Generation and Verification of Algorithms for Symbolic-Numeric Processing

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 build-in facilities of the system so that the system is used as an advanced debugging tool. After that a 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.