There is still some work to do :-) :
Warning
This list is currently very incomplete as most doctests do not use the .. todo:: markup.
Todo
Rewrite the hand-written TODOs by using the correct .. todo:: markup.
The combined to do list is only available in the html version of the reference manual.
Todo
Rewrite the hand-written TODOs by using the correct .. todo:: markup.
(The original entry is located in /usr/share/doc/sagemath/en/reference/todolist.rst, line 13.)
Todo
An example illustrating unitary flag.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra_morphism.py:docstring of sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_morphism.FiniteDimensionalAlgebraMorphism, line 35.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/algebras/free_algebra.py:docstring of sage.algebras.free_algebra.FreeAlgebra_generic.g_algebra, line 4.)
Todo
Implement multi-parameter Iwahori-Hecke algebras together with their Kazhdan-Lusztig bases. That is, Iwahori-Hecke algebras with (possibly) different parameters for each conjugacy class of simple reflections in the underlying Coxeter group.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/algebras/iwahori_hecke_algebra.py:docstring of sage.algebras.iwahori_hecke_algebra.IwahoriHeckeAlgebra, line 305.)
Todo
When given “generic parameters” we should return the generic Iwahori-Hecke algebra with these parameters and allow the user to work inside this algebra rather than doing calculations behind the scenes in a copy of the generic Iwahori-Hecke algebra. The main problem is that it is not clear how to recognise when the parameters are “generic”.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/algebras/iwahori_hecke_algebra.py:docstring of sage.algebras.iwahori_hecke_algebra.IwahoriHeckeAlgebra, line 312.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/gsl/dft.py:docstring of sage.gsl.dft, line 52.)
Todo
Read the parent of the elements of S; if or
leave as
is; if AbelianGroup, use abelian_group_dual; if some other
implemented Group (permutation, matrix), call .characters()
and test if the index list is the set of conjugacy classes.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/gsl/dft.py:docstring of sage.gsl.dft.IndexedSequence.dft, line 41.)
Todo
Add an example.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/additive_magmas.py:docstring of sage.categories.additive_magmas.AdditiveMagmas.ParentMethods.summation, line 34.)
Todo
Add an example.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/additive_magmas.py:docstring of sage.categories.additive_magmas.AdditiveMagmas.ParentMethods.summation_from_element_class_add, line 34.)
Todo
add a description of this category
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/affine_weyl_groups.py:docstring of sage.categories.affine_weyl_groups.AffineWeylGroups, line 3.)
Todo
should return an enumerated set, with iterator, ...
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/affine_weyl_groups.py:docstring of sage.categories.affine_weyl_groups.AffineWeylGroups.ParentMethods.affine_grassmannian_elements_of_given_length, line 13.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/algebra_ideals.py:docstring of sage.categories.algebra_ideals.AlgebraIdeals, line 8.)
Todo
Should be a commutative ring?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/algebras.py:docstring of sage.categories.algebras.Algebras, line 14.)
Todo
Improve this explanation.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/category.py:docstring of sage.categories.category.Category._without_axioms, line 8.)
Todo
Add an optional argument to allow for:
sage: Realizations(A, category = Blahs()) # todo: not implemented
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/category.py:docstring of sage.categories.category.Category.Realizations, line 39.)
Todo
Get a consistent hierarchy of homset categories. Currently, it is built in parallel to that of their base categories (which is plain wrong!!!)
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/category.py:docstring of sage.categories.category.HomCategory, line 3.)
Todo
Further remove the base ring (see also trac ticket #15801).
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/category.py:docstring of sage.categories.category.category_graph, line 15.)
Todo
Specify whether or not one should systematically use @cached_method in the definition of the axiom. And make sure all the definition of axioms in Sage are consistent in this respect!
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/category_with_axiom.py:docstring of sage.categories.category_with_axiom, line 376.)
Todo
We could possibly define an @axiom decorator? This could hide two little implementation details: whether or not to make the method a cached method, and the call to _with_axiom(...) under the hood. It could do possibly do some more magic. The gain is not obvious though.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/category_with_axiom.py:docstring of sage.categories.category_with_axiom, line 382.)
Todo
Explore ways to get rid of this global all_axioms tuple, and/or have automatic registration there, and/or having a register_axiom(...) method.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/category_with_axiom.py:docstring of sage.categories.category_with_axiom, line 421.)
Todo
Other categories that would be better implemented via an axiom depending on a join category include:
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/category_with_axiom.py:docstring of sage.categories.category_with_axiom, line 488.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/category_with_axiom.py:docstring of sage.categories.category_with_axiom, line 505.)
Todo
The above example violates the specifications (a category should be modelled by at most one class), so it’s appropriate that it fails. Yet, the error message could be usefully complemented by some hint at what the source of the problem is (a category implemented in two distinct classes). Leaving a large enough piece of the backtrace would be useful though, so that one can explore where the issue comes from (e.g. with post mortem debugging).
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/category_with_axiom.py:docstring of sage.categories.category_with_axiom, line 1086.)
Todo
The following specifications would be desirable but are not yet implemented:
A functorial construction category (Graded, CartesianProducts, ...) having a Category_singleton as base category should be a CategoryWithAxiom_singleton.
Nothing difficult to implement, but this will need to rework the current “no subclass of a concrete class” assertion test of Category_singleton.__classcall__().
Similarly, a covariant functorial construction category having a Category_over_base_ring as base category should be a Category_over_base_ring.
The following specification might be desirable, or not:
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/category_with_axiom.py:docstring of sage.categories.category_with_axiom, line 1248.)
Todo
Detail this a bit. What could typically go wrong is a situation where, for some category C1, C1.A() specifies a category C2 as super category such that C2.A() specifies C3 as super category such that ...; this would clearly cause an infinite execution. Note that this situation violates the specifications since C1.A() is supposed to be a subcategory of C2.A(), ... so we would have an infinite increasing chain of constructible categories.
It’s reasonnable to assume that there is a finite number of axioms defined in the code. There remains to use this assumption to argue that any infinite execution of the algorithm would give rise to such an infinite sequence.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/category_with_axiom.py:docstring of sage.categories.category_with_axiom, line 1403.)
Todo
Decide whether we care about this feature. In such a situation, we are not really defining a new axiom, but just defining an axiom as an alias for a couple others, which might not be that useful.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/category_with_axiom.py:docstring of sage.categories.category_with_axiom.Blahs.Blue_extra_super_categories, line 15.)
Todo
Improve the infrastructure to detect and report this violation of the specifications, if this is easy. Otherwise, it’s not so bad: when defining an axiom A in a category Cs the first thing one is supposed to doctest is that Cs().A() works. So the problem should not go unnoticed.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/category_with_axiom.py:docstring of sage.categories.category_with_axiom.Blahs.Blue_extra_super_categories, line 22.)
Todo
add a demo of usual computations on Coxeter groups.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/coxeter_groups.py:docstring of sage.categories.coxeter_groups.CoxeterGroups, line 40.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/finite_coxeter_groups.py:docstring of sage.categories.finite_coxeter_groups.FiniteCoxeterGroups.ParentMethods.bruhat_poset, line 44.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/finite_coxeter_groups.py:docstring of sage.categories.finite_coxeter_groups.FiniteCoxeterGroups.ParentMethods.weak_lattice, line 70.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/finite_coxeter_groups.py:docstring of sage.categories.finite_coxeter_groups.FiniteCoxeterGroups.ParentMethods.weak_poset, line 70.)
Todo
sage.combinat.debruijn_sequence.DeBruijnSequences should not inherit from this class. If that is solved, then FiniteEnumeratedSets shall be turned into a subclass of Category_singleton.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/finite_enumerated_sets.py:docstring of sage.categories.finite_enumerated_sets.FiniteEnumeratedSets, line 25.)
Todo
make this optional
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/finite_semigroups.py:docstring of sage.categories.finite_semigroups.FiniteSemigroups, line 17.)
Todo
Get rid of this workaround once there is a more systematic approach for the alias Modules(QQ) -> VectorSpaces(QQ). Probably the later should be a category with axiom, and covariant constructions should play well with axioms.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/graded_modules.py:docstring of sage.categories.graded_modules.GradedModules.extra_super_categories, line 18.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/groups.py:docstring of sage.categories.groups.Groups.Algebras, line 24.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/homset.py:docstring of sage.categories.homset.Hom, line 172.)
Todo
Refactor during the upcoming homset cleanup.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/homset.py:docstring of sage.categories.homset.Homset.element_class_set_morphism, line 8.)
Todo
Clarify the distinction, if any, with BiModules(R, R).
In particular, if is a commutative ring (e.g. a field),
some pieces of the code possibly assume that
is a
symmetric `R`-`R`-bimodule:
Make sure that non symmetric modules are properly supported by all the code, and advertise it.
Make sure that non commutative rings are properly supported by all the code, and advertise it.
Add support for base semirings.
Implement a FreeModules(R) category, when so prompted by a concrete use case: e.g. modeling a free module with several bases (using Sets.SubcategoryMethods.Realizations()) or with an atlas of local maps (see e.g. trac ticket #15916).
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/modules.py:docstring of sage.categories.modules.Modules, line 57.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/modules.py:docstring of sage.categories.modules.Modules.SubcategoryMethods.Graded, line 18.)
Todo
handle base being a category
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/modules.py:docstring of sage.categories.modules.Modules.SubcategoryMethods.base_ring, line 6.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/modules_with_basis.py:docstring of sage.categories.modules_with_basis.DiagonalModuleMorphism, line 23.)
Todo
End(X) is an algebra.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/modules_with_basis.py:docstring of sage.categories.modules_with_basis.ModulesWithBasis, line 85.)
Todo
Should codomain be self by default in the diagonal and triangular cases?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/modules_with_basis.py:docstring of sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods.module_morphism, line 189.)
Todo
Extract a method to linearize a multilinear morphism, and delegate the work there.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/modules_with_basis.py:docstring of sage.categories.modules_with_basis.ModulesWithBasis.TensorProducts.ElementMethods.apply_multilinear_morphism, line 99.)
Todo
This has nothing to do here!!! Should there be a library for pointwise operations on functions somewhere in Sage?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/modules_with_basis.py:docstring of sage.categories.modules_with_basis.pointwise_inverse_function, line 21.)
Todo
shall we accept only permutations with finite support or not?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/permutation_groups.py:docstring of sage.categories.permutation_groups.PermutationGroups, line 6.)
Todo
Give a concrete example, typically using ElementWrapper.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/primer.py:docstring of sage.categories.primer, line 276.)
Todo
Improve the printing of functorial constructions and joins to raise this potentially dangerous ambiguity.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/primer.py:docstring of sage.categories.primer, line 1451.)
Todo
Add an optional argument to allow for:
sage: Realizations(A, category = Blahs()) # todo: not implemented
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/realizations.py:docstring of sage.categories.realizations.Realizations, line 39.)
Todo
(see: http://trac.sagemath.org/sage_trac/wiki/CategoriesRoadMap)
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/rings.py:docstring of sage.categories.rings.Rings, line 27.)
Todo
Make Schemes() a singleton category (and remove Schemes from the workaround in category_types.Category_over_base._test_category_over_bases()).
This is currently incompatible with the dispatching below.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/schemes.py:docstring of sage.categories.schemes.Schemes, line 17.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/semigroups.py:docstring of sage.categories.semigroups.Semigroups.ParentMethods.cayley_graph, line 110.)
Todo
Draw the typical commutative diagram.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/sets_cat.py:docstring of sage.categories.sets_cat.Sets.SubcategoryMethods.Subquotients, line 27.)
Todo
use a more interesting example, like .
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/sets_cat.py:docstring of sage.categories.sets_cat.Sets.SubcategoryMethods.Subquotients, line 121.)
Todo
Fix the failing test by making C a singleton category. This will require some fiddling with the assertion in Category_singleton.__classcall__()
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/sets_cat.py:docstring of sage.categories.sets_cat.Sets.WithRealizations.ParentMethods.Realizations, line 14.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/sets_with_grading.py:docstring of sage.categories.sets_with_grading.SetsWithGrading, line 72.)
Todo
Implement multi-parameter Iwahori-Hecke algebras together with their Kazhdan-Lusztig bases. That is, Iwahori-Hecke algebras with (possibly) different parameters for each conjugacy class of simple reflections in the underlying Coxeter group.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/algebras/iwahori_hecke_algebra.py:docstring of sage.algebras.iwahori_hecke_algebra.IwahoriHeckeAlgebra, line 305.)
Todo
When given “generic parameters” we should return the generic Iwahori-Hecke algebra with these parameters and allow the user to work inside this algebra rather than doing calculations behind the scenes in a copy of the generic Iwahori-Hecke algebra. The main problem is that it is not clear how to recognise when the parameters are “generic”.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/algebras/iwahori_hecke_algebra.py:docstring of sage.algebras.iwahori_hecke_algebra.IwahoriHeckeAlgebra, line 312.)
Todo
Do we want to implement the following syntactic sugar:
with t.clone() as tt:
tt.labels[1,2] = 3 ?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/abstract_tree.py:docstring of sage.combinat.abstract_tree.AbstractLabelledClonableTree.set_label, line 34.)
Todo
It is currently not possible to use LabelledBinaryTree() as a shorthand for LabelledBinaryTree(None) (in analogy to similar syntax in the BinaryTree class).
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/binary_tree.py:docstring of sage.combinat.binary_tree.LabelledBinaryTree, line 50.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/combinat.py:docstring of sage.combinat.combinat, line 93.)
Todo
Incorporate this method into the _repr_ for finite Cartan type.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/crystals/alcove_path.py:docstring of sage.combinat.crystals.alcove_path.CrystalOfAlcovePathsElement.integer_sequence, line 4.)
Todo
Better doctest
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/crystals/alcove_path.py:docstring of sage.combinat.crystals.alcove_path.CrystalOfAlcovePathsElement.is_admissible, line 47.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/crystals/crystals.py:docstring of sage.combinat.crystals.crystals, line 96.)
Todo
FIXME:
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/crystals/tensor_product.py:docstring of sage.combinat.crystals.tensor_product.CrystalOfTableaux, line 72.)
Todo
Implement finite non-Desarguesian plane as in [We07] and Wikipedia article Non-Desarguesian_plane.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/designs/block_design.py:docstring of sage.combinat.designs.block_design, line 28.)
Todo
Implement DerivedDesign and ComplementaryDesign.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/designs/design_catalog.py:docstring of sage.combinat.designs.design_catalog, line 56.)
Todo
There is a slightly more general version of difference families where the stabilizers of the blocks are taken into account. A block is short if the stabilizer is not trivial. The more general version is called a partial difference family. It is still possible to construct BIBD from this more general version (see the chapter 16 in the Handbook [DesignHandbook]).
Implement recursive constructions from Buratti “Recursive for difference matrices and relative difference families” (1998) and Jungnickel “Composition theorems for difference families and regular planes” (1978)
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/designs/difference_family.py:docstring of sage.combinat.designs.difference_family.difference_family, line 136.)
Todo
The XML data from the designtheory.org database contains a wealth of information about things like automorphism groups, transitivity, cycle type representatives, etc, but none of this data is made available through the current implementation.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/designs/ext_rep.py:docstring of sage.combinat.designs.ext_rep, line 14.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/designs/orthogonal_arrays.py:docstring of sage.combinat.designs.orthogonal_arrays, line 35.)
Todo
As soon as wilson construction accepts an empty master design we should remove this intermediate functions.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/designs/orthogonal_arrays_recursive.py:docstring of sage.combinat.designs.orthogonal_arrays_recursive.simple_wilson_construction, line 9.)
Todo
extend this to m-Dyck words
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/dyck_word.py:docstring of sage.combinat.dyck_word.CompleteDyckWords_size.random_element, line 11.)
Todo
At the moment, the letters of the alphabets need to be hashable.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/finite_state_machine.py:docstring of sage.combinat.finite_state_machine.FiniteStateMachine.determine_alphabets, line 17.)
Todo
Do the iteration in place to save on copying time
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/integer_list.py:docstring of sage.combinat.integer_list.IntegerListsLex.count, line 7.)
Todo
Placeholder. Implement a proper check.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/integer_list.py:docstring of sage.combinat.integer_list.IntegerListsLexElement.check, line 4.)
Todo
Move this into Cython.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/integer_list.py:docstring of sage.combinat.integer_list.first, line 8.)
Todo
should the order of the arguments n and weight be exchanged to simplify the logic ?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/integer_vector_weighted.py:docstring of sage.combinat.integer_vector_weighted.WeightedIntegerVectors, line 39.)
Todo
Integer vectors should accept max_part as a single argument, and the following should change:
sage: S = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3,4)]]), max_part=12); S.ambient()
Integer vectors
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/integer_vectors_mod_permgroup.py:docstring of sage.combinat.integer_vectors_mod_permgroup.IntegerVectorsModPermutationGroup_with_constraints.ambient, line 10.)
Todo
To study this, it would be more natural to define
interval-posets on arbitrary ordered sets rather than just
on .
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/interval_posets.py:docstring of sage.combinat.interval_posets.TamariIntervalPoset.insertion, line 25.)
Todo
Functionality to add:
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/knutson_tao_puzzles.py:docstring of sage.combinat.knutson_tao_puzzles, line 12.)
Todo
This construction holds more generally for prime powers
congruent to
. We should implement these but we
first need to implement Quadratic character for
.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/matrices/hadamard_matrix.py:docstring of sage.combinat.matrices.hadamard_matrix.H1, line 5.)
Todo
This construction holds more generally for prime powers
congruent to
. We should implement these but we
first need to implement Quadratic character for
.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/matrices/hadamard_matrix.py:docstring of sage.combinat.matrices.hadamard_matrix.H2, line 6.)
Todo
Fix the failing test by making C a singleton category. This will require some fiddling with the assertion in Category_singleton.__classcall__()
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/ncsf_qsym/generic_basis_code.py:docstring of sage.combinat.ncsf_qsym.generic_basis_code.BasesOfQSymOrNCSF, line 14.)
Todo
Generalize this to all graded vector spaces?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/ncsf_qsym/generic_basis_code.py:docstring of sage.combinat.ncsf_qsym.generic_basis_code.BasesOfQSymOrNCSF.ElementMethods.degree_negation, line 33.)
Todo
Generalize this to all graded vector spaces?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/ncsf_qsym/generic_basis_code.py:docstring of sage.combinat.ncsf_qsym.generic_basis_code.BasesOfQSymOrNCSF.ParentMethods.degree_negation, line 47.)
Todo
Despite the __repr__, this is NOT an endomorphism!
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/ncsf_qsym/generic_basis_code.py:docstring of sage.combinat.ncsf_qsym.generic_basis_code.GradedModulesWithInternalProduct.ParentMethods.internal_product, line 34.)
Todo
Despite the __repr__, this is NOT an endomorphism!
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/ncsf_qsym/generic_basis_code.py:docstring of sage.combinat.ncsf_qsym.generic_basis_code.GradedModulesWithInternalProduct.ParentMethods.itensor, line 34.)
Todo
Despite the __repr__, this is NOT an endomorphism!
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/ncsf_qsym/generic_basis_code.py:docstring of sage.combinat.ncsf_qsym.generic_basis_code.GradedModulesWithInternalProduct.ParentMethods.kronecker_product, line 34.)
Todo
demonstrate how to customize the basis names
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/ncsf_qsym/ncsf.py:docstring of sage.combinat.ncsf_qsym.ncsf.NonCommutativeSymmetricFunctions, line 162.)
Todo
explain the other changes of bases!
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/ncsf_qsym/ncsf.py:docstring of sage.combinat.ncsf_qsym.ncsf.NonCommutativeSymmetricFunctions, line 213.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/ncsf_qsym/ncsf.py:docstring of sage.combinat.ncsf_qsym.ncsf.NonCommutativeSymmetricFunctions, line 259.)
Todo
this could be generalized to any free algebra.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/ncsf_qsym/ncsf.py:docstring of sage.combinat.ncsf_qsym.ncsf.NonCommutativeSymmetricFunctions.MultiplicativeBasesOnPrimitiveElements, line 14.)
Todo
Implement this directly on the monomial basis maybe?
The -matrices are a pain to generate from their
definition, but maybe there is a good algorithm.
If so, the above “further examples” should be moved
to the M-method.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/ncsf_qsym/qsym.py:docstring of sage.combinat.ncsf_qsym.qsym.QuasiSymmetricFunctions.Bases.ElementMethods.internal_coproduct, line 184.)
Todo
Implement this directly on the monomial basis maybe?
The -matrices are a pain to generate from their
definition, but maybe there is a good algorithm.
If so, the above “further examples” should be moved
to the M-method.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/ncsf_qsym/qsym.py:docstring of sage.combinat.ncsf_qsym.qsym.QuasiSymmetricFunctions.Bases.ElementMethods.kronecker_coproduct, line 184.)
Todo
The conversion from the M basis to the HWL basis is currently implemented in the naive way (inverting the base-change matrix in the other direction). This matrix is not triangular (not even after any permutations of the bases), and there could very well be a faster method (the one given by Hazewinkel?).
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/ncsf_qsym/qsym.py:docstring of sage.combinat.ncsf_qsym.qsym.QuasiSymmetricFunctions.HazewinkelLambda, line 39.)
Todo
accept an alphabet as input
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/ncsf_qsym/qsym.py:docstring of sage.combinat.ncsf_qsym.qsym.QuasiSymmetricFunctions.Monomial.Element.expand, line 14.)
Todo
Reimplement like remove_horizontal_border_strip using IntegerListsLex
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/partition.py:docstring of sage.combinat.partition.Partition.add_horizontal_border_strip, line 15.)
Todo
Check in Knuth AOCP4.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/partition.py:docstring of sage.combinat.partition.Partitions_n.random_element_uniform, line 21.)
Todo
This docstring needs to be fixed. First, the definition does not match the implementation (or the examples). Second, this doesn’t seem to be defined in [GarStan1984] (the descent monomial in their (7.23) is different).
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/permutation.py:docstring of sage.combinat.permutation.Permutation.descent_polynomial, line 25.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/posets/linear_extensions.py:docstring of sage.combinat.posets.linear_extensions.LinearExtensionsOfPoset.markov_chain_digraph, line 8.)
Todo
Should the vertices of the diagram have the poset as parent?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/posets/posets.py:docstring of sage.combinat.posets.posets.FinitePoset.hasse_diagram, line 5.)
Todo
The current algorithm could be improvable. See trac ticket #13223.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/posets/posets.py:docstring of sage.combinat.posets.posets.FinitePoset.is_graded, line 13.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/posets/posets.py:docstring of sage.combinat.posets.posets.FinitePoset.linear_extension, line 44.)
Todo
add tests as in combinat::rankers
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/ranker.py:docstring of sage.combinat.ranker.on_fly, line 27.)
Todo
Implement a direct action of without moving to KR crystals.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/rigged_configurations/kr_tableaux.py:docstring of sage.combinat.rigged_configurations.kr_tableaux.KirillovReshetikhinTableauxElement.e, line 3.)
Todo
Implement a direct action of without moving to
KR crystals.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/rigged_configurations/kr_tableaux.py:docstring of sage.combinat.rigged_configurations.kr_tableaux.KirillovReshetikhinTableauxElement.epsilon, line 3.)
Todo
Implement a direct action of without moving to KR crystals.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/rigged_configurations/kr_tableaux.py:docstring of sage.combinat.rigged_configurations.kr_tableaux.KirillovReshetikhinTableauxElement.f, line 3.)
Todo
Compute without moving to KR crystals.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/rigged_configurations/kr_tableaux.py:docstring of sage.combinat.rigged_configurations.kr_tableaux.KirillovReshetikhinTableauxElement.phi, line 3.)
Todo
Implement without appealing to tensor product of
KR tableaux.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/rigged_configurations/rigged_configuration_element.py:docstring of sage.combinat.rigged_configurations.rigged_configuration_element.RiggedConfigurationElement.e, line 10.)
Todo
Implement without appealing to tensor product of
KR tableaux.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/rigged_configurations/rigged_configuration_element.py:docstring of sage.combinat.rigged_configurations.rigged_configuration_element.RiggedConfigurationElement.f, line 12.)
Todo
Convert this to using multiplicities (perhaps with a dictionary?)?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/rigged_configurations/rigged_partition.py:docstring of sage.combinat.rigged_configurations.rigged_partition, line 18.)
Todo
add a method set_mutable() as, say, for matrices
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/cartan_type.py:docstring of sage.combinat.root_system.cartan_type, line 205.)
Todo
add a method set_mutable() as, say, for matrices
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/cartan_type.py:docstring of sage.combinat.root_system.cartan_type.CartanType, line 207.)
Todo
add some reducible Cartan types (suggestions?)
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/cartan_type.py:docstring of sage.combinat.root_system.cartan_type.CartanTypeFactory.samples, line 50.)
Todo
Add the picture here, once root system plots in the weight lattice will be implemented. In the mean time, the reader may look up the dual picture on Figure 2 of [HST09] which was produced by MuPAD-Combinat.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/cartan_type.py:docstring of sage.combinat.root_system.cartan_type.CartanType_affine.translation_factors, line 131.)
Todo
Add tests for the above assumptions, and also that the
classical operators from
and
coincide.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/hecke_algebra_representation.py:docstring of sage.combinat.root_system.hecke_algebra_representation.CherednikOperatorsEigenvectors, line 39.)
Todo
Add an example where
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/hecke_algebra_representation.py:docstring of sage.combinat.root_system.hecke_algebra_representation.HeckeAlgebraRepresentation.Tw_inverse, line 5.)
Todo
Add more tests
Add tests in type BC affine where the null coroot
can have non trivial coefficient in term of
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/hecke_algebra_representation.py:docstring of sage.combinat.root_system.hecke_algebra_representation.HeckeAlgebraRepresentation.Y_lambdacheck, line 66.)
Todo
At this point, this method is constant. It’s meant as a
starting point for implementing parameters depending on
the node of the Dynkin diagram.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/hecke_algebra_representation.py:docstring of sage.combinat.root_system.hecke_algebra_representation.HeckeAlgebraRepresentation.parameters, line 16.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/non_symmetric_macdonald_polynomials.py:docstring of sage.combinat.root_system.non_symmetric_macdonald_polynomials.NonSymmetricMacdonaldPolynomials, line 15.)
Todo
add his notes in latex
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/non_symmetric_macdonald_polynomials.py:docstring of sage.combinat.root_system.non_symmetric_macdonald_polynomials.NonSymmetricMacdonaldPolynomials, line 735.)
Todo
should this just return in the simply laced case?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/non_symmetric_macdonald_polynomials.py:docstring of sage.combinat.root_system.non_symmetric_macdonald_polynomials.NonSymmetricMacdonaldPolynomials.L_check, line 3.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/non_symmetric_macdonald_polynomials.py:docstring of sage.combinat.root_system.non_symmetric_macdonald_polynomials.NonSymmetricMacdonaldPolynomials.eigenvalue_experimental, line 87.)
Todo
Could we have nice
labels in this graph?(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/plot.py:docstring of sage.combinat.root_system.plot, line 452.)
Todo
Display the periodic orientation by adding a and
a
sign close to the label. Typically by using
the associated root to shift a bit from the vertex
upon which the hyperplane label is attached.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/plot.py:docstring of sage.combinat.root_system.plot.PlotOptions.reflection_hyperplane, line 37.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/root_lattice_realization_algebras.py:docstring of sage.combinat.root_system.root_lattice_realization_algebras.Algebras.ParentMethods.demazure_lusztig_operator_on_classical_on_basis, line 12.)
