SAP, a symbolic algebraic processor.
                          Andre Deprit

      U.S. National Institute of Standards and Technology,
               Gaithersburg, MD 20899--0001, U.S.A.

                              and
                   Grupo de Mecanica Espacial,
                    Universidad de Zaragoza,
                     50009 Zaragoza, Spain

                  Phone and Fax: 34 76 35 70 11
                   e-mail: deprit@enh.nist.gov

    Various  algebraic  structures  like  vectors,   quaternions, 
polynomials, algebras of trigonometric functions or vector fields 
may  be represented in MATHEMATICA as  programming  objects.  The 
context mechanism of MATHEMATICA, however crude, is sufficient to 
define  inheritance  among structures.  Each package of  code  is 
accompanied  by an extensive section of checks and  illustrations 
designed  to  provide rapid signals whenever  modifications  have 
been  made in the package itself or anywhere in the line  of  its 
ascendants.  Special effort is made for protecting users  against 
calls to procedures outside the conditions imposed by SAP.
    On  the  whole,  SAP aims at  implementing  the  perturbation 
techniques originating from the theory of Lie transformations  in 
non linear dynamics,  especially in celestial dynamics and in the 
semi classical schemes of molecular physics. Its friendliness and 
flexibility   are  continuously  checked  in  the  most   diverse 
circumstances  from  refereeing  papers  to  keeping  in  running 
condition  the calculations substantiating  manuscripts  prepared 
for publication. It has made possible, for instance, to revise in
depth  the literature of the past ten years about drag  force  in 
Point   Dynamics,   to  reframe  Stiefel's  theory  of   the   KS 
transformation within the theory of quaternions.
    All the formulas in the Tables of Elliptic Integrals by  Byrd 
and  Freedman  can now been obtained  aumotacially.  Work  is  in 
progress   for  the  construction  of  analytical  theories   for 
artificial satellites.