Opened 11 years ago
Last modified 2 years ago
#5891 closed enhancement
Categories for the working mathematics programmer — at Version 5
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 )
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).
Under development on combinat.sagemath.org/patches:
- #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
- explain-pickle-v1.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
- Combinatorial free modules
- 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?()
- Naming cleanup:
- 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 (5)
comment:1 Changed 11 years ago by
- Description modified (diff)
comment:2 Changed 11 years ago by
- Cc roed added
comment:3 Changed 11 years ago by
- Cc saliola added
comment:4 Changed 11 years ago by
- Description modified (diff)
comment:5 Changed 11 years ago by
- Description modified (diff)
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