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2023 06 21 Meeting

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affeldt-aist edited this page Jun 21, 2023 · 2 revisions

Participants: Reynald, Cyril, Pierre, Julien, Zachary, Takafumi

  • splitting files
    • topology.v into multiple files?
      • split into 4 files, all at once:
        1. filters + near
        2. topology
        3. uniformity + completeness
        4. function space topologies (because of many notations, etc.)
      • wait for hierarchy-builder (because otherwise it will be painful to cherry-pick)
      • plan the mca release 1.0.0 to be based on HB
        • wait for the FTC?
          • there is the subspace problem about derivatives
      • derivable on the interior should be a reasonable restriction to allow for the FTC
      • still we do not want to wait for this theorem to release 1.0.0
        • performance problem right now, compiling mca is 45 min. while mc is 35 min.
          • there is hope that this will improve in the near future though
        • plan a 0.6.4 and waita bit for performance improvements
        • plan 0.6.4 in July
        • plan 1.0.0 in September
        • split of topology to happen in August once master is set to HB
      • splitting of topology should maybe be thought together with an update of the documentation header to follow https://github.com/math-comp/math-comp/wiki/How-to-document (see measure.v for an example in MathComp-Analysis) (even before moving to the hiearchy-builder version)
        • there is also the problem of the changelog
    • lebesgue_integral.v into (1) one file up-to non-negative simple functions and (2) the rest?
      • yes
        • because in the near future we want to replace the integral by the Bochner integral
        • a matter of months rather than weeks, should make it easier to deal with extended real numbers though
        • need to define the space of all linear functionals, the subspace of all linear continuous functionals, etc.
        • also needs the theory of dual spaces
        • Cyril: don't we have the solution for subspaces?
        • Zachary:
          • for a function at a time yes
          • some properties are nice expressed with types, other with sets, so the subspace solution does not solve everything
      • TODO(Zachary->Cyril): illustration with a concrete problem in the path development
        • Cyril: this is not a problem of displays? (i.e., absence of robust notations)
        • Zachary: the problem is when working with the type, sometimes we want the whole type
  • about the documentation
  • what to do with https://math-comp.github.io/analysis/?
    • TODO(rei): put a link in the readme with a disclaimer
  • after the split of the classical package, what about further packages? reals? topology?
    • some user only want the real numbers (Rstruct.v, reals.v only?)
      • put reals under classical?
      • constructive_ereal is also independent
    • separate package for everything that is before topology.v? for measure theory?
    • let's wait for the HB branch
  • PR triaging:
    • https://github.com/math-comp/analysis/pull/915 (smallest filter)
      • maybe rename smallest_filter_stage
      • smallest_filter is not a good choice because there are several choices
      • current way is by taking finite intersections but it used to be built all at once
        • 2nd version: it is helpful to have it built inductively
        • 3rd version: intersection of all filters containing the a set
        • having a version without the choice type was convenient
    • Urysohn's lemma ready for review?
      • current definition of metric space does not guarantee the metric function in R
      • we need a slightly stronger structure (for a every two points, there is a ball that contains both)
      • that guarantees the metric that we need for Urysohn's lemma
      • we want it to be non-Hausdorff
      • the proof cannot be completed without HB
      • the last mile should be done with the HB branch only
    • https://github.com/math-comp/analysis/pull/939 (minor fixes and additions to exp.v)
      • used for Hoelder and Minkowski
      • TODO: zachary to take a look
    • https://github.com/math-comp/analysis/pull/950 (opam files for hierachy-builder branch)
      • merged
    • https://github.com/math-comp/analysis/pull/677 (Lebesgue-Stieltjes)
      • show case subdir for the module about Lebesgue measure?
      • Stieltjes is a strict generalization
      • merge both files?
      • Saikwa: about the Sorgenfrey line?
        • shouldn't be there anyway
        • not a blocker
        • it should simplofy a bit the definition: not a new structure but the same notion of continuous but over a different domain, but you sill need non-decreasing
      • we should have a structure for continuity but this involves subspaces
      • Cumulative makes sense anyway for probability
  • help wanted: https://github.com/math-comp/analysis/pull/917 (C1 and lipschitz)
    • what about the current definition of C1?
      • fix: derivable f b 1
      • line 75 is wrong -> ask f' to converge without saying to what it converges
      • line 76 is broken: it computes f' at a (f' is two-sided!) -> take the open interval (within + open is the same as using in, there is a lemma for that)
    • f uniformly continuous on the open interval it has a limit on the end-points (converges to the right and left correctly)
    • try to get away without the value of the derivatives of the end points
    • "don't take derivatives on closed intervals"
  • other questions?
    • status of probability.v
    • https://github.com/math-comp/analysis/pull/834
      • cantor sets are used to find counter-examples but not sure they are useful for the FTC
      • TODO(rei): review
      • outline of the proof is reasonable but the details might not be that important
      • not really an original proof but a refactoring of the standard proof two standard proofs:
        • for every compac metric space there is a continuous surjection from a cantor set
        • two approaches:
          1. embed that space in a larger one
          2. contruct a finitely branching tree and build two functions with the same technique the PR has factored out the technique
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