41CL Quiz: Determinant of 30x30 anti-Identity matrix

[Valentin Albillo]

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Hi, Gerson:

(06-03-2018 03:56 AM)Gerson W. Barbosa Wrote:  On my HP 50g:

D11 = 1486442880.
D13 = 283465647360.
D30 = 3.31153874629E34

All Ok, of course.

Quote:Probably not the formula you have in mind, but that’s what I could get so far.

D(n) = (n + 1)!*Hn+1

Exactly the formula I had in mind:

      D(N) = (N+1)!*(1+1/2+1/3+...1/(N+1)) = (N+1)!*H(N+1)

where H(N) is the sum of the first N terms of the Harmonic series. For example:

      D(10) = FACT(11)*(1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11)
            = 120543840

The sum of the Harmonic series is thus:

      H(N) = D(N-1)/FACT(N)

which surely would be one of the most inefficient ways to compute the sum. :-D ... For example

      H(11) = D(10)/FACT(11) = 120543840/39916800 = 3.01987734488

           = 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11 = 3.01987734488

This 2-line HP-71B program will create and display the NxN matrix, then compute and display its determinant for arbitrary N:

1 DESTROY ALL @ OPTION BASE 1 @ INPUT N @ DIM A(N,N) @ MAT A=CON
2 FOR I=1 TO N @ A(I,I)=I+2 @ NEXT I @ MAT DISP A; @ DISP @ DISP DET(A)

>RUN
? 11

3 1 1 1 1 1 1  1  1  1  1
1 4 1 1 1 1 1  1  1  1  1
1 1 5 1 1 1 1  1  1  1  1
1 1 1 6 1 1 1  1  1  1  1
1 1 1 1 7 1 1  1  1  1  1
1 1 1 1 1 8 1  1  1  1  1
1 1 1 1 1 1 9  1  1  1  1
1 1 1 1 1 1 1 10  1  1  1
1 1 1 1 1 1 1  1 11  1  1
1 1 1 1 1 1 1  1  1 12  1
1 1 1 1 1 1 1  1  1  1 13

1486442880

Still, the idea was that Ángel would use these determinants to check his new microcoded matrix handling functions to see what timings and accuracy they would achieve. Let's hope he sees these posts and obligues.

Are you listening, Ángel ? :-D

Thanks, Gerson, and regards.
V.
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