DoCon is a program for symbolic computation in mathematics - package of modules DoCon joins the categorial approach to the mathematical computation expressed via the Haskell type classes, and explicit processing of the domain description terms. It implements recently a good piece of commutative algebra: linear algebra, polynomial gcd, factorization, Groebner bases, and other functions. They are programmed under the very generic assumptions , like "over any Euclidean ring", over any GCD-ring, any field, and so on. DoCon also supports the constructions on domains: Fraction, Polynomial, Residue ring, and others. That is certain set of operations on a constructed domain is built automatically.
John Baez Algebraic Topological Methods in Computer Science 2008, University of Paris Diderot (Paris 7) July 7, 2008 Computation and the Periodic Table By now there is an extensive network of interlocking analogies between physics, topology, logic and computer science, which can be seen most easily by comparing the roles that symmetric monoidal closed categories play in each subject. However, symmetric monoidal categories are just the n = 1, k = 3 entry of a hypothesized "periodic table" of k-tuply monoidal n-categories. This raises the question of how these analogies extend. We present some thoughts on this question, focusing on how symmetric monoidal closed 2-categories might let us understand the lambda calculus more deeply. This is based on work in progress with Mike Stay. Click on this to see the transparencies of the talk: