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Feb 10, 2025
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some details in KR crystals #39441

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46 changes: 24 additions & 22 deletions src/sage/combinat/crystals/kirillov_reshetikhin.py
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Original file line number Diff line number Diff line change
Expand Up @@ -519,7 +519,7 @@ def module_generator(self):
r = self.r()
s = self.s()
weight = s*Lambda[r] - s*Lambda[0] * Lambda[r].level() / Lambda[0].level()
return [b for b in self.module_generators if b.weight() == weight][0]
return next(b for b in self.module_generators if b.weight() == weight)

def r(self):
"""
Expand Down Expand Up @@ -993,8 +993,8 @@ def from_pm_diagram_to_highest_weight_vector(self, pm):
sage: K.from_pm_diagram_to_highest_weight_vector(pm)
[[2], [-2]]
"""
u = [b for b in self.classical_decomposition().module_generators
if b.to_tableau().shape() == pm.outer_shape()][0]
u = next(b for b in self.classical_decomposition().module_generators
if b.to_tableau().shape() == pm.outer_shape())
ct = self.cartan_type()
rank = ct.rank() - 1
ct_type = ct.classical().type()
Expand Down Expand Up @@ -1031,7 +1031,7 @@ class KR_type_E6(KirillovReshetikhinCrystalFromPromotion):
[(1,)]
sage: b.e(0)
[(-2, 1)]
sage: b = [t for t in K if t.epsilon(1) == 1 and t.phi(3) == 1 and t.phi(2) == 0 and t.epsilon(2) == 0][0]
sage: b = next(t for t in K if t.epsilon(1) == 1 and t.phi(3) == 1 and t.phi(2) == 0 and t.epsilon(2) == 0)
sage: b
[(-1, 3)]
sage: b.e(0)
Expand Down Expand Up @@ -1622,7 +1622,7 @@ def module_generator(self):
weight = s*Lambda[r] - s*Lambda[0]
if r == self.cartan_type().rank() - 1:
weight += s*Lambda[r] # Special case for r == n
return [b for b in self.module_generators if b.weight() == weight][0]
return next(b for b in self.module_generators if b.weight() == weight)

def classical_decomposition(self):
r"""
Expand Down Expand Up @@ -2489,7 +2489,8 @@ def from_pm_diagram_to_highest_weight_vector(self, pm):
sage: K.from_pm_diagram_to_highest_weight_vector(pm)
[[2, 2], [3, 3], [-3, -1]]
"""
u = [b for b in self.classical_decomposition().module_generators if b.to_tableau().shape() == pm.outer_shape()][0]
u = next(b for b in self.classical_decomposition().module_generators
if b.to_tableau().shape() == pm.outer_shape())
ct = self.cartan_type()
rank = ct.rank()-1
ct_type = ct.classical().type()
Expand Down Expand Up @@ -2537,7 +2538,7 @@ def e0(self):
[[3, -3], [-3, -2], [-1, -1]]
"""
n = self.parent().cartan_type().n
b, l = self.lift().to_highest_weight(index_set=list(range(2, n + 1)))
b, l = self.lift().to_highest_weight(index_set=range(2, n + 1))
pm = self.parent().from_highest_weight_vector_to_pm_diagram(b)
l1, l2 = pm.pm_diagram[n-1]
if l1 == 0:
Expand All @@ -2562,7 +2563,7 @@ def f0(self):
sage: b.f(0) # indirect doctest
"""
n = self.parent().cartan_type().n
b, l = self.lift().to_highest_weight(index_set=list(range(2, n + 1)))
b, l = self.lift().to_highest_weight(index_set=range(2, n + 1))
pm = self.parent().from_highest_weight_vector_to_pm_diagram(b)
l1, l2 = pm.pm_diagram[n-1]
if l2 == 0:
Expand All @@ -2585,7 +2586,7 @@ def epsilon0(self):
1
"""
n = self.parent().cartan_type().n
b = self.lift().to_highest_weight(index_set=list(range(2, n + 1)))[0]
b = self.lift().to_highest_weight(index_set=range(2, n + 1))[0]
pm = self.parent().from_highest_weight_vector_to_pm_diagram(b)
l1, l2 = pm.pm_diagram[n-1]
return l1
Expand All @@ -2602,7 +2603,7 @@ def phi0(self):
0
"""
n = self.parent().cartan_type().n
b = self.lift().to_highest_weight(index_set=list(range(2, n + 1)))[0]
b = self.lift().to_highest_weight(index_set=range(2, n + 1))[0]
pm = self.parent().from_highest_weight_vector_to_pm_diagram(b)
l1, l2 = pm.pm_diagram[n-1]
return l2
Expand Down Expand Up @@ -2825,7 +2826,7 @@ def e0(self):
"""
n = self.parent().cartan_type().rank()-1
s = self.parent().s()
b, l = self.lift().to_highest_weight(index_set=list(range(2, n + 1)))
b, l = self.lift().to_highest_weight(index_set=range(2, n + 1))
pm = self.parent().from_highest_weight_vector_to_pm_diagram(b)
l1, l2 = pm.pm_diagram[n-1]
l3 = pm.pm_diagram[n-2][0]
Expand Down Expand Up @@ -2860,7 +2861,7 @@ def f0(self):
"""
n = self.parent().cartan_type().rank()-1
s = self.parent().s()
b, l = self.lift().to_highest_weight(index_set=list(range(2, n + 1)))
b, l = self.lift().to_highest_weight(index_set=range(2, n + 1))
pm = self.parent().from_highest_weight_vector_to_pm_diagram(b)
l1, l2 = pm.pm_diagram[n-1]
l3 = pm.pm_diagram[n-2][0]
Expand Down Expand Up @@ -2907,7 +2908,7 @@ def epsilon0(self):
True
"""
n = self.parent().cartan_type().rank() - 1
b, l = self.lift().to_highest_weight(index_set=list(range(2, n + 1)))
b, l = self.lift().to_highest_weight(index_set=range(2, n + 1))
pm = self.parent().from_highest_weight_vector_to_pm_diagram(b)
l1 = pm.pm_diagram[n-1][0]
l4 = pm.pm_diagram[n][0]
Expand Down Expand Up @@ -2940,7 +2941,7 @@ def phi0(self):
True
"""
n = self.parent().cartan_type().rank() - 1
b, l = self.lift().to_highest_weight(index_set=list(range(2, n + 1)))
b, l = self.lift().to_highest_weight(index_set=range(2, n + 1))
pm = self.parent().from_highest_weight_vector_to_pm_diagram(b)
l2 = pm.pm_diagram[n-1][1]
l4 = pm.pm_diagram[n][0]
Expand Down Expand Up @@ -3075,9 +3076,9 @@ def classical_decomposition(self):
C = self.cartan_type().classical()
s = QQ(self.s())
if self.r() == C.n:
c = [s/QQ(2)]*C.n
c = [s / QQ(2)]*C.n
else:
c = [s/QQ(2)]*(C.n-1)+[-s/QQ(2)]
c = [s / QQ(2)]*(C.n-1) + [-s / QQ(2)]
return CrystalOfTableaux(C, shape=c)

