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
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 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
(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
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/categories/homset.py:docstring of sage.categories.homset.Hom, line 168.)
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
(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 81.)
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
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
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
(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
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/combinat.py:docstring of sage.combinat.combinat, line 133.)
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
Eventually, category should be Sets by default.
(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.TestParent, line 50.)
Todo
Implement DerivedDesign, ComplementaryDesign, and Hadamard3Design
(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 50.)
Todo
Implement DyckWord_complete.to_triangulation().
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/combinat/dyck_word.py:docstring of sage.combinat.dyck_word.DyckWord_complete.to_triangulation, line 3.)
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
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
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 158.)
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 209.)
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 255.)
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
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
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 207.)
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 209.)
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
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 448.)
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
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 28.)
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
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
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 645.)
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 695.)
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 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/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 1159.)
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
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
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 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
Add instead an optional argument to MatrixSpace() to temporarily disable the category initialization in those special cases where speed is critical:
sage: MS = MatrixSpace(QQ,7, init_category=False) # todo: not implemented
sage: TestSuite(MS).run() # todo: not implemented
Traceback (most recent call last):
...
AssertionError: category of self improperly initialized
until someone recreates explicitly the same matrix space without that optional argument:
sage: MS = MatrixSpace(QQ,7) # todo: not implemented
sage: TestSuite(MS).run() # todo: not implemented
(The original entry is located in /usr/lib64/python2.7/site-packages/sage/matrix/matrix_space.py:docstring of sage.matrix.matrix_space.MatrixSpace.full_category_initialisation, line 30.)
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
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
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
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/elliptic_curves/monsky_washnitzer.py:docstring of sage.schemes.elliptic_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/elliptic_curves/monsky_washnitzer.py:docstring of sage.schemes.elliptic_curves.monsky_washnitzer.SpecialCubicQuotientRing, line 66.)
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
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
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 65.)
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
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
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.)