Computer Algebra in Scientific Computing

Scientific computing is often associated with numbers and numerical methods. This research collection looks at another powerful approach: using computer algebra to express and investigate the structure of mathematical problems. Edited by Andreas Weber, it gathers eight original articles that connect symbolic computation with questions arising across mathematics and scientific computing.

The focus is technical and research-led, with contributions spanning polynomial algorithms, geometric problems, dynamical systems, and quantum computing. For readers interested in how algebraic methods can help analyze a model’s behavior—not just calculate a numerical result—the collection offers a wide-ranging view of the field.

When computation reveals structure

Computer algebra can make relationships between a system’s properties and its parameters explicit. That perspective is useful in studying how mathematical models behave across different conditions. The collection introduces this broader role for symbolic methods through research papers addressing distinct computational challenges.

Eight research directions

• Algorithms, data structures, and implementation techniques for sparse multivariate polynomial arithmetic.
• Methods for certifying isolated zeros of polynomial systems.
• Computer algebra problems arising in quantum computing.
• Further applications involving algebraic structures, geometry, and dynamical systems.

Together, these subjects show the range of problems where exact or expression-based algebraic computation can complement numerical work.

For readers working at the intersection of fields

This volume is aimed at a specialist readership: researchers, graduate-level readers, and technically minded practitioners interested in symbolic computation and its mathematical applications. Its collection format also makes it possible to explore a particular topic or compare approaches across several areas without treating computer algebra as a single narrow technique.

A research collection with breadth

As a reprint of a special issue of Mathematics, Computer Algebra in Scientific Computing brings together focused contributions under one theme. Readers looking for research on polynomial computation, symbolic methods, or the mathematical foundations of scientific computing will find a substantial range of perspectives here.