Re: Solve chokes on Piecewise input that Reduce handles quite well??

• To: mathgroup at smc.vnet.net
• Subject: [mg72041] Re: Solve chokes on Piecewise input that Reduce handles quite well??
• From: "Lalu" <BhuvaneshBhatt at gmail.com>
• Date: Sat, 9 Dec 2006 06:09:49 -0500 (EST)
• References: <elbhsr\$jto\$1@smc.vnet.net>

```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.

This is pretty much expected. Solve does not handle inequalities. If
you give Solve input with a Piecewise containing only equalities as
conditions, that should work.

Bhuvanesh,
Wolfram Research.

```

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