Opened 11 years ago

Last modified 3 years ago

#5891 closed enhancement

Categories for the working mathematics programmer — at Version 10

Reported by: nthiery Owned by: nthiery
Priority: major Milestone: sage-4.3
Component: categories Keywords: categories parents
Cc: sage-combinat, roed, saliola Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description (last modified by nthiery)

This (series of) patch(es) extends the Sage category framework as a design pattern for organizing generic code.

(with special thanks to Robert Bradshaw, Mike Hansen, Florent Hivert, William Stein, ... for design discussions).

The latest version of the patches are available from:

Main patch:

  • #5891: categories-nt.patch: the category framework itself + updates to the sage library (import fixes, ... see below) + updates to combinatorial free modules (will be split before submission)

Related patches (will need to be applied after to recover 100% doctest pass):

  • categories-combinat-nt.patch
  • categories-numberfield_homset-nt.patch
  • family_enumset-fh.patch
  • enumset_unions-fh.patch
  • categories-sf-nt.patch Symmetric functions
  • categories-symmetric_group_algebra-nt.patch
  • ncsf-nt.patch Non commutative Symmetric Functions
  • #4326: root_systems-4326-nt.patch

Small technical patches the category patch depends on:

  • #5449: cached_in_parent_method-5449-submitted.patch
  • #5783: lazy_attributes-fixes-5783-final.patch
  • #5120: unique_representation-5120-submitted.patch
  • #5967: element_wrapper-5967-submitted.patch
  • #5979: parent-element_constructor-fix-5979-submitted.patch
  • #5985: cPickle-5985-import-submitted.patch, cPickle-5985-copy_reg_classes-submitted.patch
  • #5986: cPickle-5986-nested-classes-submitted.patch
  • #5991: dynamic_class-5991-submitted.patch
  • #5598: 5598-coerce-declare.patch
  • #5483: explain-pickle-v1.patch # probably can get rid of this dependency
  • #6000: transitive_ideal-6000-submitted.patch

Current status:

  • All test pass except for:
    • sage -t "devel/sage/sage/geometry/" (apparently caused by categories, though I don't see how)
    • sage -t "devel/sage/sage/structure/sage_object.pyx" (unpickling of old stuff)
  • Real life applications: see related patches, automatic monoids, ...
  • Categories:
    • All the mathematical categories of Axiom and MuPAD (Courtesy of Teresa Gomez Diaz)
    • (Infinite/Finite?)EnumeratedSets? (with example) (Courtesy of Florent Hivert)
    • Semigroups (with example, basic methods, subquotients)
    • FiniteSemigroups? (with example, cayley graphs, basic representation theory, ...)
    • ModulesWithBasis? (with example, morphisms)
    • HopfAlgebras? & friends (with example)
    • Cleanup:
      • Have unique representation by default (no need to inherit from Category_uniq)
      • Have construction / reduce by default
  • Functorial constructions:
    • direct sum
    • tensor product
    • cartesian product (todo)
    • dual (in progress)
    • subquotient, subset, quotient (in progress)
    • isomorphism type (todo)
  • Homomorphisms
    • Integrates with current sage morphisms
    • Adds morphisms for some categories
    • Some general infrastructure
    • Hom:
      • Simplification of the logic. Hopefuly completely compatible.
      • X._Hom_(Y, category) may now return NotImplemented?
      • failed attempt at using cached_function (to be pursued)
    • Systematic use of category = ... instead of cat = This may be backward incompatible.
  • Generic test framework
    • Functional, final design clear, needs cleanup (2/3 hours)
  • Reorganization of the Sage library to start using the category framework:
    • Combinatorial free modules
      • Have unique representation, use coercion, are more robust
      • Improved _repr_
      • Handle combinatorial classes that can't be sorted as indices
    • Groups:
      • AbelianGroup_class.init was missing a call to Groups.init
      • NAME CONFLICT: AbelianGroups? are *not* in AbelianGroups?() With the current conventions:
      • Support for Group.init(category = ...)
    • Fixed some import loops
    • Added temporary list() methods to:
    • Added sage.sets.finite_enumerated_set
  • Todo:
    • Naming cleanup:
      • Parent -> ParentMethods? (or _ParentMethods? or ?)
      • Element -> ElementMethods? + move them as a nested class of ParentMethods?
      • super_categories should be a method
      • zero, one should be methods
      • standardize the names: mult / product / multiplication / multiply?
      • check -> test
      • self.tester(keywords)
      • intrusive cat.tensor_category / ...
      • cat.example() -> /an_example/an_object/... ?
      • class.an_instance() ?
      • all_weakly_super_categories -> ?
      • move all examples in examples/
      • AbelianGroups?() versus CommutativeGroups?()
  • Category graph picture
  • Fixes:
    • Pickling: essentially works; polish the remaining
    • Integration in the Sage library: some tests are broken. Help welcome!
    • Pickling from old sage: technically feasible. Need help!
    • Inheritance from category for Cython classes: technically feasible. Need help!
  • Hom is *not* a functorial construction, the design and user interface needs to be discussed
  • Support for multivariate morphims, i.e. morphisms A x B -> C where the specializations A x b -> C are morphisms for a given category and a x B -> C are morphisms for a possibly different category
  • Discussion:
    • Defining new inline operators, at least within the sage interpreter

Change History (10)

comment:1 Changed 11 years ago by nthiery

  • Description modified (diff)

comment:2 Changed 11 years ago by roed

  • Cc roed added

comment:3 Changed 11 years ago by saliola

  • Cc saliola added

comment:4 Changed 11 years ago by nthiery

  • Description modified (diff)

comment:5 Changed 11 years ago by nthiery

  • Description modified (diff)

comment:6 Changed 11 years ago by nthiery

  • Description modified (diff)

comment:7 Changed 11 years ago by nthiery

  • Description modified (diff)

comment:8 Changed 11 years ago by robertwb

Where is categories-nt.patch itself?

comment:9 Changed 11 years ago by nthiery

  • Description modified (diff)

comment:10 Changed 11 years ago by nthiery

  • Description modified (diff)
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