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gh-37338: Speedup database_matroids.py tests
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I strategically recast a few matroids in `database_matroids.py` to
`CircuitsMatroid`s (given #37148).
On my old laptop, this results in a `x5` speedup in the testing of the
file, and in a `x2` speedup in the testing of the whole of the
`matroids` module (saving `~1m`).
    
URL: #37338
Reported by: gmou3
Reviewer(s): Travis Scrimshaw
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Release Manager committed Feb 21, 2024
2 parents 0f35a69 + 31d6130 commit ec7b486
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164 changes: 65 additions & 99 deletions src/sage/matroids/database_matroids.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1088,25 +1088,20 @@ def P8pp():
sage: from sage.matroids.advanced import *
sage: M = matroids.catalog.P8pp(); M
P8'': Matroid of rank 4 on 8 elements with circuit-closures
{3: {{'a', 'b', 'f', 'h'}, {'a', 'c', 'e', 'f'}, {'a', 'c', 'g', 'h'},
{'a', 'd', 'e', 'g'}, {'b', 'c', 'e', 'g'}, {'b', 'd', 'e', 'h'},
{'b', 'd', 'f', 'g'}, {'c', 'd', 'f', 'h'}},
4: {{'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h'}}}
P8'': Matroid of rank 4 on 8 elements with 8 nonspanning circuits
sage: M.is_isomorphic(M.dual()) and not M.equals(M.dual())
True
sage: len(get_nonisomorphic_matroids([M.contract(i) for i in M.groundset()]))
1
sage: M.is_valid() # long time
sage: M.is_valid() and M.is_paving()
True
REFERENCES:
[Oxl2011]_, p. 651.
"""
CC = {3: ['abfh', 'bceg', 'cdfh', 'adeg', 'acef', 'bdfg', 'acgh', 'bdeh'],
4: ['abcdefgh']}
M = CircuitClosuresMatroid(groundset='abcdefgh', circuit_closures=CC)
NSC = ['abfh', 'bceg', 'cdfh', 'adeg', 'acef', 'bdfg', 'acgh', 'bdeh']
M = Matroid(groundset='abcdefgh', rank=4, nonspanning_circuits=NSC)
M.rename("P8'': " + repr(M))
return M

Expand Down Expand Up @@ -1336,11 +1331,7 @@ def Pappus(groundset=None):
sage: from sage.matroids.advanced import setprint
sage: M = matroids.catalog.Pappus(); M
Pappus: Matroid of rank 3 on 9 elements with circuit-closures
{2: {{'a', 'b', 'c'}, {'a', 'e', 'i'}, {'a', 'f', 'h'},
{'b', 'd', 'i'}, {'b', 'f', 'g'}, {'c', 'd', 'h'},
{'c', 'e', 'g'}, {'d', 'e', 'f'}, {'g', 'h', 'i'}},
3: {{'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i'}}}
Pappus: Matroid of rank 3 on 9 elements with 9 nonspanning circuits
sage: setprint(M.nonspanning_circuits())
[{'a', 'b', 'c'}, {'a', 'e', 'i'}, {'a', 'f', 'h'}, {'b', 'd', 'i'},
{'b', 'f', 'g'}, {'c', 'd', 'h'}, {'c', 'e', 'g'}, {'d', 'e', 'f'},
Expand All @@ -1356,9 +1347,8 @@ def Pappus(groundset=None):
[Oxl2011]_, p. 655.
"""
CC = {2: ['abc', 'def', 'ceg', 'bfg', 'cdh', 'afh', 'bdi', 'aei', 'ghi'],
3: ['abcdefghi']}
M = CircuitClosuresMatroid(groundset='abcdefghi', circuit_closures=CC)
NSC = ['abc', 'def', 'ceg', 'bfg', 'cdh', 'afh', 'bdi', 'aei', 'ghi']
M = Matroid(groundset='abcdefghi', rank=3, nonspanning_circuits=NSC)
M.rename("Pappus: " + repr(M))
return M

