This patch implements translation for elements of a root lattice and related features and fixes::
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New method translation for elements of a root lattice
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New methods reduced_word_of_alcove_morphism, dynkin_diagram_automorphism_of_alcove_morphism, reduced_word_of_translation, _test_reduced_word_of_translation
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Added extensive TESTS to compare with Kashiwara's private notes
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Fixed dynkin diagram for type BC
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Fixed CartanType.translation_factors to implement its specification correctly in affine type BC. Imported the full test suite from MuPAD-Combinat. Also fixes and tests for proper typing of the coefficients (ZZ/QQ).
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Bug fix in WeylGroup: the matrices were defined over QQ instead of the base ring of the underlying root lattice realization.
CC: @sagetrac-sage-combinat
Component: combinatorics
Keywords: root systems, affine weyl groups, translations
Author: Nicolas M. Thiéry
Reviewer: Anne Schilling
Merged: sage-4.4.4.alpha0
Issue created by migration from https://trac.sagemath.org/ticket/8811
This patch implements translation for elements of a root lattice and related features and fixes::
New method
translationfor elements of a root latticeNew methods
reduced_word_of_alcove_morphism,dynkin_diagram_automorphism_of_alcove_morphism,reduced_word_of_translation,_test_reduced_word_of_translationAdded extensive TESTS to compare with Kashiwara's private notes
Fixed dynkin diagram for type BC
Fixed CartanType.translation_factors to implement its specification correctly in affine type BC. Imported the full test suite from MuPAD-Combinat. Also fixes and tests for proper typing of the coefficients (ZZ/QQ).
Bug fix in WeylGroup: the matrices were defined over QQ instead of the base ring of the underlying root lattice realization.
CC: @sagetrac-sage-combinat
Component: combinatorics
Keywords: root systems, affine weyl groups, translations
Author: Nicolas M. Thiéry
Reviewer: Anne Schilling
Merged: sage-4.4.4.alpha0
Issue created by migration from https://trac.sagemath.org/ticket/8811