Todo
type free definition (Viviane’s definition uses that we are in the ambient space)
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/root_lattice_realization_algebras.py:docstring of sage.combinat.root_system.root_lattice_realization_algebras.Algebras.ParentMethods.divided_difference_on_basis, line 8.)
Todo
make this work for Laurent polynomials too
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/root_lattice_realization_algebras.py:docstring of sage.combinat.root_system.root_lattice_realization_algebras.Algebras.ParentMethods.from_polynomial, line 26.)
Todo
Choose a good set of Cartan Type to run on. Rank >4 is
too big. But and
are boring.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/root_lattice_realization_algebras.py:docstring of sage.combinat.root_system.root_lattice_realization_algebras.Algebras.ParentMethods.twisted_demazure_lusztig_operators, line 75.)
Todo
Investigate why currently does not satisfy
the quadratic relation in type
. This should
hopefuly be fixed when
will have a more
uniform implementation:
sage: cartan_type = CartanType(["BC",1,2])
sage: KL = RootSystem(cartan_type).weight_lattice().algebra(K)
sage: T = KL.twisted_demazure_lusztig_operators(q1,q2, convention="dominant")
sage: T._test_relations()
... tester.assert_(Ti(Ti(x,i,-q2),i,-q1).is_zero()) ...
AssertionError: False is not true
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/root_lattice_realization_algebras.py:docstring of sage.combinat.root_system.root_lattice_realization_algebras.Algebras.ParentMethods.twisted_demazure_lusztig_operators, line 92.)
Todo
This implementation is only valid in the root or weight lattice
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/root_lattice_realizations.py:docstring of sage.combinat.root_system.root_lattice_realizations.RootLatticeRealizations.ElementMethods.is_parabolic_root, line 7.)
Todo
add a non simply laced example
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/root_lattice_realizations.py:docstring of sage.combinat.root_system.root_lattice_realizations.RootLatticeRealizations.ParentMethods.alphacheck, line 17.)
Todo
Provide an option for transparency?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/root_lattice_realizations.py:docstring of sage.combinat.root_system.root_lattice_realizations.RootLatticeRealizations.ParentMethods.plot_reflection_hyperplanes, line 57.)
Todo
The result should be an enumerated set, and handle infinite root systems.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/root_lattice_realizations.py:docstring of sage.combinat.root_system.root_lattice_realizations.RootLatticeRealizations.ParentMethods.roots, line 27.)
Todo
Rename to is_quantum_root
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/root_space.py:docstring of sage.combinat.root_system.root_space.RootSpaceElement.quantum_root, line 13.)
Todo
Lift to CombinatorialFreeModule.Element as canonical_inner_product
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/type_affine.py:docstring of sage.combinat.root_system.type_affine.AmbientSpace.Element.inner_product, line 23.)
Todo
Lift to CombinatorialFreeModule.Element as canonical_inner_product
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/type_affine.py:docstring of sage.combinat.root_system.type_affine.AmbientSpace.Element.scalar, line 23.)
Todo
Factor out this code with the classical ambient space.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/type_affine.py:docstring of sage.combinat.root_system.type_affine.AmbientSpace.coroot_lattice, line 6.)
Todo
Factor out this code with the classical ambient space.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/type_affine.py:docstring of sage.combinat.root_system.type_affine.AmbientSpace.simple_coroot, line 16.)
Todo
Currently subdivide is currently ignored.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/type_reducible.py:docstring of sage.combinat.root_system.type_reducible.CartanType.cartan_matrix, line 6.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/weight_space.py:docstring of sage.combinat.root_system.weight_space.WeightSpaceElement.scalar, line 4.)
Todo
Try to compute this directly without actually calculating the full symmetric and exterior squares.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/weyl_characters.py:docstring of sage.combinat.root_system.weyl_characters.WeylCharacterRing.Element.frobenius_schur_indicator, line 17.)
Todo
implement:
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/root_system/weyl_group.py:docstring of sage.combinat.root_system.weyl_group.ClassicalWeylSubgroup, line 26.)
Todo
delete this class once all coercions will be handled by Sage’s coercion model
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/sf/classical.py:docstring of sage.combinat.sf.classical.SymmetricFunctionAlgebra_classical, line 3.)
Todo
Is there a not too difficult way to get the power-sum computations
to work over any ring, not just one with coercion from ?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/sf/monomial.py:docstring of sage.combinat.sf.monomial.SymmetricFunctionAlgebra_monomial.antipode_by_coercion, line 25.)
Todo
Get rid of said technical “reasons”.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/sf/new_kschur.py:docstring of sage.combinat.sf.new_kschur.kSchur, line 93.)
Todo
to be described
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/sf/sf.py:docstring of sage.combinat.sf.sf.SymmetricFunctions, line 644.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/sf/sf.py:docstring of sage.combinat.sf.sf.SymmetricFunctions, line 694.)
Todo
Most of the methods in this class are generic (manipulations of morphisms, ...) and should be generalized (or removed)
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/sf/sfa.py:docstring of sage.combinat.sf.sfa.SymmetricFunctionAlgebra_generic, line 3.)
Todo
This method is fast on the monomial and the powersum bases, while all other bases get converted to the monomial basis. For most bases, this is probably the quickest way to do, but at least the Schur basis should have a better option. (Quoting from Stanley’s EC2 [STA]: “D. G. Duncan, J. London Math. Soc. 27 (1952), 235-236, or Y. M. Chen, A. M. Garsia, and J. B. Remmel, Contemp. Math. 34 (1984), 109-153”.)
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/sf/sfa.py:docstring of sage.combinat.sf.sfa.SymmetricFunctionAlgebra_generic_Element.adams_operation, line 120.)
Todo
This method is fast on the monomial and the powersum bases, while all other bases get converted to the monomial basis. For most bases, this is probably the quickest way to do, but at least the Schur basis should have a better option. (Quoting from Stanley’s EC2 [STA]: “D. G. Duncan, J. London Math. Soc. 27 (1952), 235-236, or Y. M. Chen, A. M. Garsia, and J. B. Remmel, Contemp. Math. 34 (1984), 109-153”.)
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/sf/sfa.py:docstring of sage.combinat.sf.sfa.SymmetricFunctionAlgebra_generic_Element.frobenius, line 120.)
Todo
This implementation of the reduced Kronecker product is painfully slow.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/sf/sfa.py:docstring of sage.combinat.sf.sfa.SymmetricFunctionAlgebra_generic_Element.reduced_kronecker_product, line 155.)
Todo
This function is an ugly hack using strings. It should be rewritten as soon as the bases of SymmetricFunctions are put on a more robust and systematic footing.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/sf/sfa.py:docstring of sage.combinat.sf.sfa.SymmetricFunctionsBases.ParentMethods.corresponding_basis_over, line 72.)
