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Re: Want to 'Solve' a piecewise equation for a common term
*To*: mathgroup at smc.vnet.net
*Subject*: [mg79796] Re: Want to 'Solve' a piecewise equation for a common term
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Sat, 4 Aug 2007 06:02:38 -0400 (EDT)
*Organization*: The Open University, Milton Keynes, UK
*References*: <f8v16h$d96$1@smc.vnet.net>
misnomer at gmail.com wrote:
> I've been battling to try to get a solution to my equation, but it
> requires solving of a piecewise function, which I cannot work out how
> to do. Say I have a piecewise function of the form
>
> temp = Piecewise[{
> { 2*N*x, x < 0},
> { N*x, x >= 0}
> }]
>
> I want to either solve this via
> Solve[1==temp, N]
> and either get, with the inequalities,
>
> N -> Piecewise[{
> {1/(2*x), x < 0},
> {1/x, x >= 0}
> }]
>
> or just get mathematica to realise that there is a common term - N,
> and factor it out to, say,
> N * Piecewise[{
> {2*x, x < 0},
> {x, x >= 0}
> }]
> from where solve can handle it perfectly well.
>
> Is this type of operation possible, or am I stuck editing them by hand?
Use *Reduce* for it knows how to handle correctly expressions with
*Piecewise*.
In[1]:= temp = Piecewise[{{2*n*x, x < 0}, {n*x, x >= 0}}];
Reduce[1 == temp, n]
Out[2]= (x > 0 && n == 1/x) || (x < 0 && n == 1/(2 x))
In[3]:= Reduce[1 == n*Piecewise[{{2*x, x < 0}, {x, x >= 0}}], n]
Out[3]= (x > 0 && n == 1/x) || (x < 0 && n == 1/(2 x))
*Solve* does /not/ know what to do with *Piecewise*.
In[4]:= Solve[1 == n*Piecewise[{{2*x, x < 0}, {x, x >= 0}}], n]
Out[4]= {{n -> 1/\[Piecewise] {
{2 x, x < 0},
{x, x >= 0}
}}}
(Also, note that I have replaced capital N by n because N has already a
built-in meaning.)
Regards,
Jean-Marc
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