When I am asked to summarize my research activity in a
short and simple sentence, I answer that *I am applying
Computer Science to Mathematics.*
Indeed, even if certain questions such as computing GCDs of integers
have been studied for centuries, it remains a challenge today
to solve them efficiently on computers, in particular on
parallel architectures.

Another example, which is in fact my favorite problem, is the solving of systems of polynomial equations. This fundamental question, well studied in Algebra textbooks, still offers many algorithmic and implementation challenges in order to address users' needs.

My research activity has four directions.
First, I study theoretical aspects of systems of polynomial equations
and try to answer the question
``what is the best form for the set of solutions?''
Then, I study algorithmic answers to the question
``how to compute this form of the set of solutions at the lowest cost?''
Next, I study implementation techniques for my algorithms
to make the best use of today's computers.
When the prototype solver is ready, I apply it to unsolved problems.
This last step terminates with the distribution of a new solver,
before entering a new cycle *theory, algorithms, implementation,
applications* motivated by new challenging problems or architectures.

These four research directions are supported by three research grants

**High Performance Computer Algebra and Applications**- which is a Discovery grant funded by
`NSERC` **Mathematics of Computer Algebra and Analysis (MOCAA)**- which is a project funded by
`MITACS`and*Maplesoft,* **A framework for parallel symbolic computation**- which is a project funded by
`SHARCNET`

More details can be found in my
`CV in PDF format`

moreno 2009-09-07