Abstract: Symbolic calculations of 1. the molecular integrals of computational chemistry and 2. the dependence of eigenvalues on parameters in the matrix elements of secular determinants by the speaker have spun off transferable 1. examples of several unexpected benefits and challenges of symbolic calculation, 2. methods to speed up symbolic and numeric recurrence schemes by vectorizing and telescoping, 3. an input style for proofs and derivations that parallels some basic features of conventional presentations in applied mathematics, 4. experience of the construction and utilization of very large tables of formulas, 5. extensive dialogue with people in the computer algebra community who seek increased interaction with people in the natural sciences.
The speaker will introduce these topics, provide pointers to follow-up material, and invite critical comment on the realistic benefits of both some novel methods and some classical methods that were too tedious to use previously, that include
1. multinomial equation solvers (Gröbner bases, resultants), 2. fast unrestricted precision and polynomial operations (Karatsuba algorithm), 3. fast linear algebra (Strassen and related algorithms), 4. differential equation solvers (Lie symmetry methods).