wiki:CategoriesRoadMap

Version 25 (modified by hivert, 4 years ago) (diff)

Set positive review on categories-combinat

#5891: Categories for the working mathematics programmer (status and roadmap)

This page describes the status and roadmap for the category patches.

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, David Roe, William Stein, ... for design discussions).

The latest version of all the patches are available from:  http://combinat.sagemath.org/patches/file/ -> browse Please review them from there!

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
  • #5985: cPickle-5985-import-submitted.patch, cPickle-5985-copy_reg_classes-submitted.patch (positive review shortly?)
  • #5991: dynamic_class-5991-submitted.patch (positive review)
  • #6000: transitive_ideal-6000-submitted.patch
  • #5483: explain-pickle-v1.patch
  • #5979: parent-element_constructor-fix-5979-submitted.patch
  • #5986: cPickle-5986-nested-classes-submitted.patch (Craig)
  • #5598: 5598-coerce-declare.patch (positive review)
  • #6097: abstract_method-6097-nt.patch
  • #6343: sage_object-test-6343-nt.patch (with patch, needs review)

Main patches #5891:

Second batch of patches that will need to go in at once (in separate tickets). Up to final polishing, they are ready for inclusion.

Later patches using categories:

Current status:

  • All test pass (except sage_object, unpickling, see below)
  • Categories:
    • Infrastructure:
      • sage.categories.category (500 lines of code)
      • sage.structure.parent (100 lines of code)
      • class manipulation: (25 lines of code)
    • All the mathematical categories of Axiom and MuPAD (Courtesy of Teresa Gomez Diaz) (except *WithSeveralBases? which are not needed anymore; see .abstract_category())
    • (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 a couple examples)
    • Cleanup:
      • Have unique representation by default (no need to inherit from Category_uniq)
      • Have construction / reduce by default
  • Functorial constructions:
    • cartesian product (todo)
    • subquotient, subset, quotient (in progress)
    • direct sum
    • tensor product
    • dual (very preliminary)
    • isomorphism type (very preliminary)
  • 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. See Todo's in Sets.Parent.check? for possible improvements
  • Lazy attributes: Non essential, and essentially invisible from the user interface Powerful tool for:
    • Conditionaly defined methods
    • Enriched methods
  • Pickling: Works; the strategy could be improved at some point; see also below
  • Categories and Cython: Proof-of-concept for Cython classes to inherit code from categories See: sage.categories.examples.semigroups_cython
  • 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:
    • NumberFields?: bug fix (categories-numberfield_homset-nt.patch / needs review): Hom(SomeNumberField?,SomeVectorSpace?) returned a numberfield homset
    • Fixed some import loops
    • Added temporary list() methods to:
    • Added sage.sets.finite_enumerated_set
    • Added aliases one = one_element, zero = zero_element to start the transition (to be discussed)
    • Naming conventions and cleanup:
      • parent.product(x,y) parent.product parent.product_on_basis (was: multiply, _multiply, multiply_basis, _multiply_basis)
      • parent.summation(x,y) parent.summation # risk of confusion with infinite summation / ...
  • parent.sum ([x,y,z,y])
  • parent.prod([x,y,z,y])
  • parent.coproduct, parent.coproduct_on_basis, parent.coproduct_on_generators
  • parent.antipode, parent.antipode_on_basis, parent.antipode_on_generators
  • cat.example() cat.counter_example()
  • A.one() A.zero() a.is_one() a.is_zero() A(1) A(0) when it makes sense A.one_element() A.zero_element() deprecated in the doc; fully deprecated later
  • Use class.an_instance() whenever meaningful
  • parent.an_element() parent.some_elements(); possibly parent.example() parent.counterexample()
  • all_weakly_super_categories -> all_super_categories(proper=False)
  • Todo before integration of this patch:
  • Documentation cleanup (HELP!):
    • Get to 100% doctests
    • Fix ReST incorrectness
    • Check and put appropriate entry points
  • Add more examples of parents (HELP!): Ultimately, this should be for all categories, Those are needed urgently:
    • Modules (for doctests for mul / rmul / ...)
    • Algebras (for doctests for mul / rmul / ...)
    • CommutativeAdditiveSemigroups? (for doctesting add / sub / ...)
  • Todo for after:
    • Allow for super classes to also provide .Element
    • Make nice pictures of the category hierarchy! HELP!
    • Make sure that ? and ?? on categories / examples / ... point to the right place e.g.: Semigroups??, Semigroups().example()?? Semigroups().parent_class?, Semigroups.element_class?
    • abstract / isomorphism type / with_several_representations
  • Long run discussions:
    • init_add
    • Writing and linking to generic documentation
    • Standardize the functorial constructions, and streamline with variants (finite / finite dimensional / graded / abstract / ...)
    • Hom is *not* a functorial construction. This works for now, but the design and user interface needs to be discussed for the long run implementation.
    • what's the right inheritance structure for homsets? Also, how should one specify that a category's homsets are enriched in another category? Via a method like "enriched_in()" on the category? By extra_super_categories() in a custom HomCategory??
  • Support for multivariate morphims, i.e. morphisms (A x B) -> C where the specializations (A x b) -> C and and (a x B) -> C are morphisms for possibly different categories
  • Defining new inline operators, at least within the sage interpreter
  • Convention for the order in super_categories (see primer)
  • Cythonification, and merging of the code with sage.structure.element.*Element?
  • Inheritance from existing parents
  • How to specify the category of a parent (overloading of method / argument to init)

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