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#34 |
Sep 2017
1438 Posts |
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Signing off
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#35 |
"Hugo"
Jul 2019
Germany
31 Posts |
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From where do you take the conviction that there is no shortcut? I do not know if you should call it a shortcut, if someone realizes what I said a few posts above with "Much more promising would be good ideas regarding a structure of the matrices."?
I've been wondering if I should give this information here, but normally the puzzle team at IBM should have already provided an update to the website. I am rather disappointed because no feedback on the state of the competition is visible and the idea with the *-awards does not fulfill the purpose as I had imagined. |
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#36 | |
"Ed Hall"
Dec 2009
Adirondack Mtns
1110010111012 Posts |
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How do you figure out a determinant? Edit: (I think) I at least understand what a Latin Square is. . . Last fiddled with by EdH on 2019-11-15 at 01:34 |
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#37 |
"Rashid Naimi"
Oct 2015
Remote to Here/There
5·401 Posts |
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That one just comes naturally for me, for square matrices of any size.
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matdet(a) https://pari.math.u-bordeaux.fr/dochtml/html-stable/ What do I win? ![]() Last fiddled with by a1call on 2019-11-15 at 03:32 |
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#38 |
"Ed Hall"
Dec 2009
Adirondack Mtns
3,677 Posts |
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#39 | |
"Rashid Naimi"
Oct 2015
Remote to Here/There
37258 Posts |
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#40 |
"Ed Hall"
Dec 2009
Adirondack Mtns
1110010111012 Posts |
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OK, I learned how to pencil and paper the determinants of matrices, so maybe I'll play. I created a Latin Square with 556434705 and then made a non-Latin Square with 309945592. Does this sound like I'm in the ballpark of knowing enough to proceed?
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#41 |
Oct 2017
11011102 Posts |
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For comparison of computing times:
My actual code permutating some digits of a matrix - Latin or not, but saving the total number of digits in the matrix - needs 1 hour and 51 minutes for 10.216.206.000 determinants, when I use one thread. Using two threads: twice this number in the same time. Using four threads: Don’t know the time, but I‘ll check it. |
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#42 |
"Hugo"
Jul 2019
Germany
3110 Posts |
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Well, 9x9 is normally not done with pencil and paper. But doable, block-wise. And when talking of the "structure" of a matrix, there are many things to consider. E.g. symmetry, block-structure (think of a Sudoku), norms of rows and columns, correlations between rows, geometric interpretation as volume of an n-dimensional polytope, dot products of row or column vectors. For Latin squares and their special cases of circulant or Sudoku matrices all 1- or 2-norms of rows and column vectors are identical.
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#43 | |
"Ben"
Feb 2007
D4B16 Posts |
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Since the recent pseudo-hints I've looked more at matrix structure but discovered nothing useful. I'm tending to either immediately rediscover det=929587995 circulant latin squares or find nothing but singular matrices... |
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#44 |
"Ed Hall"
Dec 2009
Adirondack Mtns
3,677 Posts |
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I have set the paper and pencil aside now that I think I know a tiny amount of what I'm doing and started using machines to play. If this gets me sidetracked. . .
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