Some Basic Machine Algorithms for Integral Order Computat

Three machine implemented algorithms for computing with integral orders are described. The algorithms are: 1. For an integral order R given in terms of its left regular representation relative to any basis, compute the nil radical J(R) and a left regular representation of R/J(R). 2. For a semisimple order R given in terms of its left regular representation relative to any basis, compute a new basis for R and the associated left regular representation of R such that the first basis element of the transformed basis is an integral multiple of the identity element in Q % R. 3. Relative to any fixed Z-basis for R, compute a unique canonical form for any given finitely generated Z-submodule of Q @ R described in terms of that basis. This research was supported mainly by the National Science Foundation -under grant number GP-16793 and in part by CNR 00014-67-A-0112-0057NR 044-402. Reproduction in whole or in part is permitted for any purpose of the United States ,%vernment.