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Merge branch 'circuits_matroid' into develop
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@gmou3
gmou3 committed May 6, 2024
2 parents d8b44d8 + fb657df commit c0c45aa
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Showing 3 changed files with 32 additions and 31 deletions.
5 changes: 3 additions & 2 deletions src/sage/matroids/circuits_matroid.pxd
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Original file line number Diff line number Diff line change
Expand Up @@ -2,10 +2,11 @@ from sage.matroids.matroid cimport Matroid
from sage.matroids.set_system cimport SetSystem

cdef class CircuitsMatroid(Matroid):
cdef frozenset _groundset # _E
cdef int _matroid_rank # _R
cdef frozenset _groundset
cdef int _matroid_rank
cdef set _C # circuits
cdef dict _k_C # k-circuits (k=len)
cdef list _sorted_C_lens
cdef bint _nsc_defined
cpdef groundset(self)
cpdef _rank(self, X)
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49 changes: 25 additions & 24 deletions src/sage/matroids/circuits_matroid.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -80,6 +80,7 @@ cdef class CircuitsMatroid(Matroid):
except KeyError:
self._k_C[len(C)] = set()
self._k_C[len(C)].add(C)
self._sorted_C_lens = sorted(self._k_C)
self._matroid_rank = self.rank(self._groundset)
self._nsc_defined = nsc_defined

