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

*To*: mathgroup at smc.vnet.net*Subject*: [mg79778] Re: Want to 'Solve' a piecewise equation for a common term*From*: dimitris <dimmechan at yahoo.com>*Date*: Sat, 4 Aug 2007 05:53:16 -0400 (EDT)*References*: <f8v16h$d96$1@smc.vnet.net>

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