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00:48:38 <esolangs> [[Eigenratio]] M https://esolangs.org/w/index.php?diff=104923&oldid=89006 * PythonshellDebugwindow * (+23) Category
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01:20:17 <esolangs> [[Brainfuck+10]]  https://esolangs.org/w/index.php?diff=104924&oldid=104903 * Watermelyn * (+27) 
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04:05:52 <shachaf> Hmm, the simplex algorithm sure seems very similar to Gaussian elimination.
04:08:16 <int-e> sure, especially when you do it on an extended tableaux
04:09:07 <shachaf> Uh oh, I don't know what that is.
04:12:21 <shachaf> Ugh, so many things to learn.
04:12:44 <shachaf> Apparently this is what Gröbner bases are about too?
04:14:17 <int-e> Or is that called a full tableau? The one that has an identity matrix rather than labeling rows with basic variables
04:15:56 <shachaf> Is that similar to an augmented matrix thing?
04:16:27 <int-e> Gröbner bases have more of a gcd flavor to me. There's a connection (Bezout's identity can be turned into a linear combination of rows comprised of the coefficients of the polynomials, shifted... cf. resultants)
04:16:29 <shachaf> I thought with basic variables you still ended up having an identity matrix, though I didn't work through examples very much so maybe that's not maintained.
04:18:02 <int-e> the identity matrix can be completely implicit, but then the variable exchange step (swapping a basic variable and a non-basic one) loses some of its Gaussian elimination flavor.
04:18:45 <shachaf> Hmm, I see, I think.
04:25:16 <shachaf> Hmm, can phase 2 of the simplex method start with any feasible point, or does it need to be on a boundary of some sort?
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04:30:21 <int-e> I think you'll have a boundary point by force (simply by the presence of that identity matrix in the full tableau)
04:31:38 <shachaf> Oh, you mean a boundary point in the full problem when you add the slack variables, not in the original problem?
04:32:02 <shachaf> Hmm, does that sentence even make sense?
04:34:01 <shachaf> I should implement this so I know what's going on.
04:38:26 <int-e> The slack variables don't really change the set of feasible solutions... they embed it in a higher-dimensional space.
04:39:25 <int-e> For example, rather than x,y >= 0, x+y <= 1, you have x,y,z >= 0 and x+y+z = 1. Both sets are two-dimensional triangles.
04:39:51 <int-e> But one of them is embedded in R^3
04:41:08 <int-e> And the point of this is... the boundary is not affected by whether you take slack variables into account or not.
04:42:27 <int-e> Or... more abstractly... You can project the slack variables away (projecting from R^(n+m) to R^n), and that's a bijection because you can recompute the slack variables from the constraints.
04:43:17 <shachaf> Right, fair enough.
04:43:57 <shachaf> So why do you end up with a boundary point by force?
04:45:27 <int-e> because you've set the maximum number of variables to 0... meaning that the solution touches the corresponding hyperplanes
04:46:51 <int-e> I mean, when you start with a *basic* feasible solution. Which you do if you reconstruct the solution from the tableau (setting the non-basic variables to 0)
05:16:06 <shachaf> Should I think of the variables in the dual linear program as corresponding the slack variables in the primal program, or is that going down the wrong path?
05:18:47 <int-e> dunno
05:19:50 <int-e> I have not internalized the Farkas lemma.
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05:37:49 <shachaf> What about when you start solving an LP problem directly in phase 2, when all constraints are nonnegative and you can pick the 0 vector as a starting point?
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05:37:54 <shachaf> Presumably that's not on the boundary.
05:38:16 <shachaf> Or, hmm, maybe it is. Right.
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15:04:48 <esolangs> [[Brainfuckconsole74]]  https://esolangs.org/w/index.php?diff=104925&oldid=104217 * Andor ch * (+269) 
15:07:38 <esolangs> [[Brainfuckconsole74]]  https://esolangs.org/w/index.php?diff=104926&oldid=104925 * Andor ch * (+260) 
15:09:02 <esolangs> [[Special:Log/upload]] upload  * Andor ch *  uploaded "[[File:BrainfuckConsole running as a compilation on processing.png]]"
15:09:10 <esolangs> [[Brainfuckconsole74]]  https://esolangs.org/w/index.php?diff=104928&oldid=104926 * Andor ch * (+74) 
15:10:02 <esolangs> [[Brainfuckconsole74]]  https://esolangs.org/w/index.php?diff=104929&oldid=104928 * Andor ch * (+91) 
15:12:01 <esolangs> [[Special:Log/upload]] upload  * Andor ch *  uploaded "[[File:Swiss Alpine Racing.png]]"
15:12:07 <esolangs> [[Brainfuckconsole74]]  https://esolangs.org/w/index.php?diff=104931&oldid=104929 * Andor ch * (+39) 
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16:34:02 <esolangs> [[Truth-machine]]  https://esolangs.org/w/index.php?diff=104932&oldid=104871 * Watermelyn * (+31) 
16:35:00 <esolangs> [[Brainfuck+10]]  https://esolangs.org/w/index.php?diff=104933&oldid=104924 * Watermelyn * (+52) 
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22:39:04 <esolangs> [[Antgrid]] M https://esolangs.org/w/index.php?diff=104934&oldid=92203 * Nakilon * (+27) added category Unimplemented
22:39:25 <esolangs> [[Antgrid]] M https://esolangs.org/w/index.php?diff=104935&oldid=104934 * Nakilon * (+0) 
23:27:20 <b_jonas> https://twitter.com/gro_tsen/status/1595411477065830400 (David Madore on the statement "a monad is a monoid in the category of endufunctors")
23:29:18 <shachaf> Yes, there are many monoidal structures you can put on that category, and people always leave that bit implicit.