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PR for #36198: fix return types in permutation.py so that methods return type Integer instead of type int. #36199

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PR for #36198: fix return types in permutation.py so that methods return type Integer instead of type int. #36199

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47 changes: 24 additions & 23 deletions src/sage/combinat/permutation.py
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Original file line number Diff line number Diff line change
Expand Up @@ -720,7 +720,7 @@ def size(self) -> Integer:
sage: Permutation([3,4,1,2,5]).size()
5
"""
return len(self)
return Integer(len(self))

grade = size # for the category SetsWithGrading()

Expand Down Expand Up @@ -1167,7 +1167,7 @@ def signature(self) -> Integer:
sage: Permutation([]).sign()
1
"""
return (-1)**(len(self)-len(self.to_cycles()))
return Integer((-1)**(len(self)-len(self.to_cycles())))

#one can also use sign as an alias for signature
sign = signature
Expand Down Expand Up @@ -1476,21 +1476,23 @@ def to_inversion_vector(self):
l = len(p)
# lightning fast if the length is less than 3
# (is it really useful?)
zero = Integer(0)
one = Integer(1)
if l < 4:
if l == 0:
return []
if l == 1:
return [0]
return [zero]
if l == 2:
return [p[0] - 1, 0]
return [Integer(p[0] - 1), zero]
if l == 3:
if p[0] == 1:
return [0, p[1] - 2, 0]
return [zero, Integer(p[1] - 2), zero]
if p[0] == 2:
if p[1] == 1:
return [1, 0, 0]
return [2, 0, 0]
return [p[1], 1, 0]
return [one, zero, zero]
return [Integer(2), zero, zero]
return [Integer(p[1]), one, zero]
# choose the best one
if l < 411:
return self._to_inversion_vector_small()
Expand Down Expand Up @@ -1548,7 +1550,7 @@ def _to_inversion_vector_small(self):
for pi in reversed(p):
checked[pi] = 0
iv[pi] = sum(checked[pi:])
return iv[1:]
return [Integer(a) for a in iv[1:]]

def _to_inversion_vector_divide_and_conquer(self):
r"""
Expand Down Expand Up @@ -1614,7 +1616,7 @@ def sort_and_countv(L):
return merge_and_countv(sort_and_countv(L[:l]),
sort_and_countv(L[l:]))

return sort_and_countv(self._list)[0]
return [Integer(a) for a in sort_and_countv(self._list)[0]]

def inversions(self) -> list:
r"""
Expand Down Expand Up @@ -1883,8 +1885,8 @@ def number_of_noninversions(self, k) -> Integer:
"""
if k > len(self):
return 0
return sum(1 for pos in itertools.combinations(self, k)
if all(pos[i] < pos[i + 1] for i in range(k - 1)))
return Integer(sum(1 for pos in itertools.combinations(self, k)
if all(pos[i] < pos[i + 1] for i in range(k - 1))))

def length(self) -> Integer:
r"""
Expand Down Expand Up @@ -1934,7 +1936,7 @@ def inverse(self) -> Permutation:
"""
w = list(range(len(self)))
for i, j in enumerate(self):
w[j - 1] = i + 1
w[j - 1] = Integer(i + 1)
return Permutations()(w)

__invert__ = inverse
Expand Down Expand Up @@ -2239,7 +2241,7 @@ def longest_increasing_subsequence_length(self) -> Integer:
else:
# We replace y by x
r[idx] = x
return len(r)
return Integer(len(r))

def longest_increasing_subsequences(self):
r"""
Expand Down Expand Up @@ -3082,8 +3084,7 @@ def number_of_fixed_points(self) -> Integer:
sage: Permutation([1,2,3,4]).number_of_fixed_points()
4
"""

return len(self.fixed_points())
return Integer(len(self.fixed_points()))

def is_derangement(self) -> bool:
r"""
Expand Down Expand Up @@ -3209,7 +3210,7 @@ def number_of_recoils(self) -> Integer:
sage: Permutation([1,4,3,2]).number_of_recoils()
2
"""
return len(self.recoils())
return Integer(len(self.recoils()))

def recoils_composition(self) -> Composition:
r"""
Expand Down Expand Up @@ -3382,7 +3383,7 @@ def number_of_descents(self, final_descent=False) -> Integer:
sage: Permutation([1,4,3,2]).number_of_descents(final_descent=True)
3
"""
return len(self.descents(final_descent))
return Integer(len(self.descents(final_descent)))

def number_of_idescents(self, final_descent=False) -> Integer:
r"""
Expand All @@ -3400,7 +3401,7 @@ def number_of_idescents(self, final_descent=False) -> Integer:
sage: Permutation([1,4,3,2]).number_of_idescents(final_descent=True)
3
"""
return len(self.idescents(final_descent))
return Integer(len(self.idescents(final_descent)))

@combinatorial_map(name='descent composition')
def descents_composition(self) -> Composition:
Expand Down Expand Up @@ -3497,7 +3498,7 @@ def major_index(self, final_descent=False) -> Integer:
6
"""
descents = self.descents(final_descent)
return sum(descents)
return Integer(sum(descents))

def multi_major_index(self, composition):
r"""
Expand Down Expand Up @@ -3566,7 +3567,7 @@ def imajor_index(self, final_descent=False) -> Integer:
sage: Permutation([4,3,2,1]).imajor_index()
6
"""
return sum(self.idescents(final_descent))
return Integer(sum(self.idescents(final_descent)))

def to_major_code(self, final_descent=False):
r"""
Expand Down Expand Up @@ -3655,7 +3656,7 @@ def number_of_peaks(self) -> Integer:
sage: Permutation([4,1,3,2,6,5]).number_of_peaks()
2
"""
return len(self.peaks())
return Integer(len(self.peaks()))

#############
# Saliances #
Expand Down Expand Up @@ -3701,7 +3702,7 @@ def number_of_saliances(self) -> Integer:
sage: Permutation([5,4,3,2,1]).number_of_saliances()
5
"""
return len(self.saliances())
return Integer(len(self.saliances()))

################
# Bruhat Order #
Expand Down
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