

Information technologies for studying physical-mathematical disciplines on base of mathematical modeling in the computer algebra system Maple are described.

The report is devoted to the current state of the MathPartner computer algebra web project. We discuss the main directions of development of the project and give several examples of using it to solve selected problems.

The paper develops a symbolic calculus for Fourier integral operators associated with canonical transformations.