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Re: Solve chokes on Piecewise input that Reduce handles quite well??
*To*: mathgroup at smc.vnet.net
*Subject*: [mg72045] Re: [mg72007] Solve chokes on Piecewise input that Reduce handles quite well??
*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>
*Date*: Sat, 9 Dec 2006 06:09:54 -0500 (EST)
*References*: <200612081117.GAA20182@smc.vnet.net>
I can see no reason at all why Solve should handle Piecewise with
inequalities. Solve is meant for solving algebraic equations over the
complex numbers and what you have got are inequalities, which do not
make sense in this setting. The following does make sense
Solve[Piecewise[{{2, x == 3}, {3, x == 2}}] == 3, x]
{{x -> 2}}
But but my aesthetic judgment would be seriously offended if this
worked:
Solve[Piecewise[{{2, x >= 2}, {3, x == 2}}] == 3, x]
Fortunately, it does not.
Andrzej Kozlowski
On 8 Dec 2006, at 20:17, Chris Chiasson wrote:
> Solve[{0 == Piecewise[{{1/(-1 + X[1] + X[2])^2, X[1] + X[2] <= -1}},
> (1/2)*(3/2 + (1/2)*(-1 + X[1] + X[2]))] +
> Piecewise[{{(1/2)*(-(3/2) + X[1]/2), X[1] < 2}, {-(1/4), X[1] ==
> 2}}, -(1/X[1]^2)] + 2*(-1 + X[1]),
> 0 == Piecewise[{{1/(-1 + X[1] + X[2])^2, X[1] + X[2] <= -1}},
> (1/2)*(3/2 + (1/2)*(-1 + X[1] + X[2]))] +
> 2*(-1 + X[2])}, {X[1], X[2]}]
>
> Solve::eqf: X[1]+X[2]\[LessEqual]-1 is not a well-formed equation.
>
> ...
>
> (and it returns the input)
>
> Here is the same command using Reduce:
>
> Reduce[{0 == Piecewise[{{1/(-1 + X[1] + X[2])^2, X[1] + X[2] <= -1}},
> (1/2)*(3/2 + (1/2)*(-1 + X[1] + X[2]))] +Piecewise[{{(1/2)*(-(3/2) +
> X[1]/2), X[1] < 2}, {-(1/4), X[1] == 2}}, -(1/X[1]^2)] + 2*(-1 +
> X[1]),
> 0 == Piecewise[{{1/(-1 + X[1] + X[2])^2, X[1] + X[2] <= -1}},
> (1/2)*(3/2 + (1/2)*(-1 + X[1] + X[2]))] +
> 2*(-1 + X[2])}, {X[1], X[2]}]
>
> X[1] == 75/89 && X[2] == 51/89
>
> Did I do anything wrong? Is this a bug? If it is a bug, please file it
> and fix it.
>
> --
> http://chris.chiasson.name/
>
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