#12774: various enhancements for Coxeter and Weyl groups
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Reporter: mshimo | Owner: sage-combinat
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.0
Component: combinatorics | Keywords: coxeter group, weyl group
Work issues: | Report Upstream: N/A
Reviewers: | Authors: Mark Shimozono
Merged in: | Dependencies: #6588, #12667
Stopgaps: |
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Various enhancements to Coxeter groups and Weyl groups.
1. Computes inversions for Coxeter/Weyl groups. They occur in three forms:
reflections, roots, and coroots.
New Coxeter group element methods:
categories/coxeter_groups.py
apply_conjugation_by_simple_reflection
length_decreasing_reflections_right
length_decreasing_reflections_left
New Weyl group element methods:
categories/weyl_groups.py
reflection_to_root
reflection_to_coroot
inversions
New root space element method:
combinat/root_system/root_space.py
associated_reflection
Bruhat covering relations have an associated inversion. Accordingly,
we have added versions of the Coxeter group element methods
bruhat_lower_covers and bruhat_upper_covers which incorporate the
inversion data:
New Coxeter group element methods:
categories/coxeter_groups.py
bruhat_cocovers_reflections
bruhat_covers_reflections
New Weyl group element methods:
categories/weyl_groups.py
bruhat_cocovers_coroots
bruhat_covers_coroots
2. Installs the Demazure or 0-Hecke product for Coxeter groups
New Coxeter group parent method:
categories/coxeter_groups.py
demazure_product
New Coxeter group element methods:
categories/coxeter_groups.py
apply_demazure_simple_reflection
apply_demazure_product
min_demazure_product_greater
3. Computes canonical lifts from quotients by parabolic subgroups.
This requires Deodhar's recovery of the Bruhat order on a Coxeter group
from that on a parabolic subgroup and the quotient by that subgroup.
New Coxeter group element methods:
categories/coxeter_groups.py
deodhar_factor_element
deodhar_lift_up
deodhar_lift_down
4. Two random little methods for root systems
sage/combinat/root_system/root_lattice_realizations.py:
new parent method:
positive_roots_by_height
sage/combinat/root_system/root_space.py:
new element method:
max_coroot_le
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12774>
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