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
Despite asech(x) having both real and
imaginary parts,
(%i1) realpart(asech(x));
(%o1) asech(x)
(%i2) imagpart(asech(x));
(%o2) 0
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
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)))
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