GENERATION AND VERIFICATION OF ALGORITHMS FOR SYMBOLIC-NUMERIC PROCESSING

Some large scale physical computations require algorithms performing s ymbolic computations with a particular class of algebraic formulas in a numerical code. Developing and implementing such algorithms in a num erical programming language is a tedious and error prone task. The alg orithms can be developed in a computer algebra system and their correc tness can be checked by comparison with build-in facilities of the sys tem so that the system is used as an advanced debugging tool. After th at 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 eleme nts of Coulomb interaction and two-centre exchange integrals needed in atomic collision codes, are described. The method makes the developin g and debugging of such algorithms easier and faster. (C) 1998 Academi c Press Limited.