Add the downward monotonic cone to the cone catalogue #37802
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Add the paper "Group majorization and Schur type inequalities" by Marek Niezgoda to src/doc/en/reference/references/index.rst, which contains the global reference list. This paper mentions several convex cones in the context of group majorization, and can be used as a reference for some things in the cone catalogue. Here's a BibTeX entry for good measure: @Article{ niez1998, author = "Marek Niezgoda", title = "Group majorization and {S}chur type inequalities", journal = "Linear Algebra and its Applications", volume = 268, number = 1, year = 1998, pages = "9--30", doi = "10.1016/S0024-3795(97)89322-6" }
The downward-monotonic cone is the dual of the Schur cone that one can obtain by running sage: cones.schur(n) It is used in convex optimization, and is nice to have available independent of the Schur cone, because cones.schur_cone(n).dual() not only gives you back a cone that lives in the dual lattice of the Schur cone, but is slower than constructing the downward- monotonic cone directly. The new cone is available as sage: cones.downward_monotonic(n) in the cone catalogue.
I have used the phrase "majorization order" in the cone catalogue in a few places. It is however only a preorder, and not a partial order, so the first order of business is to change that phrase. There was also one test case that used a majorized_by() function whose implementation was incorrect. No harm was caused by this, but as a personal rule I prefer it if a function called majorized_by() actually implements the majorization order. This commit fixes that as well, by rearranging the arguments' elements in nonincreasing order, so that the function truly tests whether or not one argument majorizes the other.
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Thanks to Matthias Koeppe for the suggestion.
...and rewrap the docstrings afterwards. Thanks to Matthias Koeppe for the suggestion.
For example, (x,y) = foo becomes x,y = foo Thanks to Matthias Koeppe for the suggestion.
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Done, thanks. |
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Now I remember that we had a discussion about terminology back then that was not finished. I'll withdraw my suggestion to consider renaming it
So I think it should be renamed as |
…otone Rename this cone. "Monotone" is more popular than "monotonic", but once you include the upward- or downward- prefix, "monotonic" begins to win. I like the bike shed just the way it is, but the color isn't important enough to me to leave the bike outside for another four years while we ponder it.
OK you win. Bare "monotone" is ambiguous (the upwards monotonic cone is also used), and switching from "downward monotonic" to "downward monotone" drops the number of google hits from ~10 to zero. But it's not worth keeping this PR open for another four years. |
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Thanks. "Monotone cone" by itself is clearly a fixed, well-understood term in a (pretty large ...) community; but for purposes of Sage, adding "downward" in front does add useful extra clarity. |
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This an an old PR that I never migrated from trac. We have a catalogue of convex cones accessible through `cones.foo()`, and this PR adds the downward monotonic cone to the catalogue. It will also close sagemath#30200. URL: sagemath#37802 Reported by: Michael Orlitzky Reviewer(s): Matthias Köppe
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This an an old PR that I never migrated from trac. We have a catalogue of convex cones accessible through
cones.foo(), and this PR adds the downward monotonic cone to the catalogue. It will also close #30200.