BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-72-258
       ENTRY:: October 16, 1995
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: Some basic machine algorithms for integral order
               computations.
        TYPE:: Technical Report
      AUTHOR:: Brown, Harold
        DATE:: February 1972
       PAGES:: 16
    ABSTRACT:: 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
               $\bigotimes$ R.

               3. Relative to any fixed Z-basis for R, compute a unique
               canonical form for any given finitely generated Z-submodule
               of Q $\bigotimes$ R described in terms of that basis.
       NOTES:: [Adminitrivia V1/Prg/19951016]
         END:: STAN//CS-TR-72-258