Generation and verfication of algorithms for symbolic-numeric processing (Q1264454)

Some large scale physical computations require algorithms performing symbolic computations with a particular class of algebraic formulas in a numerical code. Developing and implementing such algorithms in a numerical programming language is a tedious and error prone task. The algorithms can be developed in a computer algebra system and their correctness can be checked by comparison with built-in facilities of the system so that the system is used as an advanced debugging tool. After that the numerical code for the algorithms is automatically generated from the same source code. The proposed methodology is explained in detail on a simple example. Real applications to calculation of matrix elements of Coulomb interaction and two-centre exchange integrals needed in atomic collision codes, are described. The method makes the developing and debugging of such algorithms easier and faster.