00:48:38 <esolangs> [[Eigenratio]] M https://esolangs.org/w/index.php?diff=104923&oldid=89006 * PythonshellDebugwindow * (+23) Category

01:20:17 <esolangs> [[Brainfuck+10]] https://esolangs.org/w/index.php?diff=104924&oldid=104903 * Watermelyn * (+27)

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

04:16:27 <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.

04:25:16 <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?

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?

04:38:26 <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.

04:41:08 <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.

04:45:27 <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?

05:37:49 <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?

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)

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)

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.