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some details in coxeter groups #36085

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merged 3 commits into from
Aug 27, 2023
Merged

some details in coxeter groups #36085

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70e7bfb
minor details in Coxeter groups
fchapoton Aug 13, 2023
49d17c0
remove todo
fchapoton Aug 13, 2023
d5495ae
Merge branch 'develop' into details-in-coxeter-cat
fchapoton Aug 13, 2023
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14 changes: 5 additions & 9 deletions src/sage/categories/coxeter_groups.py
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Original file line number Diff line number Diff line change
Expand Up @@ -513,9 +513,10 @@ def succ(u):

from sage.categories.finite_coxeter_groups import FiniteCoxeterGroups
default_category = FiniteEnumeratedSets() if self in FiniteCoxeterGroups() else EnumeratedSets()
cat = default_category.or_subcategory(category)
return RecursivelyEnumeratedSet_forest((self.one(),), succ,
algorithm='breadth',
category=default_category.or_subcategory(category))
algorithm='breadth',
category=cat)

@cached_method
def coxeter_element(self):
Expand Down Expand Up @@ -1229,10 +1230,6 @@ def random_element_of_length(self, n):
x = x.apply_simple_reflection_right(antiD[rnd])
return x

# TODO: Groups() should have inverse() call __invert__
# With strong doc stating that this is just a convenience for the user
# and links to ~ / __invert__

# parabolic_subgroup

def _test_simple_projections(self, **options):
Expand Down Expand Up @@ -2236,7 +2233,6 @@ def binary_factorizations(self, predicate=ConstantFunction(True)):
if not predicate(W.one()):
from sage.sets.finite_enumerated_set import FiniteEnumeratedSet
return FiniteEnumeratedSet([])
s = W.simple_reflections()

def succ(u_v):
u, v = u_v
Expand Down Expand Up @@ -2372,7 +2368,7 @@ def bruhat_lower_covers_reflections(self):
wi = self.apply_simple_reflection(i, side='right')
return [(u.apply_simple_reflection(i, side='right'),
r.apply_conjugation_by_simple_reflection(i))
for u,r in wi.bruhat_lower_covers_reflections()
for u, r in wi.bruhat_lower_covers_reflections()
if not u.has_descent(i, side='right')] + [
(wi, self.parent().simple_reflection(i))]

Expand Down Expand Up @@ -3109,7 +3105,7 @@ def kazhdan_lusztig_cell(self, side='left'):

The cell computation uses the optional package ``coxeter3`` in
the background if available to speed up the computation,
even in the different implementations implementations::
even in the different implementations::

sage: W = WeylGroup('A3', prefix='s') # optional - coxeter3
sage: s1,s2,s3 = W.simple_reflections() # optional - coxeter3
Expand Down
2 changes: 2 additions & 0 deletions src/sage/categories/monoids.py
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Expand Up @@ -377,6 +377,8 @@ def inverse(self):
This is an alias for inversion, which can also be invoked
by ``~x`` for an element ``x``.

Nota Bene: Element classes should implement ``__invert__`` only.

EXAMPLES::

sage: AA(sqrt(~2)).inverse() # optional - sage.symbolic sage.rings.number_field
Expand Down
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