Todo
generalize to Modules.Graded.Connected.ParentMethods
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/sf/sfa.py:docstring of sage.combinat.sf.sfa.SymmetricFunctionsBases.ParentMethods.one_basis, line 17.)
Todo
As is, this set is essentially the composition of Compositions(n) (which give the row lengths) and SkewPartition(n, row_lengths=...), and one would want to “inherit” list and cardinality from this composition.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/skew_partition.py:docstring of sage.combinat.skew_partition.SkewPartitions_n, line 15.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/subword.py:docstring of sage.combinat.subword, line 27.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/symmetric_group_representations.py:docstring of sage.combinat.symmetric_group_representations, line 1.)
Todo
Implement semistandard tableau tuples as defined in [DJM].
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/tableau_tuple.py:docstring of sage.combinat.tableau_tuple, line 180.)
Todo
Add link to some thematic tutorial on graphs
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/tutorial.py:docstring of sage.combinat.tutorial, line 17.)
Todo
add link to some tutorial on quotient rings
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/tutorial.py:docstring of sage.combinat.tutorial, line 468.)
Todo
hide the results by default
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/tutorial.py:docstring of sage.combinat.tutorial, line 1157.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/databases/oeis.py:docstring of sage.databases.oeis, line 123.)
Todo
Ask OEIS for a keyword ensuring that a sequence is infinite.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/databases/oeis.py:docstring of sage.databases.oeis.OEISSequence.is_finite, line 12.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/databases/oeis.py:docstring of sage.databases.oeis.OEISSequence.natural_object, line 18.)
Todo
ask OEIS to add a “Sage program” field in the database ;)
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/databases/oeis.py:docstring of sage.databases.oeis.OEISSequence.programs, line 12.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/databases/oeis.py:docstring of sage.databases.oeis, line 123.)
Todo
Ask OEIS for a keyword ensuring that a sequence is infinite.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/databases/oeis.py:docstring of sage.databases.oeis.OEISSequence.is_finite, line 12.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/databases/oeis.py:docstring of sage.databases.oeis.OEISSequence.natural_object, line 18.)
Todo
ask OEIS to add a “Sage program” field in the database ;)
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/databases/oeis.py:docstring of sage.databases.oeis.OEISSequence.programs, line 12.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/dynamics/interval_exchanges/template.py:docstring of sage.dynamics.interval_exchanges.template, line 9.)
Todo
This function could probably be made faster.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/rings/algebraic_closure_finite_field.py:docstring of sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteFieldElement.nth_root, line 12.)
Todo
When trac ticket #10963 is merged we should remove that method and set the category to infinite fields (i.e. Fields().Infinite()).
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/rings/algebraic_closure_finite_field.py:docstring of sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteField_generic.cardinality, line 5.)
Todo
When trac ticket #10963 is merged we should remove that method and set the category to infinite fields (i.e. Fields().Infinite()).
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/rings/algebraic_closure_finite_field.py:docstring of sage.rings.algebraic_closure_finite_field.AlgebraicClosureFiniteField_generic.is_finite, line 3.)
Todo
Implement associated Legendre polynomials and Zernike polynomials. (Neither is in Maxima.) Wikipedia article Associated_Legendre_polynomials Wikipedia article Zernike_polynomials
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/functions/orthogonal_polys.py:docstring of sage.functions.orthogonal_polys, line 261.)
Todo
Eventually, category should be Sets by default.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/geometry/lattice_polytope.py:docstring of sage.geometry.lattice_polytope.SetOfAllLatticePolytopesClass, line 50.)
Todo
Make it possible to draw Schlegel diagram for 4-polytopes.
sage: P=Polyhedron(vertices=[[1,1,0,0],[1,2,0,0],[2,1,0,0],[0,0,1,0],[0,0,0,1]])
sage: P
A 4-dimensional polyhedron in ZZ^4 defined as the convex hull of 5 vertices
sage: P.projection().tikz()
Traceback (most recent call last):
...
NotImplementedError: The polytope has to live in 2 or 3 dimensions.
Make it possible to draw 3-polytopes living in higher dimension.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/geometry/polyhedron/plot.py:docstring of sage.geometry.polyhedron.plot.Projection.tikz, line 88.)
Todo
This method sequentially tests each of the forbidden subgraphs in order to know whether the graph is a line graph, which is a very slow method. It could eventually be replaced by root_graph() when this method will not require an exponential time to run on general graphs anymore (see its documentation for more information on this problem)... and if it can be improved to return negative certificates !
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/graphs/graph.py:docstring of sage.graphs.graph.Graph.is_line_graph, line 17.)
Todo
Find a beautiful layout for this beautiful graph.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/graphs/graph_generators.py:docstring of sage.graphs.graph_generators.GraphGenerators.SchlaefliGraph, line 14.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/graphs/graph_plot_js.py:docstring of sage.graphs.graph_plot_js, line 54.)
Todo
Technical things:
Long-term stuff:
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/graphs/isgci.py:docstring of sage.graphs.isgci, line 282.)
Todo
This method sequentially tests each of the forbidden subgraphs in order to know whether the graph is a line graph, which is a very slow method. It could eventually be replaced by root_graph() when this method will not require an exponential time to run on general graphs anymore (see its documentation for more information on this problem)... and if it can be improved to return negative certificates !
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/graphs/line_graph.py:docstring of sage.graphs.line_graph.is_line_graph, line 17.)
Todo
This code could probably be made more efficient by using FLINT polynomials and being written in Cython, using an array of fmpz_poly_t pointers or something... Right now just about the whole complement optimization is written in Python, and could be easily sped up.
(The original entry is located in docstring of sage.graphs.matchpoly.complete_poly, line 7.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/groups/conjugacy_classes.py:docstring of sage.groups.conjugacy_classes, line 9.)
Todo
Implement a non-naive algorithm, cf. for instance G. Butler: “An Inductive Schema for Computing Conjugacy Classes in Permutation Groups”, Math. of Comp. Vol. 62, No. 205 (1994)
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/groups/conjugacy_classes.py:docstring of sage.groups.conjugacy_classes.ConjugacyClass.set, line 4.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/groups/finitely_presented.py:docstring of sage.groups.finitely_presented.RewritingSystem, line 46.)
Todo
Currently the label is implemented as
in the Coxeter
matrix.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/groups/matrix_gps/coxeter_group.py:docstring of sage.groups.matrix_gps.coxeter_group.CoxeterMatrixGroup, line 31.)
Todo
Fix the broken hash.
sage: G = SymmetricGroup(6)
sage: G3 = G.subgroup([G((1,2,3,4,5,6)),G((1,2))])
sage: hash(G) == hash(G3) # todo: Should be True!
False
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/groups/perm_gps/permgroup_named.py:docstring of sage.groups.perm_gps.permgroup_named.PermutationGroup_unique, line 1.)
Todo
Up to now, this group is only implemented for finite fields because of the limited support of automorphisms for arbitrary rings.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/groups/semimonomial_transformations/semimonomial_transformation_group.py:docstring of sage.groups.semimonomial_transformations.semimonomial_transformation_group, line 29.)
