[Maxima] Symbolic pseudo-inverse

[Barton Willis]

This bug is due to a limit bug:

 (%i38) e : (2*sin(x)*z+cos(x)*sin(2*x)-2*cos(x)^2*sin(x))/(z^2+(-sin
 (2*x)^2-4*sin(x)^2-cos(x)^2-1)*z+sin(2*x)^2-4*cos(x)*sin(x)*sin(2*x)+4*cos
 (x)^2*sin(x)^2);

 (%o38) (2*sin(x)*z+cos(x)*sin(2*x)-2*cos(x)^2*sin(x))/(z^2+(-sin
 (2*x)^2-4*sin(x)^2-cos(x)^2-1)*z+sin(2*x)^2-4*cos(x)*sin(x)*sin(2*x)+4*cos
 (x)^2*sin(x)^2)

Bogus:

 (%i39) limit(e,z,0);
 (%o39) cos(x)/(sin(2*x)-2*cos(x)*sin(x))

 (%i40) trigexpand(%);
  Division by 0 -- an error.  To debug this try debugmode(true);

Correct, I think:

 (%i41) limit(trigexpand(e),z,0);
 (%o41) -(2*sin(x))/((4*cos(x)^2+4)*sin(x)^2+cos(x)^2+1)

 (%i42) trigexpand(%);
 (%o42) -(2*sin(x))/((4*cos(x)^2+4)*sin(x)^2+cos(x)^2+1)


Barton

-----maxima-bounces at math.utexas.edu wrote: -----


>This seems to work nicely except for one very big problem: it does not
>check for expression zero equivalence except syntactically.  See below for
>an example.
>
>              -s
>