#5891: Categories for the working mathematics programmer
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Reporter: nthiery | Owner: nthiery
Type: enhancement | Status: new
Priority: major | Milestone: sage-combinat
Component: misc | Keywords: categories parents
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Description changed by nthiery:
Old description:
> 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:
> http://combinat.sagemath.org/patches/file/
>
> 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/lattice_polytope.py" (apparently
> caused by categories, though I don't see how)
> - sage -t "devel/sage/sage/structure/sage_object.pyx" (unpickling
> of old stuff)
>
> - Documentation:
> - sage.categories? Category quickref card
> - sage.categories.primer? Element/Parent/Category primer (in writing)
> - Category? Technical background on categories
> - Semigroups().example()?? A template of semigroup
> - See also the discussion on sage-devel in November 2009:
> - http://groups.google.com/group/sage-devel/msg/d4065154e2e8cbd9
>
> - 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:
> - AbelianGroups is about additive abelian groups
> - AbelianGroup is about multiplicative abelian group
> * Support for Group.__init__(category = ...)
> * Fixed some import loops
> * Added temporary list() methods to:
> - FreeModule_generic
> - MatrixSpace_generic
> - Set_object_enumerated
> - ParentWithAdditiveAbelianGens
> - ParentWithMultiplicativeAbelianGens
> They should eventually be inherited from the EnumeratedSets()
> category
> * 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
New description:
This (series of) patch(es) extends the Sage category framework as a
design pattern for organizing generic code.
- Latest version of the patches:
http://combinat.sagemath.org/patches/file/
- Status and roadmap: http://sagetrac.org/sage_trac/wiki/CategoriesRoadMap
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5891#comment:12>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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