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fix permanent of empty square matrix #40952

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fix permanent of empty square matrix #40952

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50bfd2c
fix permanent of empty square matrix
fchapoton Oct 1, 2025
f09d27f
Update src/sage/matrix/matrix2.pyx
fchapoton Oct 2, 2025
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35 changes: 22 additions & 13 deletions src/sage/matrix/matrix2.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -1607,7 +1607,16 @@ cdef class Matrix(Matrix1):
sage: A = matrix(R, 2,2, [x, y, x^2, y^2])
sage: A.permanent()
x^2*y + x*y^2

TESTS::

sage: A = matrix(ZZ, 0, 0, [])
sage: A.permanent()
1
"""
if not self.nrows():
return self.base_ring().one()

if algorithm == "Ryser":
return self._permanent_ryser()

Expand Down Expand Up @@ -2899,7 +2908,7 @@ cdef class Matrix(Matrix1):
"""
M = self.parent().change_ring(phi.codomain())
if self.is_sparse():
values = {(i, j): phi(z) for (i, j), z in self.dict()}
values = {ij: phi(z) for ij, z in self.dict()}
else:
values = [phi(z) for z in self.list()]
image = M(values)
Expand Down Expand Up @@ -3009,7 +3018,7 @@ cdef class Matrix(Matrix1):
return self.dense_matrix()

if self.is_sparse():
values = {(i, j): phi(v) for (i, j), v in self.dict().iteritems()}
values = {ij: phi(v) for ij, v in self.dict().iteritems()}
if R is None:
R = sage.structure.sequence.Sequence(values.values()).universe()
else:
Expand Down Expand Up @@ -12227,7 +12236,7 @@ cdef class Matrix(Matrix1):
evals = eigenvalues
else:
evals = A.charpoly().roots()
if sum(mult for (_, mult) in evals) < n:
if sum(mult for _, mult in evals) < n:
raise RuntimeError("Some eigenvalue does not exist in %s." % (A.base_ring()))

# Compute the block information. Here, ``blocks`` is a list of pairs,
Expand All @@ -12254,7 +12263,7 @@ cdef class Matrix(Matrix1):
# are ordered firstly by the eigenvalues, in the same order as obeyed
# by ``.roots()``, and secondly by size from greatest to smallest.
J = block_diagonal_matrix([jordan_block(eval, size, sparse=sparse)
for (eval, size) in blocks],
for eval, size in blocks],
subdivide=subdivide)

if transformation:
Expand Down Expand Up @@ -12513,7 +12522,7 @@ cdef class Matrix(Matrix1):

# check if the sum of algebraic multiplicities equals the number of rows
evals = A.charpoly().roots()
if sum(mult for (_, mult) in evals) < self._nrows:
if sum(mult for _, mult in evals) < self._nrows:
raise ValueError('not diagonalizable over {}'.format(A.base_ring()))

# compute diagonalization from the eigenspaces
Expand Down Expand Up @@ -12706,7 +12715,7 @@ cdef class Matrix(Matrix1):

# check if the sum of algebraic multiplicities equals to the number of rows
evals = A.charpoly().roots()
if sum(mult for (_, mult) in evals) < self._nrows:
if sum(mult for _, mult in evals) < self._nrows:
return False

# Obtaining a generic minimal polynomial requires much more
Expand Down Expand Up @@ -17082,9 +17091,9 @@ cdef class Matrix(Matrix1):
return R.ideal(prod(elemdiv[:rank_minors]))
except (TypeError, NotImplementedError, ArithmeticError):
pass
for (nr, r) in enumerate(self.rows()):
for nr, r in enumerate(self.rows()):
nz = [e for e in enumerate(r) if e[1]]
if len(nz) == 0:
if not nz:
N = self.delete_rows([nr])
return N.fitting_ideal(i)
elif len(nz) == 1:
Expand All @@ -17093,7 +17102,7 @@ cdef class Matrix(Matrix1):
N = N.delete_columns([nz[0][0]])
F2 = N.fitting_ideal(i)
return F1 + nz[0][1]*F2
for (nc, c) in enumerate(self.columns()):
for nc, c in enumerate(self.columns()):
nz = [e for e in enumerate(c) if e[1]]
if len(nz) == 0:
N = self.delete_columns([nc])
Expand Down Expand Up @@ -18679,7 +18688,7 @@ cdef class Matrix(Matrix1):
raise ValueError(msg)

return all(s * (self * x) >= 0
for (x, s) in K.discrete_complementarity_set())
for x, s in K.discrete_complementarity_set())

def is_Z_operator_on(self, K):
r"""
Expand Down Expand Up @@ -18955,7 +18964,7 @@ cdef class Matrix(Matrix1):
# many inequalities as the number of equalities that we're
# about to check.
return all(s * (self * x) == 0
for (x, s) in K.discrete_complementarity_set())
for x, s in K.discrete_complementarity_set())

def LLL_gram(self, flag=0):
"""
Expand Down Expand Up @@ -19775,7 +19784,7 @@ cdef class Matrix(Matrix1):
[ 0 0 27], ((0, 0, 0), (0, 1, 1), (0, 2, 2))
)
sage: rows.sort(key=lambda x: (x[1] + shifts[x[0]], x[0]))
sage: [(i, j) for (i, j, k) in rows[:3]]
sage: [(i, j) for i, j, k in rows[:3]]
[(0, 0),
(0, 1),
(0, 2)]
Expand All @@ -19798,7 +19807,7 @@ cdef class Matrix(Matrix1):
[ 0 0 50], ((1, 0, 0), (1, 1, 1), (1, 2, 2))
)
sage: rows.sort(key=lambda x: (x[1] + shifts[x[0]], x[0]))
sage: [(i, j) for (i, j, k) in rows[:3]]
sage: [(i, j) for i, j, k in rows[:3]]
[(1, 0),
(1, 1),
(1, 2)]
Expand Down
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