This is very experimental (start of) interface to Lapack.
Before trying you need to have Lapack installed -- if you
use binary package make sure you have "developement"
version.

1) Check that you can use Lapack from C code.  Try to compile
   the 'tsdgees.c' using command line like:

  gcc -Wall tsdgees.c -L... -llapack -l.... ....

where after '-L' you may need to put directory where your Lapack
library lives and after '-l' you have auxilary libraries
needed by Lapack.  On my machine I needed '-lf77blas -lcblas -latlas'
but what gets here depends on how your Lapack was compiled.
If compilation goes fine you should get 'a.out' binary in
current directory.  Running it should produce result like:

w[0] = (0.101021, i*0.000000), w[1] = (9.898979, i*0.000000)

Note: if Lapack is in some nonstandard location you may need
to run 'a.out' like:

(export LD_LIBRARY_PATH=/path/to/lapack/dir; ./a.out)

If this step does not work, there is no hope that the
interface will work.

2) Compile interface library (ATM this is single file
   which contains a few functions):

gcc -Wall -fPIC -shared -o eig.so eig.c -L... -llapack -l...

The '-L...' and '-l...' options are the ones you found in step 1.

3) Edit the provide 'neig0.lisp' file replacing '/path/to/lapack/dir/'
   by real path to Lapack directory.

4) Start up FriCAS.  Only sbcl based FriCAS will work.  Type

)lisp (load "neig0.lisp")
)lisp (load (compile-file "neig.lisp"))
)compile numeig.spad

5) Now you should be able to compute eigenvalues of DoubleFloat
matrix like below:

(12) -> am := matrix([[3.0, 4.0], [5.0, 7.0]])$DoubleFloatMatrix

         +3.0  4.0+
   (12)  |        |
         +5.0  7.0+
                                                      Type: DoubleFloatMatrix
                                      Time: 0.001 (IN) + 0.01 (OT) = 0.01 sec
(13) -> eigenvalues(am)                                         

   (13)  [0.10102051443364424,9.898979485566356]
                                           Type: Vector(Complex(DoubleFloat))
                                                 Time: 0.002 (OT) = 0.002 sec