[Mma 2.0] What are the semantics of "Reduce"?

*To*: mathgroup at yoda.physics.unc.edu*Subject*: [Mma 2.0] What are the semantics of "Reduce"?*From*: franz at cs.washington.edu (Franz G. Amador)*Date*: Mon, 5 Oct 92 11:55:41 -0700

[Mathematica 2.0 for Sun SPARC] Is there a formal semantics for Mathematica's "Reduce" function? In particular, what behavior can I count on, if any, when I give to Reduce a set of non-independent equations (i.e. equations which cannot actually be solved for the desired variables)? So far, its results have taken the following form: - Reduce returns a sequence of alternative "solutions" separated by "Or". - Each "solution" is a sequence of equations conjoined by "And". - The first equation(s) in a solution establish equality or inequality conditions upon any parameters (i.e. variables not being solved for). - The remaining equations in a solution express each solved-for variable (except the first) in terms of the first solved-for variable. This last part, solving for each variable in terms of the first, is not documented in "Mathematica, A System for Doing Mathematics by Computer" (2nd ed), and it is what I am most interested in. Can I depend on this behavior? Thanks, Franz Amador franz at cs.washington.edu {rutgers,cornell,ucsd,ubc-cs,tektronix}!uw-beaver!june!franz