# Ticket #6588: latest_change.patch

File latest_change.patch, 5.3 KB (added by nthiery, 9 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 class RootLatticeRealizations(Category_o """ EXAMPLES:: sage: r = RootSystem(['A',4]).root_space() sage: r.cartan_type() ['A', 4] sage: r = RootSystem(['A',4]).root_space() sage: r.cartan_type() ['A', 4] """ return self.root_system.cartan_type() def index_set(self): """ EXAMPLES: sage: r = RootSystem(['A',4]).root_space() sage: r.index_set() [1, 2, 3, 4] EXAMPLES:: sage: r = RootSystem(['A',4]).root_space() sage: r.index_set() [1, 2, 3, 4] """ return self.root_system.index_set() class RootLatticeRealizations(Category_o ['F', 4]  48  48 ['G', 2]  12  12 Todo: the result should be an enumerated set, and handle infinite root systems .. todo:: the result should be an enumerated set, and handle infinite root systems """ return list(self.positive_roots()) + list(self.negative_roots()) class RootLatticeRealizations(Category_o INPUT: - restricted -- (default:False) if True, only non-simple roots are considered. - restricted -- (default:False) if True, only non-simple roots are considered. EXAMPLES:: class RootLatticeRealizations(Category_o (-1, 0, 1) TODO: add a non simply laced example .. todo:: add a non simply laced example Finaly, here is an affine example:: class RootLatticeRealizations(Category_o @cached_method def cohighest_root(self): """ Returns the associated coroot of the highest root.  Note that this is usually not the highest coroot. Returns the associated coroot of the highest root. .. note:: this is usually not the highest coroot. EXAMPLES:: class RootLatticeRealizations(Category_o @cached_method def null_coroot(self): """ Returns the null coroot of self. The null coroot is the smallest non trivial positive coroot which is orthogonal to all simple roots. It exists for any affine root system. Returns the null coroot of self. The null coroot is the smallest non trivial positive coroot which is orthogonal to all simple roots. It exists for any affine root system. EXAMPLES:: class RootLatticeRealizations(Category_o r""" The orbit of self under the action of the Weyl group EXAMPLES:: EXAMPLES: \rho is a regular element whose orbit is in bijection with the Weyl group. 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 class WeightLatticeRealizations(Category def dynkin_diagram_automorphism_of_alcove_morphism(self, f): """ Returns the Dynkin diagram automorphism induced by an alcove morphism INPUT: - f - a linear map from self to self which preserves alcoves - f - a linear map from self to self which preserves alcoves This method returns the Dynkin diagram automorphism for the decomposition f = d w (see This method returns the Dynkin diagram automorphism for the decomposition f = d w (see :meth:reduced_word_of_alcove_morphism), as a dictionnary mapping elements of the index set to itself. class WeightLatticeRealizations(Category sage: R.dynkin_diagram_automorphism_of_alcove_morphism(alpha[2].translation) {0: 0, 1: 1, 2: 2} This is no more the case for translation by general elements of the (classical) weight lattice at level 0: This is no more the case for translations by general elements of the (classical) weight lattice at level 0:: sage: omega1 = Lambda[1] - Lambda[0] sage: omega2 = Lambda[2] - Lambda[0] class WeightLatticeRealizations(Category sage: R.reduced_word_of_translation(omega2) [0, 2, 1, 3, 2, 4, 3, 5, 3, 2, 1, 4, 3, 2] A non simply laced case: A non simply laced case:: sage: R = RootSystem(["C",2,1]).weight_lattice() sage: Lambda = R.fundamental_weights()