Want to 'Solve' a piecewise equation for a common term - comp.soft-sys.math.mathematica

Message from discussion Want to 'Solve' a piecewise equation for a common term

dimitris

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More options 4 Aug 2007, 10:59

Newsgroups: comp.soft-sys.math.mathematica

From: dimitris <dimmec...@yahoo.com>

Date: Sat, 4 Aug 2007 09:59:32 +0000 (UTC)

Local: Sat 4 Aug 2007 10:59

Subject: Re: Want to 'Solve' a piecewise equation for a common term

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On 3 , 13:48, "misno...@gmail.com" <misno...@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?

Do not use symbols that already are used as built in symbols.

In[55]:=
Information[N]

>From In[55]:=

"N[expr] gives the numerical value of expr. N[expr, n] attempts to
give a result with n-digit precision."

>From In[55]:=

Attributes[N] = {Protected}

N /: Default[N, 2] := {MachinePrecision, Infinity}

So, how about

In[57]:=
temp = Piecewise[{{2*n*x, x < 0}, {n*x, x >= 0}}]

Out[57]=
Piecewise[{{2*n*x, x < 0}, {n*x, x >= 0}}]

In[59]:=
Reduce[temp == 1, n]

Out[59]=
(x > 0 && n == 1/x) || (x < 0 && n == 1/(2*x))

Cheers
Dimitris

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