Computer Algebra and Determinants

There is a large body of work on the art of computing (specific, often very large) numerical determinants, starting with Gauss(ian elimination). It is much slower to compute specific symbolic determinants, whose entries are expressions in several variables rather than numbers. But in this talk I will describe how, sometimes, one can use computer algebra to automatically discover, and rigorously prove, general, closed-form formulas (as an expression in the dimension n) for determinants of infinite families of matrices (a_{i,j}(n))(1<=i,j<=n) where a_{i,j}(n) is an explicit expression in i,j, and n, for example, Hilbert's matrix a_{i,j}=(1/(i+j)). An important ingredient is the so-called "Dodgson Rule" for determinant-evaluation, invented by the inventor of Alice in Wonderland.