Expand Down Expand Up @@ -160,7 +161,7 @@ cdef class CircuitsMatroid(Matroid):
"""
cdef set XX = set(X)
cdef int i, l = len(XX)
for i in sorted(self._k_C):
for i in self._sorted_C_lens:
if i > l:
break
for C in self._k_C[i]:
Expand Down Expand Up @@ -220,7 +221,7 @@ cdef class CircuitsMatroid(Matroid):
"""
cdef set XX = set(X)
cdef int i, l = len(XX)
for i in sorted(self._k_C):
for i in self._sorted_C_lens:
if i > l:
break
for C in self._k_C[i]:
Expand Down Expand Up @@ -249,8 +250,9 @@ cdef class CircuitsMatroid(Matroid):
cdef set XX = set(X)
cdef frozenset S
cdef int i
for i in sorted(self._k_C):
if i > len(XX) + 1: break
for i in self._sorted_C_lens:
if i > len(XX) + 1:
break
for C in self._k_C[i]:
S = C - XX
if len(S) == 1:
Expand Down Expand Up @@ -569,7 +571,7 @@ cdef class CircuitsMatroid(Matroid):
SetSystem of 0 sets over 8 elements
sage: sorted([sorted(X) for X in M.dependent_r_sets(4)])
[['a', 'b', 'c', 'd'], ['a', 'b', 'e', 'f'], ['a', 'b', 'g', 'h'],
['c', 'd', 'e', 'f'], ['e', 'f', 'g', 'h']]
['c', 'd', 'e', 'f'], ['e', 'f', 'g', 'h']]
"""
cdef int i
cdef set NB = set()
Expand All @@ -578,7 +580,8 @@ cdef class CircuitsMatroid(Matroid):
if i in self._k_C:
for S in self._k_C[i]:
NB.add(S)
if i == r: break
if i == r:
break
for S in NB.copy():
NB.remove(S)
for e in S ^ self._groundset:
Expand Down Expand Up @@ -770,27 +773,27 @@ cdef class CircuitsMatroid(Matroid):
EXAMPLES::
sage: M = Matroid(circuits=[[1,2,3], [3,4,5], [1,2,4,5]])
sage: M = Matroid(circuits=[[1, 2, 3], [3, 4, 5], [1, 2, 4, 5]])
sage: SimplicialComplex(M.no_broken_circuits_sets())
Simplicial complex with vertex set (1, 2, 3, 4, 5)
and facets {(1, 2, 4), (1, 2, 5), (1, 3, 4), (1, 3, 5)}
sage: SimplicialComplex(M.no_broken_circuits_sets([5,4,3,2,1]))
sage: SimplicialComplex(M.no_broken_circuits_sets([5, 4, 3, 2, 1]))
Simplicial complex with vertex set (1, 2, 3, 4, 5)
and facets {(1, 3, 5), (1, 4, 5), (2, 3, 5), (2, 4, 5)}
::
sage: M = Matroid(circuits=[[1,2,3], [1,4,5], [2,3,4,5]])
sage: SimplicialComplex(M.no_broken_circuits_sets([5,4,3,2,1]))
sage: M = Matroid(circuits=[[1, 2, 3], [1, 4, 5], [2, 3, 4, 5]])
sage: SimplicialComplex(M.no_broken_circuits_sets([5, 4, 3, 2, 1]))
Simplicial complex with vertex set (1, 2, 3, 4, 5)
and facets {(1, 3, 5), (2, 3, 5), (2, 4, 5), (3, 4, 5)}
TESTS::
sage: M = Matroid(circuits=[[1,2,3], [3,4,5], [1,2,4,5]])
sage: M = Matroid(circuits=[[1, 2, 3], [3, 4, 5], [1, 2, 4, 5]])
sage: C1 = SimplicialComplex(M.no_broken_circuits_sets())
sage: from sage.matroids.basis_matroid import BasisMatroid
sage: M = BasisMatroid(Matroid(circuits=[[1,2,3], [3,4,5], [1,2,4,5]]))
sage: M = BasisMatroid(Matroid(circuits=[[1, 2, 3], [3, 4, 5], [1, 2, 4, 5]]))
sage: C2 = SimplicialComplex(M.no_broken_circuits_sets())
sage: C1 == C2
True
Expand Down Expand Up @@ -820,21 +823,21 @@ cdef class CircuitsMatroid(Matroid):
EXAMPLES::
sage: M = Matroid(circuits=[[1,2,3], [3,4,5], [1,2,4,5]])
sage: M = Matroid(circuits=[[1, 2, 3], [3, 4, 5], [1, 2, 4, 5]])
sage: M.broken_circuit_complex()
Simplicial complex with vertex set (1, 2, 3, 4, 5)
and facets {(1, 2, 4), (1, 2, 5), (1, 3, 4), (1, 3, 5)}
sage: M.broken_circuit_complex([5,4,3,2,1])
sage: M.broken_circuit_complex([5, 4, 3, 2, 1])
Simplicial complex with vertex set (1, 2, 3, 4, 5)
and facets {(1, 3, 5), (1, 4, 5), (2, 3, 5), (2, 4, 5)}
sage: M.broken_circuit_complex([5,4,3,2,1], reduced=True)
sage: M.broken_circuit_complex([5, 4, 3, 2, 1], reduced=True)
Simplicial complex with vertex set (1, 2, 3, 4)
and facets {(1, 3), (1, 4), (2, 3), (2, 4)}
For a matroid with loops, the broken circuit complex is not defined,
and the method yields an error::
sage: M = Matroid(groundset=[0,1,2], circuits=[[0]])
sage: M = Matroid(groundset=[0, 1, 2], circuits=[[0]])
sage: M.broken_circuit_complex()
Traceback (most recent call last):
...
Expand Down Expand Up @@ -899,15 +902,15 @@ cdef class CircuitsMatroid(Matroid):
sage: M = Matroid(circuits=C)
sage: M.is_valid()
True
sage: C = [[1,2], [1, 2, 3], [3, 4, 5], [1, 2, 4, 5]]
sage: C = [[1, 2], [1, 2, 3], [3, 4, 5], [1, 2, 4, 5]]
sage: M = Matroid(circuits=C)
sage: M.is_valid()
False
sage: C = [[3,6], [1, 2, 3], [3, 4, 5], [1, 2, 4, 5]]
sage: C = [[3, 6], [1, 2, 3], [3, 4, 5], [1, 2, 4, 5]]
sage: M = Matroid(circuits=C)
sage: M.is_valid()
False
sage: C = [[3,6], [1, 2, 3], [3, 4, 5], [1, 2, 6], [6, 4, 5], [1, 2, 4, 5]]
sage: C = [[3, 6], [1, 2, 3], [3, 4, 5], [1, 2, 6], [6, 4, 5], [1, 2, 4, 5]]
sage: M = Matroid(circuits=C)
sage: M.is_valid()
True
Expand All @@ -921,10 +924,9 @@ cdef class CircuitsMatroid(Matroid):
False
"""
from itertools import combinations_with_replacement
cdef int i, j, k
cdef frozenset C1, C2, C3, I12, U12
cdef bint flag
for (i, j) in combinations_with_replacement(sorted(self._k_C), 2):
cdef int i, j
cdef frozenset C1, C2, I12, U12
for (i, j) in combinations_with_replacement(self._sorted_C_lens, 2):
# loop through all circuit length pairs (i, j) with i <= j
for C1 in self._k_C[i]:
if not C1: # the empty set can't be a circuit
Expand All @@ -941,7 +943,6 @@ cdef class CircuitsMatroid(Matroid):
# check circuit elimination axiom
U12 = C1 | C2
for e in I12:
flag = False
S = U12 - {e}
if self._is_independent(S):
return False
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9 changes: 4 additions & 5 deletions src/sage/matroids/matroid.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -2891,9 +2891,8 @@ cdef class Matroid(SageObject):
sage: M = matroids.catalog.Pappus()
sage: M.independent_r_sets(4)
SetSystem of 0 sets over 9 elements
sage: S = M.independent_r_sets(3)
sage: len(S)
75
sage: S = M.independent_r_sets(3); S
SetSystem of 75 sets over 9 elements
sage: frozenset({'a', 'c', 'e'}) in S
True
Expand Down Expand Up @@ -8342,11 +8341,11 @@ cdef class Matroid(SageObject):
For a matroid with loops, the broken circuit complex is not defined,
and the method yields an error::
sage: M = Matroid(flats={0:['a'], 1:['ab', 'ac'], 2:['abc']})
sage: M = Matroid(flats={0: ['a'], 1: ['ab', 'ac'], 2: ['abc']})
sage: M.broken_circuit_complex()
Traceback (most recent call last):
...
ValueError: raise ValueError("broken circuit complex of matroid with loops is not defined")
ValueError: broken circuit complex of matroid with loops is not defined
TESTS::
Expand Down

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