Todo
Up to now, this group is only implemented for finite fields because of the limited support of automorphisms for arbitrary rings.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/groups/semimonomial_transformations/semimonomial_transformation_group.py:docstring of sage.groups.semimonomial_transformations.semimonomial_transformation_group.SemimonomialTransformationGroup, line 31.)
Todo
Create an animated image file (GIF) if spin is on and put data extracted from a file into a variable/string/structure to return
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/interfaces/jmoldata.py:docstring of sage.interfaces.jmoldata.JmolData, line 1.)
Todo
use this library in the SymmetricFunctions code, to make it easy to apply it to linear combinations of Schur functions.
(The original entry is located in docstring of sage.libs.lrcalc.lrcalc, line 76.)
Todo
Implement this method.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/logic/logic.py:docstring of sage.logic.logic.SymbolicLogic.prove, line 4.)
Todo
Implement this method.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/logic/logic.py:docstring of sage.logic.logic.SymbolicLogic.simplify, line 4.)
Todo
Implement faster algorithms, including a division-free one. Does [Rote2001], section 3.3 give one?
Check the implementation of the matchings used here for performance?
(The original entry is located in docstring of sage.matrix.matrix2.Matrix.pfaffian, line 82.)
Todo
Write abstract RelabeledMatroid class, and add relabel() method to the main Matroid class, together with _relabel() method that can be replaced by subclasses. Use the code from is_isomorphism() in relabel() to deal with a variety of input methods for the relabeling.
(The original entry is located in docstring of sage.matroids.basis_matroid.BasisMatroid.relabel, line 15.)
Todo
Add optional argument groundset to each method so users can customize the groundset of the matroid. We probably want some means of relabeling to accomplish that.
Add option to specify the field for represented matroids.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/matroids/catalog.py:docstring of sage.matroids.catalog, line 10.)
Todo
Optional arguments ring and x, such that the resulting matroid is represented over ring by a reduced matrix like [-1 0 x] [ 1 -1 0] [ 0 1 -1]
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/matroids/catalog.py:docstring of sage.matroids.catalog.Whirl, line 28.)
Todo
This important method can (and should) be optimized considerably. See [Hlineny] p.1219 for hints to that end.
(The original entry is located in docstring of sage.matroids.linear_matroid.LinearMatroid.has_field_minor, line 16.)
Todo
This important method can (and should) be optimized considerably. See [Hlineny] p.1219 for hints to that end.
(The original entry is located in docstring of sage.matroids.matroid.Matroid.has_minor, line 16.)
Todo
Implement this using the efficient algorithm from [BC79].
(The original entry is located in docstring of sage.matroids.matroid.Matroid.is_3connected, line 11.)
Todo
Make implementation more efficient, e.g. generalizing the approach from trac ticket #1314 from graphs to matroids.
(The original entry is located in docstring of sage.matroids.matroid.Matroid.tutte_polynomial, line 31.)
Todo
(The original entry is located in docstring of sage.misc.c3_controlled.CmpKey, line 45.)
Todo
Make the following work nicely:
sage: b.x? # todo: not implemented
sage: b.x?? # todo: not implemented
(The original entry is located in docstring of sage.misc.lazy_attribute.lazy_attribute, line 175.)
Todo
Improve the error message:
sage: B().unimplemented_A # todo: not implemented
Traceback (most recent call last):
...
AttributeError: 'super' object has no attribute 'unimplemented_A'
(The original entry is located in docstring of sage.misc.lazy_attribute.lazy_attribute, line 387.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/misc/profiler.py:docstring of sage.misc.profiler.Profiler, line 40.)
Todo
This should be moved to sage.matrix.matrix_modn_dense at some point.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/modular/overconvergent/hecke_series.py:docstring of sage.modular.overconvergent.hecke_series.ech_form, line 4.)
Todo
Refactor modules such that it only counts what category the base ring belongs to, but not what is its Python class.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/modules/free_module.py:docstring of sage.modules.free_module.FreeModuleFactory, line 122.)
Todo
Should implement a version of the algorithm that guarantees correct output. See Algorithm 4 in [Doyle-Krumm] for details of an implementation that takes precision issues into account.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/rings/number_field/number_field.py:docstring of sage.rings.number_field.number_field.NumberField_absolute.elements_of_bounded_height, line 34.)
Todo
The _new() method should be overridden in this class to copy the D and standard_embedding attributes
(The original entry is located in docstring of sage.rings.number_field.number_field_element_quadratic, line 14.)
Todo
doctests for converting from other types of -adic rings
(The original entry is located in docstring of sage.rings.padics.padic_fixed_mod_element.pAdicFixedModElement, line 82.)
Todo
(The original entry is located in docstring of sage.rings.padics.padic_generic_element.pAdicGenericElement.log, line 46.)
Todo
See comments at trac ticket #4805. Currently the absolute precision of the result may be less than the given value of absprec, and error-handling is imperfect.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/elliptic_curves/ell_point.py:docstring of sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_number_field.padic_elliptic_logarithm, line 26.)
Todo
make GaloisAutomorphism derive from GroupElement, so that one gets powers for free, etc.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/elliptic_curves/heegner.py:docstring of sage.schemes.elliptic_curves.heegner.GaloisAutomorphism, line 3.)
Todo
Unify UnionOfIntervals with the class RealSet introduced by trac ticket #13125; see trac ticket #16063.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/elliptic_curves/height.py:docstring of sage.schemes.elliptic_curves.height.UnionOfIntervals, line 19.)
Todo
Eventually we will want to run this in characteristic 3, so we
need to: (a) Allow to contain an
term, and (b) Remove
the requirement that 3 be invertible. Currently this is used in
the Toom-Cook algorithm to speed multiplication.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/hyperelliptic_curves/monsky_washnitzer.py:docstring of sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialCubicQuotientRing, line 17.)
Todo
write an example checking multiplication of these polynomials against Sage’s ordinary quotient ring arithmetic. I can’t seem to get the quotient ring stuff happening right now...
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/hyperelliptic_curves/monsky_washnitzer.py:docstring of sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialCubicQuotientRing, line 66.)
Todo
Working with sparse matrices should usually give faster results, but with the current implementation it actually works slower. There should be a way to improve performance with regards to this.
(The original entry is located in docstring of sage.rings.polynomial.multi_polynomial_ring_generic.MPolynomialRing_generic.macaulay_resultant, line 39.)
Todo
What should we do about this method? Is nilpotency of a power series even decidable (assuming a nilpotency oracle in the base ring)? And I am not sure that returning True just because the series has finite precision and zero constant term is a good idea.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/rings/multi_power_series_ring_element.py:docstring of sage.rings.multi_power_series_ring_element.MPowerSeries.is_nilpotent, line 13.)
Todo
This currently does not work for quivers with cycles, even if there are only finitely many paths from start to end.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/quivers/path_semigroup.py:docstring of sage.quivers.path_semigroup.PathSemigroup.all_paths, line 16.)
