#2313 real and imaginary parts asech(x)

[Ted Woollett]

Despite asech(x) having both real and
imaginary parts,

(%i1) realpart(asech(x));

(%o1) asech(x)

(%i2) imagpart(asech(x));

(%o2) 0

[Ted Woollett]

system info:
Maxima version: 5.25.1
Maxima build date: 10:2 9/6/2011
Host type: i686-pc-mingw32
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.8

[Kris Katterjohn]

I'm getting the following results now (SBCL 1.2.4 + git HEAD). It looks like these are correct, just glancing at some plots.

Anyone want to confirm? I'm marking this ticket as pending for now.

(%i1) realpart(asech(x));
(%o1) log((1/x-sin(atan2(0,1/x-1)/2)*sin(atan2(0,1/x+1)/2)*sqrt(abs(1/x-1))
                                    *sqrt(abs(1/x+1))
              +cos(atan2(0,1/x-1)/2)*cos(atan2(0,1/x+1)/2)*sqrt(abs(1/x-1))
                                    *sqrt(abs(1/x+1)))
           ^2
           +(cos(atan2(0,1/x-1)/2)*sin(atan2(0,1/x+1)/2)
            +sin(atan2(0,1/x-1)/2)*cos(atan2(0,1/x+1)/2))
            ^2
            *abs(1/x-1)*abs(1/x+1))
 /2
(%i2) imagpart(asech(x));
(%o2) atan2((cos(atan2(0,1/x-1)/2)*sin(atan2(0,1/x+1)/2)
             +sin(atan2(0,1/x-1)/2)*cos(atan2(0,1/x+1)/2))
             *sqrt(abs(1/x-1))*sqrt(abs(1/x+1)),
            1/x+(cos(atan2(0,1/x-1)/2)*cos(atan2(0,1/x+1)/2)
                -sin(atan2(0,1/x-1)/2)*sin(atan2(0,1/x+1)/2))
                *sqrt(abs(1/x-1))*sqrt(abs(1/x+1)))