#5891: Categories for the working mathematics programmer
-------------------------+--------------------------------------------------
Reporter: nthiery | Owner: nthiery
Type: enhancement | Status: new
Priority: major | Milestone: sage-combinat
Component: misc | Keywords: categories parents
-------------------------+--------------------------------------------------
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).
>
> 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
> - #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.
(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
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5891#comment:10>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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