Ticket #6588: latest_change.patch

File latest_change.patch, 5.3 KB (added by nthiery, 8 years ago)
  • sage/combinat/root_system/root_lattice_realizations.py

    diff --git a/sage/combinat/root_system/root_lattice_realizations.py b/sage/combinat/root_system/root_lattice_realizations.py
    a b class RootLatticeRealizations(Category_o 
    197197            """
    198198            EXAMPLES::
    199199
    200                sage: r = RootSystem(['A',4]).root_space()
    201                sage: r.cartan_type()
    202                ['A', 4]
     200                sage: r = RootSystem(['A',4]).root_space()
     201                sage: r.cartan_type()
     202                ['A', 4]
    203203            """
    204204            return self.root_system.cartan_type()
    205205
    206206        def index_set(self):
    207207            """
    208             EXAMPLES:
    209                sage: r = RootSystem(['A',4]).root_space()
    210                sage: r.index_set()
    211                [1, 2, 3, 4]
     208            EXAMPLES::
     209
     210                sage: r = RootSystem(['A',4]).root_space()
     211                sage: r.index_set()
     212                [1, 2, 3, 4]
    212213            """
    213214            return self.root_system.index_set()
    214215
    class RootLatticeRealizations(Category_o 
    482483                ['F', 4]  48  48
    483484                ['G', 2]  12  12
    484485
    485             Todo: the result should be an enumerated set, and handle infinite root systems
    486 
     486            .. todo:: the result should be an enumerated set, and handle infinite root systems
    487487            """
    488488            return list(self.positive_roots()) + list(self.negative_roots())
    489489
    class RootLatticeRealizations(Category_o 
    512512
    513513            INPUT:
    514514
    515             - restricted -- (default:False) if True, only non-simple roots are considered.
     515            - ``restricted`` -- (default:False) if True, only non-simple roots are considered.
    516516
    517517            EXAMPLES::
    518518
    class RootLatticeRealizations(Category_o 
    665665
    666666                (-1, 0, 1)
    667667
    668             TODO: add a non simply laced example
     668            .. todo:: add a non simply laced example
    669669
    670670            Finaly, here is an affine example::
    671671
    class RootLatticeRealizations(Category_o 
    685685        @cached_method
    686686        def cohighest_root(self):
    687687            """
    688             Returns the associated coroot of the highest root.  Note that this is
    689             usually not the highest coroot.
     688            Returns the associated coroot of the highest root.
     689
     690            .. note:: this is usually not the highest coroot.
    690691
    691692            EXAMPLES::
    692693
    class RootLatticeRealizations(Category_o 
    726727        @cached_method
    727728        def null_coroot(self):
    728729            """
    729             Returns the null coroot of self. The null coroot is the smallest
    730             non trivial positive coroot which is orthogonal to all simple
    731             roots. It exists for any affine root system.
     730            Returns the null coroot of self.
     731
     732            The null coroot is the smallest non trivial positive
     733            coroot which is orthogonal to all simple roots. It exists
     734            for any affine root system.
    732735
    733736            EXAMPLES::
    734737
    class RootLatticeRealizations(Category_o 
    12281231            r"""
    12291232            The orbit of self under the action of the Weyl group
    12301233
    1231             EXAMPLES::
     1234            EXAMPLES:
    12321235
    12331236            `\rho` is a regular element whose orbit is in bijection with the Weyl group.
    12341237            In particular, it as 6 elements for the symmetric group `S_3`::
  • sage/combinat/root_system/weight_lattice_realizations.py

    diff --git a/sage/combinat/root_system/weight_lattice_realizations.py b/sage/combinat/root_system/weight_lattice_realizations.py
    a b class WeightLatticeRealizations(Category 
    498498
    499499        def dynkin_diagram_automorphism_of_alcove_morphism(self, f):
    500500            """
     501            Returns the Dynkin diagram automorphism induced by an alcove morphism
     502
    501503            INPUT:
    502504
    503              - `f` - a linear map from ``self`` to ``self`` which
    504                preserves alcoves
     505            - ``f`` - a linear map from ``self`` to ``self`` which preserves alcoves
    505506
    506             This method returns the Dynkin diagram automorphism for the
    507             decomposition `f = d w` (see
     507            This method returns the Dynkin diagram automorphism for
     508            the decomposition `f = d w` (see
    508509            :meth:`reduced_word_of_alcove_morphism`), as a dictionnary
    509510            mapping elements of the index set to itself.
    510511
    class WeightLatticeRealizations(Category 
    524525                sage: R.dynkin_diagram_automorphism_of_alcove_morphism(alpha[2].translation)
    525526                {0: 0, 1: 1, 2: 2}
    526527
    527             This is no more the case for translation by general elements
    528             of the (classical) weight lattice at level 0:
     528            This is no more the case for translations by general
     529            elements of the (classical) weight lattice at level 0::
    529530
    530531                sage: omega1 = Lambda[1] - Lambda[0]
    531532                sage: omega2 = Lambda[2] - Lambda[0]
    class WeightLatticeRealizations(Category 
    598599                sage: R.reduced_word_of_translation(omega2)
    599600                [0, 2, 1, 3, 2, 4, 3, 5, 3, 2, 1, 4, 3, 2]
    600601
    601             A non simply laced case:
     602            A non simply laced case::
    602603
    603604                sage: R = RootSystem(["C",2,1]).weight_lattice()
    604605                sage: Lambda = R.fundamental_weights()