[Maxima-discuss] A question about how changevar expands roots

[Eduardo O. <edu...@gm...>]

Hi list,

sometimes changevar "expanded roots" in a way that was not what I
wanted but I was able to fix its results using just rootscontract,
like here:

  [trans,nvar,ovar] : [x=sin(theta), theta, x];
  obody : sqrt(1-x^2);
  oexpr : 'integrate(obody, ovar);
  nexpr : changevar(oexpr,trans,nvar,ovar);
  nexpr : rootscontract(nexpr);

but here is a case in which changevar decides to pull some "%i"s out
of the roots, and rootscontract contracts the roots but leaves the
"%i"s outside:

  [trans,nvar,ovar] : [x=2*u, u, x];
  obody : sqrt(4-x^2)^3;
  oexpr : 'integrate(obody, ovar);
  nexpr : changevar(oexpr,trans,nvar,ovar);
  nexpr : rootscontract(nexpr);

  display2d : false;
  nexpr;            /* 'integrate(sqrt(u^2-1)*(16*%i-16*%i*u^2),u) */
  display2d : true;

Here is a way to do that change of variables by hand that gives the
result that I was trying to get - if I didn't commit any errors, of
course...

  [trans,nvar,ovar] : [x=2*u, u, x];
  obody : sqrt(4-x^2)^3;
  oexpr : 'integrate(obody, ovar);
  ovar_eq_tfun_nvar : solve(trans, ovar)[1];
  deriv : diff(rhs(solve(trans, nvar)[1]), ovar);
  nbody : subst(ovar_eq_tfun_nvar, obody/deriv);
  nexpr_by_hand : 'integrate(nbody, nvar);
  nexpr_maxima  : changevar(oexpr, trans, nvar, ovar);
  nexpr_maxima  : rootscontract(nexpr_maxima);

I thought that I would be able to find the flags that control how
changevar expands roots by reading its source in src/outmis.lisp and
trying to understand what it does... but that didn't work - I'm not
even sure where in the (defun changevar ...) it calls the thing that
expands roots.

  Any suggestions, pointers, or whatever else?
  Thanks in advance!
    Eduardo Ochs
    http://anggtwu.net/eev-maxima.html