This is a regression in 5.30.0 from 5.29.1:
(%i1) m: matrix([%i*%pi]);
(%o1) [ %i %pi ]
(%i6) matrixexp(m),keepfloat:true;
Unable to find the spectral representation
-- an error. To debug this try: debugmode(true);
(%i7) matrixexp(m),keepfloat:false;
Unable to find the spectral representation
-- an error. To debug this try: debugmode(true);
Point of info - Barton W. has a workaround:
This bug is due to circa January 2013 changes to matrix inversion. A workaround is to set ratmx to true:
Maxima branch_5_30_base_98_g29f9239_dirty http://maxima.sourceforge.net
using Lisp Clozure Common Lisp Version 1.9-r15764 (WindowsX8632)
(%i1) matrixexp(matrix([%i*%pi]));
Unable to find the spectral representation
(%i2) matrixexp(matrix([%i*%pi])), ratmx=true;
(%o2) - 1
kcrisman
2014-05-16
Potential fix reported downstream on Sage ticket #13973:
--- a/share/linearalgebra/matrixexp.lisp 2013-10-07 04:37:12.000000000 +0100 +++ b/share/linearalgebra/matrixexp.lisp 2014-05-16 02:16:09.112011893 +0100 @@ -138,8 +138,8 @@ (print `(ratvars = ,$ratvars gcd = '$gcd algebraic = ,$algebraic)) (print `(ratfac = ,$ratfac)) (merror "Unable to find the spectrum"))) - - (setq res ($fullratsimp (ncpower (sub (mult z ($ident n)) mat) -1) z)) + + (setq res ($fullratsimp ($invert (sub (mult z ($ident n)) mat) '$crering) z)) (setq m (length sp)) (dotimes (i m) (setq zi (nth i sp))
kcrisman
2014-08-14
Here is another example from 5.33. The ratmx
workaround does not help here.
(%i2) m:matrix([1,2,3],[3,2,0],[1,2,1]); [ 1 2 3 ] [ ] (%o2) [ 3 2 0 ] [ ] [ 1 2 1 ] (%i3) m:%i*m; [ %i 2 %i 3 %i ] [ ] (%o3) [ 3 %i 2 %i 0 ] [ ] [ %i 2 %i %i ] (%i4) matrixexp(m),keepfloat:true; Unable to find the spectral representation -- an error. To debug this try: debugmode(true); (%i5) matrixexp(m),ratmx:true; Unable to find the spectral representation -- an error. To debug this try: debugmode(true);
kcrisman
2014-08-14
That said, I am not claiming this is a regression, just an example which it doesn't seem ever worked (perhaps for good theoretical reasons, though of course it has such an exp). See http://ask.sagemath.org/question/23784/imaginary-matrix-exponential/ where it came up.