def dynkin_diagram_automorphism(self, i):
Expand Down Expand Up @@ -3155,6 +3156,7 @@ def neg(x):
y = list(x) # map a (shallow) copy
y[0] = -y[0]
return tuple(y)

return {dic_weight[w]: dic_weight_dual[neg(w)] for w in dic_weight}

@cached_method
Expand Down Expand Up @@ -3779,7 +3781,7 @@ def __init__(self, pm_diagram, from_shapes=None):
self._list = [i for a in reversed(pm_diagram) for i in a]
self.width = sum(self._list)

def _repr_(self):
def _repr_(self) -> str:
r"""
Turning on pretty printing allows to display the `\pm` diagram as a
tableau with the `+` and `-` displayed.
Expand All @@ -3791,7 +3793,7 @@ def _repr_(self):
"""
return repr(self.pm_diagram)

def _repr_diagram(self):
def _repr_diagram(self) -> str:
"""
Return a string representation of ``self`` as a diagram.

Expand Down Expand Up @@ -3910,7 +3912,7 @@ def intermediate_shape(self):
p = [p[i] + ll[2*i+1] for i in range(self.n)]
return Partition(p)

def heights_of_minus(self):
def heights_of_minus(self) -> list:
r"""
Return a list with the heights of all minus in the `\pm` diagram.

Expand All @@ -3930,7 +3932,7 @@ def heights_of_minus(self):
heights += [n-2*i]*((self.outer_shape()+[0]*n)[n-2*i-1]-(self.intermediate_shape()+[0]*n)[n-2*i-1])
return heights

def heights_of_addable_plus(self):
def heights_of_addable_plus(self) -> list:
r"""
Return a list with the heights of all addable plus in the `\pm` diagram.

Expand Down Expand Up @@ -4176,7 +4178,7 @@ def _call_(self, x):
self._cache[x] = y
return y

def _repr_type(self):
def _repr_type(self) -> str:
"""
Return a string describing ``self``.

Expand All @@ -4188,7 +4190,7 @@ def _repr_type(self):
"""
return "Diagram automorphism"

def is_isomorphism(self):
def is_isomorphism(self) -> bool:
"""
Return ``True`` as ``self`` is a crystal isomorphism.

Expand Down
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