Grant: Research Tools and Instruments - Category 1 (<$150,000)

With the development of MUPAD and MAPLE, multiplication and addition ofvery complex algebraic structures is now possible. We can explore verydifficult algebras with the computer and understand their structuremuch better than only a few years earlier. This allows us to stateclear conjectures on these algebras and large examples can guide us toproving them.Very often, a particular computation reduces itself to a problem oflinear algebra on very large matrices  (manipulating tables of numberswith 100,000's of rows and columns). This can take years of computationif it  is not done properly even on the fastest and most powerfulcomputers. We plan to develop a better interface between  MUPAD andLINBOX [LINBOX is one of the best package to handle linear algebra withlarge matrices] to help in those kind of computations.Our system will also be used by an international group of tenresearchers coming from Canada, USA, Chile and France. This is part ofa NSF focus group on "Affine Schubert Calculus: Combinatorial,geometric, physical  and computational aspects."The computer system we plan to obtain will be use to: help further thedevelopment of a combinatorial symbolic package in MUPAD, compute largeexamples and  more complicated algebras, solve linear problems usingLINBOX, help the exchange of results between  specialists in this area(with a Wiki system), disseminate knowledge via the web, and more.