The **Symbolic Computation Laboratory** performs research in algorithms and software systems for symbolic computation.

Some specific topics are:

- Solving systems of linear equations and inequalities
- Solving systems of polynomial equations, inequalities and inequations
- Solving ordinary differential equations (ODE's)
- Solving systems of partial differential equations (PDE's)
- Symbolic analysis of analytic and special functions)
- high-performance aspects of computer algebra systems
- Applications of the above

We support both research projects and software projects.

These research projects are

- Weierstrass preparation theorem (and its extensions) which essentially reduces the local study of analytic functions (and more general functions) to the local study of polynomials via the manipulation of power series.
- Newton–Puiseux algorithm (and its extensions) which essentially allows for the local study of curves (separating their branches about a point) via the manipulation of Laurent and and Puiseux series.

These software projects are:

- either used and supported by our industrial partners Maplesoft and IBM Canada
- or made publicly available in source on dedicated web sites and GitHub.

- an Applied Math student helping a Computer Science student on a mathematical question,
- a Computer Science student helping an Applied Math student on an software implementation issue.

All four principal scientists and their students have been contributing to every release of Maple. for more 20 years. The following Maple libraries are being developed in the SCL lab: SNAP, RegularChains library, PowerSeries, PolyhedralSets, CodeTools:-ProgramAnalysis as well as many Maple commands for special functions, eigen values computation, symbolic integration, solving systems of ODEs and PDEs, etc.

Thanks to our contributions to Maple, a site licence allows everyone at the University of Western Ontario to freely use Maple. Note that there are more than 5,000,000 Maple licences world-wide, which implies that millions of people are using the software tools developed in our lab.

These topics are of common interest to the four principal scientists. Different approaches are studied: numerical methods (DJJ, RMC), symbolic methods (GJR, MMM) and hybrid (DJJ, GJR, RMC). All are being implemented in Maple by the PIs and their students. These topics are a driving application for the subject of polynomial system solving and thus our RegularChains library.