Calculation of determinant on HP-15C

[J-F Garnier]

(03-10-2021 05:47 PM)Werner Wrote:  The 15C, as well as the 42S, have one peculiarity not mentioned before: they will alter a degenerate factorisation (ie. DET=0) by a small amount (1e-12 in the case of the 42S).
Take the obvious case

[[ 1 1 0 ]
[ 1 1 0 ]
[ 0 0 1 ]]

and compute its determinant.. the 42S returns -2e-12.

I got 1E-12 for this matrix on the 42S, same on the 75C Math ROM, the 71B Math ROM 1A and the 28C.

Starting from the 28S, the DET is no more using the altered pivots but the real ones (possibly null) and the DET is exactly zero (for these cases, without rounding errors).

On the 71B Math ROM 2B, I aligned the algorithm to the 28S.

The 42S has another quirk, that I didn't find in any other Saturn-based machines:
Try:
[[ 1E10 0 0 ]
[ 0 0 0 ]
[ 0 0 1E10 ]]
DET is 1E-492. This is the result of 1E10 x 1E-512 x 1E10.

J-F