IMPLEMENTING DOMAINS AND CATEGORIES IN MATHEMATICA BY MEANS OF PARAMETERIZED TYPES Presented at 4 International Workshop SYMBOLIC AND NUMERIC ALGORITHMS FOR SCIENTIFIC COMPUTING
نویسندگان
چکیده
Symbolic computation in algebraic categories provides computer implementations for modern algebra theories. The present paper reveals the utility of the parameterized categorical approach by deriving a multivariate polynomial category (over various coefficient domains), which is used by our Mathematica implementation of Buchberger’s algorithms for determining the Gröbner basis. These implementations reveal the advantages of object oriented programming in symbolic computation, their practical importance relying in the extension of Mathematica, a widely used symbolic computation system, with a new type system. The approach we propose for Mathematica is inspired from D. Gruntz and M. Monagan’s work in Gauss, for Maple.
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