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Re: Reduce

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22581] Re: [mg22530] Reduce
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Sat, 11 Mar 2000 17:52:52 -0500 (EST)
  • References: <200003090824.DAA20465@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Christian Gut wrote:
> 
> I am interested in getting full solutions of equations with parameters.
> Can anyone give me some background information about Mathematica's
> function "Reduce"? What algorithm does it use to get the parameter
> conditions? Is there any literature (except chapter 3.4.6 of the
> Mathematica book)?

It finds a lexicographic Groebner basis with parameters ordered last
(just like Solve, actually). Then for all polynomials whose leading
coefficient in its main variable involves parameters, spawn two
subsystems by augmenting with leadcoeff==0 and leadcoeff!=0
respectively. Repeat the process on all subsystems thus formed, result
is disjunction of all cases encountered.

Not sure what you seek in the way of literature. The technical end is
related to comprehensive Groebner bases, which topic is mentioned in the
Springer text on Groebner bases by Becker, Weispfenning, and Kredel (and
references the original article by Weispfenning). If you cannot locate
these from the descriptions above I can come up with more complete
references. But I'm sure you'll have no trouble finding them at ETH.


Daniel Lichtblau
Wolfram Research


  • References:
    • Reduce
      • From: Christian Gut <gut@inf.ethz.ch>
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