> restart:
> f:=(exp(alpha*(x-mu))-exp(-beta*(x-mu)))/(exp(alpha*(x-mu))+exp(-beta*
> (x-mu)));

                 exp(alpha (x - mu)) - exp(-beta (x - mu))
            f := -----------------------------------------
                 exp(alpha (x - mu)) + exp(-beta (x - mu))

> with(plots):
> for i from 0 to 6 do
>   p[i]:=plot(subs(alpha=3,beta=i,mu=1,f),x=-5..5);
>  
> q[i]:=plot(subs(alpha=i,beta=3,mu=1,f),x=-5..5,color="green",style="po
> int",symbol="circle");
> od:
> display(seq(p[i],i=0..5),seq(q[i],i=0..5));
> 

> plot(subs(mu=1,alpha=2,beta=0.3,factor(diff(f,x))),x=-5..5);

> F:=exp(-alpha*exp(-(x-mu)/beta));

                                          x - mu
                    F := exp(-alpha exp(- ------))
                                           beta

> for i from 1 to 6 do
>   p[i]:=plot(subs(alpha=1,beta=i,mu=1,F),x=-5..5);
> od:
> display(seq(p[i],i=0..5));

> 
> phi:=tanh((x-mu)/alpha);

                                     x - mu
                         phi := tanh(------)
                                     alpha

> phi := tanh((x-mu)/alpha);

                                     x - mu
                         phi := tanh(------)
                                     alpha

> restart:
> phi := tanh((x-mu)/alpha);
> assume(q>-1,q<1);
> sys:=subs(x=x1,phi)=0,subs(x=x2,phi)=q;

                                     x - mu
                         phi := tanh(------)
                                     alpha


                         x1 - mu            x2 - mu
             sys := tanh(-------) = 0, tanh(-------) = q~
                          alpha              alpha

> sol:=allvalues(solve({sys},{mu,alpha}));

                           2 (-x2 + x1)
  sol := {mu = x1, alpha = -------------},
                                -1 + q~
                           ln(- -------)
                                1 + q~

                               -x2 + x1
        {mu = x1, alpha = -------------------}
                              /  -1 + q~\1/2
                          ln(-|- -------|   )
                              \  1 + q~ /

> phiinv:=subs(sol[1],convert(solve(phi=y,x),ln));

                    2 (1/2 ln(y + 1) - 1/2 ln(1 - y)) (-x2 + x1)
     phiinv := x1 + --------------------------------------------
                                        -1 + q~
                                   ln(- -------)
                                        1 + q~

> J:=convert(subs(sol[1],x=phiinv,diff(phi,x)),exp);

                                  2       -1 + q~
                            (1 - y ) ln(- -------)
                                          1 + q~
                   J := 1/2 ----------------------
                                   -x2 + x1

> simplify(subs(x=solve(phi=q,x),diff(phi,x)));

                                       2
                                -1 + q~
                              - --------
                                 alpha

> ff:=collect(factor(convert(solve(phi=q,x),ln)),ln);

        ff := mu + 1/2 alpha ln(1 + q~) - 1/2 alpha ln(1 - q~)

> subs(q=0,ff);
> evalf[25](simplify(solve(subs(q=3/4,ff)-subs(q=1/4,ff)=m3-m1,alpha)));

                                  mu


    1.393646133559127220494626 m3 - 1.393646133559127220494626 m1

> 

                             -1.386294361

> 
