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

  • To: mathgroup at
  • Subject: [Mma 2.0] What are the semantics of "Reduce"?
  • From: franz at (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?


Franz Amador
franz at

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