Todo
Change the wording Reverse of () into something more meaningful.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/quivers/representation.py:docstring of sage.quivers.representation, line 389.)
Todo
Implement this method.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/rings/ideal.py:docstring of sage.rings.ideal.Ideal_generic.absolute_norm, line 9.)
Todo
This is not implemented for many rings. Implement it!
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/rings/ideal.py:docstring of sage.rings.ideal.Ideal_generic.is_maximal, line 4.)
Todo
Code is naive. Only keeps track of ideal generators as set during initialization of the ideal. (Can the base ring change? See example below.)
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/rings/ideal.py:docstring of sage.rings.ideal.Ideal_generic.is_principal, line 4.)
Todo
The following skipped tests should be removed once trac ticket #13999 is fixed:
sage: TestSuite(S).run(skip=['_test_nonzero_equal', '_test_elements', '_test_zero'])
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/rings/quotient_ring.py:docstring of sage.rings.quotient_ring, line 15.)
Todo
Not yet implemented!
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/rings/quotient_ring.py:docstring of sage.rings.quotient_ring.QuotientRing_nc.characteristic, line 3.)
Todo
Note that ngens counts 0 as a generator. Does this make sense? That is, since 0 only generates itself and the fact that this is true for all rings, is there a way to “knock it off” of the generators list if a generator of some original ring is modded out?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/rings/quotient_ring.py:docstring of sage.rings.quotient_ring.QuotientRing_nc.ngens, line 3.)
Todo
Implement ComplexIntervalFieldElement multiplicative order similar to ComplexNumber multiplicative order with _set_multiplicative_order(n) and ComplexNumber.multiplicative_order() methods.
(The original entry is located in docstring of sage.rings.complex_interval, line 23.)
Todo
Implement ComplexIntervalFieldElement multiplicative order and set this output to have multiplicative order n.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/rings/complex_interval_field.py:docstring of sage.rings.complex_interval_field.ComplexIntervalField_class.zeta, line 3.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/rings/universal_cyclotomic_field/universal_cyclotomic_field.py:docstring of sage.rings.universal_cyclotomic_field.universal_cyclotomic_field, line 23.)
Todo
add heights to integer.pyx and remove special case
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/affine/affine_morphism.py:docstring of sage.schemes.affine.affine_morphism.SchemeMorphism_polynomial_affine_space.global_height, line 30.)
Todo
This could be improved.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/affine/affine_morphism.py:docstring of sage.schemes.affine.affine_morphism.SchemeMorphism_polynomial_affine_space.nth_iterate_map, line 7.)
Todo
p-adic heights
add heights to integer.pyx and remove special case
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/affine/affine_point.py:docstring of sage.schemes.affine.affine_point.SchemeMorphism_point_affine.global_height, line 34.)
Todo
Currently, SchemeMorphism copies code from Map rather than inheriting from it. This is to work around a bug in Cython: We want to create a common sub-class of ModuleElement and SchemeMorphism, but Cython would currently confuse cpdef attributes of the two base classes. Proper inheritance should be used as soon as this bug is fixed.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/generic/morphism.py:docstring of sage.schemes.generic.morphism.SchemeMorphism, line 7.)
Todo
Do the division when the base ring is p-adic or a function field so that the output is a polynomial.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/projective/projective_morphism.py:docstring of sage.schemes.projective.projective_morphism.SchemeMorphism_polynomial_projective_space.dynatomic_polynomial, line 41.)
Todo
It would be nice to get this to actually be a polynomial.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/projective/projective_morphism.py:docstring of sage.schemes.projective.projective_morphism.SchemeMorphism_polynomial_projective_space.dynatomic_polynomial, line 124.)
Todo
add heights to integer.pyx and remove special case
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/projective/projective_morphism.py:docstring of sage.schemes.projective.projective_morphism.SchemeMorphism_polynomial_projective_space.global_height, line 42.)
Todo
would be better to keep the dehomogenizations for reuse
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/projective/projective_morphism.py:docstring of sage.schemes.projective.projective_morphism.SchemeMorphism_polynomial_projective_space.multiplier, line 70.)
Todo
Is there a more efficient way to do this?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/projective/projective_morphism.py:docstring of sage.schemes.projective.projective_morphism.SchemeMorphism_polynomial_projective_space.nth_iterate, line 7.)
Todo
This could be improved.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/projective/projective_morphism.py:docstring of sage.schemes.projective.projective_morphism.SchemeMorphism_polynomial_projective_space.nth_iterate_map, line 9.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/projective/projective_morphism.py:docstring of sage.schemes.projective.projective_morphism.SchemeMorphism_polynomial_projective_space_field.rational_periodic_points, line 66.)
Todo
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/projective/projective_morphism.py:docstring of sage.schemes.projective.projective_morphism.SchemeMorphism_polynomial_projective_space_finite_field.possible_periods, line 41.)
Todo
p-adic heights
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/projective/projective_point.py:docstring of sage.schemes.projective.projective_point.SchemeMorphism_point_projective_ring.global_height, line 34.)
Todo
error bounds for dimension > 1
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/projective/projective_point.py:docstring of sage.schemes.projective.projective_point.SchemeMorphism_point_projective_ring.green_function, line 46.)
Todo
Is there a more efficient way to do this?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/schemes/projective/projective_point.py:docstring of sage.schemes.projective.projective_point.SchemeMorphism_point_projective_ring.nth_iterate, line 52.)
Todo
good name?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/sets/family.py:docstring of sage.sets.family.AbstractFamily.map, line 4.)
Todo
generalize to any number of families and merge with map?
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/sets/family.py:docstring of sage.sets.family.AbstractFamily.zip, line 5.)
Todo
FIXME: What should be the order of the result? That of self.object()? Or the order given by set(self.object())? Note that __getitem__() is currently implemented in term of this list method, which is really inefficient ...
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/sets/set.py:docstring of sage.sets.set.Set_object_enumerated.list, line 13.)
Todo
It is not yet possible to use set_from_method in conjunction with cached_method.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/sets/set_from_iterator.py:docstring of sage.sets.set_from_iterator.EnumeratedSetFromIterator_method_decorator, line 66.)
Todo
Move this method elsewhere (typically in the Modules category) so as not to pollute the namespace of all category objects.
(The original entry is located in docstring of sage.structure.category_object.CategoryObject.base_ring, line 33.)
Todo
title
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/structure/global_options.py:docstring of sage.structure.global_options.GlobalOptions.dispatch, line 1.)
Todo
Eventually, category should be Sets by default.
(The original entry is located in docstring of sage.structure.parent.Parent, line 50.)
Todo
Create a custom-made SourPickle for the last example.
(The original entry is located in docstring of sage.structure.sage_object.unpickle_all, line 62.)
Todo
Illustrate how this can be fixed on a case by case basis.
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/structure/unique_representation.py:docstring of sage.structure.unique_representation.CachedRepresentation, line 361.)
Todo
should reuse something preexisting ...
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/structure/unique_representation.py:docstring of sage.structure.unique_representation.unreduce, line 6.)