GNU APL's domino gives a domain error for matrices that are close to
singular, but aren't.
)clear
CLEAR WS
A←100 100⍴101↑1
A[1;1]←0
[IBM APL2]
10 10 ↑⌹A+⎕CT×100
1.000000001E11 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1 ¯1
¯1.000000000E0 1 0 0 0 0 0 0 0 0
¯1.000000000E0 0 1 0 0 0 0 0 0 0
¯1.000000000E0 0 0 1 0 0 0 0 0 0
¯1.000000000E0 0 0 0 1 0 0 0 0 0
¯1.000000000E0 0 0 0 0 1 0 0 0 0
¯1.000000000E0 0 0 0 0 0 1 0 0 0
¯1.000000000E0 0 0 0 0 0 0 1 0 0
¯1.000000000E0 0 0 0 0 0 0 0 1 0
¯1.000000000E0 0 0 0 0 0 0 0 0 1
[GNU APL]
10 10 ↑⌹A+⎕CT×100
DOMAIN ERROR
10 10↑⌹A+⎕CT×100
^^
A matrix whose determinant is 1E¯11 is obviously not singular.
