Unexpected result calculating the determinant of a singular matrix (42S)

[Werner]

Hi everyone.

The 48GX (and up) does not check whether the matrix elements are integer - it determines the least significant digit in the input (say it is of the order 10^s) and with Flag -54 clear it will round the result to 10^(s*n), with n the order of the matrix.

(10-21-2019 02:36 AM)Valentin Albillo Wrote:  Try the 7x7 matrix I give as an example in the linked paper in the 48G and see if you get 1 as the determinant. You won't, the cheat doesn't work.

? of course the cheat works. With Flag -54 clear, the 48GX returns 1 exactly, with Flag -54 set it returns .999945522778. The condition number is about 10^11, and the 48GX works with 15 digits internally, so we get 15-11=4 correct digts.

Also, Valentin, the 42S uses a*b-c*d when calculating the determinant of a 2x2 system, as you can see when you calculate the determinant of

1 2
3 1

and

1 2 0
3 1 0
0 0 1

The former returns -5 exactly, the latter -5.00000000001

Best Regards,
Werner