Categories for the working mathematics programmer

[nthiery]

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

Latest version of the patches:

• categories-framework-nt.patch (reviewer: David Roe; review essentially complete up to some doctests)
• categories-categories-nt.patch (reviewer: Florent Hivert, Javier, David Kohel, Anne Schilling, ...) See CategoriesCategoriesReview
• categories-fixsagelib-nt.patch (positive review: Robert Bradshaw)
  updates to the sage library (import fixes, ...)
• categories-fix-combinat-nt.patch (positive review: Florent)
• categories-numberfield_homset-nt.patch (reviewer: William)
• categories-unpickle_backward_compatibility_aliases-nt.patch (positive review: Florent)

Status and roadmap: http://trac.sagemath.org/sage_trac/wiki/CategoriesRoadMap

Some of the things done in this ticket:

• 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())
    See the category graph: attachment: sage-category-graph.pdf
  • (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
    • Can systematically use the idiom P in Rings()
  • Lattice structure (join, meet); meet needs cleanup; join and meet
    should be swapped.

• Reorganization of the Sage library to start using the category framework:

  • Groups:
    • AbelianGroup_class.init was missing a call to Groups.init
    • Support for Group.init(category = ...)
    • AbelianGroups was renamed to CommutativeAdditiveGroups (idem for Semigroups, ...)
      (note: AbelianGroup are about commutative multiplicative groups)
  • NumberFields: bug fix (categories-numberfield_homset-nt.patch):
    Hom(SomeNumberField,SomeVectorSpace) returned a numberfield homset
  • Fixed some import loops
  • Square MatrixSpace in Algebras(...)
  • 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
  • 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
      Transitional aliases one = one_element, zero = zero_element

    • 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)

CC: @sagetrac-sage-combinat @roed314 @saliola

Component: categories

Keywords: categories parents

Author: Nicolas M. Thiéry, Teresa Gomez-Diaz

Reviewer: Robert Bradshaw, Craig Citro, Florent Hivert, David Kohel, David Roe, Anne Schilling, William Stein, Javier Vengoroso

Merged: sage-4.3.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/5891

[nthiery]

Description changed:

--- 
+++ 
@@ -1,7 +1,7 @@
 This (series of) patch(es) extends the Sage category framework as a
 design pattern for organizing generic code.
 
-Under development on combinat.sagemath.org/patches:
+Under development on http://combinat.sagemath.org/patches:
 
 - categories-nt.patch:    the category framework itself
                         + updates to combinatorial free modules (will be split before submission)

[nthiery]

Description changed:

--- 
+++ 
@@ -1,33 +1,45 @@
 This (series of) patch(es) extends the Sage category framework as a
 design pattern for organizing generic code.
 
-Under development on http://combinat.sagemath.org/patches:
+(with special thanks to Robert Bradshaw, Mike Hansen, Florent Hivert,
+William Stein, ... for design discussions).
 
-- categories-nt.patch:    the category framework itself
-                        + updates to combinatorial free modules (will be split before submission)
+Under development on combinat.sagemath.org/patches:
 
-Related patches (will need to be applied to recover all previous functionalities):
+- 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
 - root_systems-4326-nt.patch
 
-Small technical patches they depend on:
+Small technical patches the category patch depends on:
+- cached_in_parent_method-5449-submitted.patch
+- lazy_attributes-fixes-5783-final.patch
 - unique_representation-5120-submitted.patch
-- lazy_attributes-fixes-5783-final.patch
-- element_wrapper-nt.patch
+- element_wrapper-5967-submitted.patch
+- parent-element_constructor-fix-5979-submitted.patch
+- explain-pickle-v1.patch
+- cPickle-5985-import-submitted.patch
+- cPickle-5985-copy_reg_classes-submitted.patch
+- cPickle-5986-nested-classes-submitted.patch
+- dynamic_class-5991-submitted.patch
 - 5598-coerce-declare.patch
-- cached_in_parent_method-5449.new
-- explain-pickle-v1.patch
-- cPickle-copy_reg_classes-nt.patch
-- cPickle-nested-classes-nt.patch
-- dynamic_class-nt.patch
-- compositions-cleanup-5600-nt.patch
-- transitive_ideal-nt.patch
-
+- explain-pickle-v1.patch			# probably can get rid of this dependency
+- 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
@@ -41,12 +53,12 @@
   see related patches, automatic monoids, ...
 
