Re: [Maxima-discuss] Yet another output format question

[Leo B. <l_b...@us...>]

   I've been using Maxima for over a year now for nearly everything and
   am still astonished that it is hard to find a problem maxima has no
   solution for. And I am aware that there is no "simplest" form of an
   equation simply due to the fact that for every purpose a different
   form might be the right one.
   But there are two things I found neither in the manual nor in the web
   even if I am sure maxima will do this if I find out how:

   1.) If desolve generates an equation like
   exp(t*2)*sinh(t*4)=0;
   trigrat will easily carry me to
   (%e^(−2*t)*(%e^(8*t)−1))/2.
   Is there a way to arrive at a sum of exp() functions like
   (%e^(6*t)-%e^(-2*t))/2
   instead?

Here are possible solutions:

(%i1) exp(t*2)*sinh(t*4)=0,exponentialize=true;
(%o1) %e^(2*t)*(%e^(4*t)-%e^-(4*t))/2 = 0
(%i2) ratexpand(%);
(%o2) %e^(6*t)/2-%e^-(2*t)/2 = 0

   2.) How do I factor out a specific variable?
   If it is halfway obvious which variable to factor out the factor()
   function will do wonders without even being told what to do. But if I
   have the equation
   b*c+2*a*c+4*a*b=0
   and want to factor out the b to arrive at
   b*(4*a+c)+2*a*c=0
   there just has to be a way to avoid using an actual pencil.

(%i3) collectterms(b*c+2*a*c+4*a*b,b);
(%o3) b*(c+4*a)+2*a*c


Leo