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Re: Want a general method to extract cases resulting from Reduce

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88485] Re: Want a general method to extract cases resulting from Reduce
  • From: dontdont at gmail.com
  • Date: Tue, 6 May 2008 06:43:07 -0400 (EDT)
  • References: <fvmmr3$8e2$1@smc.vnet.net>

On May 5, 6:17 am, dontd... at gmail.com wrote:
> Someone recently posted asking "How to remove unneeded constraints."
> I can see a general use for something perhaps related to this.
>
> Reduce often gives back fairly complicated nested boolean structures
> of constraints.  Consider the results from the following concrete
> example:
>
> Reduce[{a x1^2 + b x1 + c == y1, a x2^2 + b x2 + c == y2, a( -b/
> (2a))^2+ b ( -b/(2a)) + c == y3, y1 < y3, y2 < y3, x1 < x2,
> Element[Alternatives[x1,x2,x3,y1,y2,y3,a,b,c],Reals]}, {a,b,c}]
=2E..

Here is another common example where the output of Reduce could
be enhanced.

I often find results of the form

(x==y && ALongExpressionOfConditions) ||
(SomeLongExpressionOfConditions && x<y) ||
(SameLongExpressionOfConditions && y<x)

The useful information density could be increased via

(x==y && ALongExpressionOfConditions) ||
(x!=y && SomeLongExpressionOfConditions)


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