 * Categories:
-  - All the mathematical categories of Axiom and MuPAD
-  - EnumeratedSets         (with example)
-  - Semigroups             (with example, basic methods, subquotients)
-  - FiniteSemigroups       (with example, cayley graphs, basic representation theory, ...)
-  - ModulesWithBasis       (with example, morphisms)
-  - HopfAlgebras & friends (with example)
+  - 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
@@ -63,14 +75,28 @@
   - 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)
 
-* Combinatorial free modules
-  * Have unique representation
-
 * 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
@@ -79,7 +105,7 @@
     - ParentWithAdditiveAbelianGens
     - ParentWithMultiplicativeAbelianGens
     They should eventually be inherited from the EnumeratedSets() category
-  * ...
+  * Added sage.sets.finite_enumerated_set
 
 * Todo:
   * Naming cleanup:
@@ -94,6 +120,9 @@
     * 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:
@@ -112,3 +141,4 @@
 * Discussion:
   * Defining new inline operators, at least within the sage interpreter
 
+

[nthiery]

Description changed:

--- 
+++ 
@@ -6,7 +6,7 @@
 
 Under development on combinat.sagemath.org/patches:
 
-- categories-nt.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)
@@ -19,22 +19,21 @@
 - categories-sf-nt.patch 	Symmetric functions
 - categories-symmetric_group_algebra-nt.patch
 - ncsf-nt.patch		Non commutative Symmetric Functions
-- root_systems-4326-nt.patch
+- #4326: root_systems-4326-nt.patch
 
 Small technical patches the category patch depends on:
-- cached_in_parent_method-5449-submitted.patch
-- lazy_attributes-fixes-5783-final.patch
-- unique_representation-5120-submitted.patch
-- element_wrapper-5967-submitted.patch
-- parent-element_constructor-fix-5979-submitted.patch
+- #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
-- cPickle-5985-import-submitted.patch
-- cPickle-5985-copy_reg_classes-submitted.patch
-- cPickle-5986-nested-classes-submitted.patch
-- dynamic_class-5991-submitted.patch
-- 5598-coerce-declare.patch
-- explain-pickle-v1.patch			# probably can get rid of this dependency
-- transitive_ideal-6000-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:
@@ -141,4 +140,3 @@
 * Discussion:
   * Defining new inline operators, at least within the sage interpreter
 
-

[nthiery]

Description changed:

--- 
+++ 
@@ -27,7 +27,6 @@
 - #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
@@ -36,6 +35,7 @@
 - #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)

[nthiery]

Description changed:

--- 
+++ 
@@ -36,22 +36,22 @@
 
 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)
+- 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
+- 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:
+- Real life applications:
   see related patches, automatic monoids, ...
 
-* Categories:
+- 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)
@@ -62,7 +62,7 @@
     - Have unique representation by default (no need to inherit from Category_uniq)
     - Have construction / reduce by default
 
-* Functorial constructions:
+- Functorial constructions:
   - direct sum
   - tensor product
   - cartesian product (todo)
@@ -70,7 +70,7 @@
   - subquotient, subset, quotient (in progress)
   - isomorphism type (todo)
 
-* Homomorphisms
+- Homomorphisms
   - Integrates with current sage morphisms
   - Adds morphisms for some categories
   - Some general infrastructure
@@ -81,10 +81,10 @@
   - Systematic use of category = ... instead of cat =
     This may be backward incompatible.
 
-* Generic test framework
+- Generic test framework
   - Functional, final design clear, needs cleanup (2/3 hours)
 
-* Reorganization of the Sage library to start using the category framework:
+- Reorganization of the Sage library to start using the category framework:
   * Combinatorial free modules
     * Have unique representation, use coercion, are more robust
     * Improved `_repr_`
@@ -106,7 +106,7 @@
     They should eventually be inherited from the EnumeratedSets() category
   * Added sage.sets.finite_enumerated_set
 
-* Todo:
+- Todo:
   * Naming cleanup:
     * Parent -> ParentMethods (or _ParentMethods? or ?)
     * Element -> ElementMethods + move them as a nested class of ParentMethods
@@ -137,6 +137,7 @@
     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:
+- Discussion:
   * Defining new inline operators, at least within the sage interpreter
 
+

[robertwb]

comment:8

Where is categories-nt.patch itself?

[nthiery]

Description changed:

--- 
+++ 
@@ -22,7 +22,9 @@
 - #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

[nthiery]

Description changed:

--- 
+++ 
@@ -4,7 +4,10 @@
 (with special thanks to Robert Bradshaw, Mike Hansen, Florent Hivert,
 William Stein, ... for design discussions).
 
-Under development on combinat.sagemath.org/patches:
+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
@@ -22,9 +25,7 @@
 - #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
@@ -61,8 +62,8 @@
   - 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
+   - Have unique representation by default (no need to inherit from Category_uniq)
+   - Have construction / reduce by default
 
 - Functorial constructions:
   - direct sum
@@ -77,67 +78,67 @@
   - 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)
+   - 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.
+   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
+   * 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 = ...)
+   * 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
+   - 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()
+   * 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!
+   * 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
+   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
+   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

[nthiery]

comment:11

Replying to @robertwb:

Where is categories-nt.patch itself?

On the sage-combinat patch server. It changes too often to keep it updated on trac.
I highlighted the link on top of the description (and improved the ReSTing)

[nthiery]

Description changed:

--- 
+++ 
@@ -1,146 +1,5 @@
 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
-
-
+- Latest version of the patches: http://combinat.sagemath.org/patches/file/
+- Status and roadmap: http://sagetrac.org/sage_trac/wiki/CategoriesRoadMap