Expand All @@ -1375,11 +1365,7 @@ def NonPappus():
sage: from sage.matroids.advanced import setprint
sage: M = matroids.catalog.NonPappus(); M
NonPappus: Matroid of rank 3 on 9 elements with circuit-closures
{2: {{'a', 'b', 'c'}, {'a', 'e', 'i'}, {'a', 'f', 'h'},
{'b', 'd', 'i'}, {'b', 'f', 'g'}, {'c', 'd', 'h'},
{'c', 'e', 'g'}, {'g', 'h', 'i'}},
3: {{'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i'}}}
NonPappus: Matroid of rank 3 on 9 elements with 8 nonspanning circuits
sage: setprint(M.nonspanning_circuits())
[{'a', 'b', 'c'}, {'a', 'e', 'i'}, {'a', 'f', 'h'}, {'b', 'd', 'i'},
{'b', 'f', 'g'}, {'c', 'd', 'h'}, {'c', 'e', 'g'}, {'g', 'h', 'i'}]
Expand All @@ -1394,9 +1380,8 @@ def NonPappus():
[Oxl2011]_, p. 655.
"""
CC = {2: ['abc', 'ceg', 'bfg', 'cdh', 'afh', 'bdi', 'aei', 'ghi'],
3: ['abcdefghi']}
M = CircuitClosuresMatroid(groundset='abcdefghi', circuit_closures=CC)
NSC = ['abc', 'ceg', 'bfg', 'cdh', 'afh', 'bdi', 'aei', 'ghi']
M = Matroid(groundset='abcdefghi', rank=3, nonspanning_circuits=NSC)
M.rename("NonPappus: " + repr(M))
return M

Expand Down Expand Up @@ -1447,6 +1432,7 @@ def K5dual():
[Oxl2011]_, p. 656.
"""
M = CompleteGraphic(5).dual()
# M = Matroid(circuits=M.circuits())
M.rename("M*(K5): " + repr(M))
return M

Expand Down Expand Up @@ -2284,7 +2270,7 @@ def Psi(r):
EXAMPLES::
sage: matroids.Psi(7)
Psi_7: Matroid of rank 7 on 14 elements with 2060 bases
Psi_7: Matroid of rank 7 on 14 elements with 105 nonspanning circuits
The matroid `\Psi_r` is `3`-connected but, for all `r \ge 4`, not `4`-connected::
Expand Down Expand Up @@ -2346,18 +2332,7 @@ def genbin(n, bs=""):
j += 1
NSC += [C]

import itertools
B = [] # bases
for b in itertools.combinations(E, r):
flag = True
for C in NSC:
if set(b) >= set(C):
flag = False
break
if flag:
B += [list(b)]

M = Matroid(groundset=E, bases=B)
M = Matroid(groundset=E, rank=r, nonspanning_circuits=NSC)
M.rename("Psi_" + str(r) + ": " + repr(M))
return M

Expand Down Expand Up @@ -4253,6 +4228,7 @@ def complement(groundset, subset):
6: [gs],
},
)
M = Matroid(circuits=M.circuits())
M.rename("NestOfTwistedCubes: " + repr(M))
return M

Expand Down Expand Up @@ -4747,16 +4723,15 @@ def R9A():
EXAMPLES::
sage: M = matroids.catalog.R9A()
sage: M.is_valid() # long time
sage: M = matroids.catalog.R9A(); M
R9A: Matroid of rank 4 on 9 elements with 13 nonspanning circuits
sage: M.is_valid()
True
"""
E = 'abcdefghi'
CC = {3: ['abde', 'bcdf', 'aceg', 'abch', 'aefh', 'adgh', 'acdi', 'abfi',
'defi', 'begi', 'bdhi', 'cehi', 'fghi'],
4: [E]}
M = CircuitClosuresMatroid(groundset=E, circuit_closures=CC)
M.rename('R9A: ' + repr(M))
NSC = ['abch', 'abde', 'abfi', 'acdi', 'aceg', 'adgh', 'aefh', 'bcdf',
'bdhi', 'begi', 'cehi', 'defi', 'fghi']
M = Matroid(groundset='abcdefghi', rank=4, nonspanning_circuits=NSC)
M.rename("R9A: " + repr(M))
return M


Expand All @@ -4771,16 +4746,15 @@ def R9B():
EXAMPLES::
sage: M = matroids.catalog.R9B()
sage: M.is_valid() # long time
sage: M = matroids.catalog.R9B(); M
R9B: Matroid of rank 4 on 9 elements with 13 nonspanning circuits
sage: M.is_valid() and M.is_paving()
True
"""
E = 'abcdefghi'
CC = {3: ['abde', 'bcdf', 'aceg', 'abch', 'befh', 'cdgh', 'bcei', 'adfi',
'abgi', 'degi', 'bdhi', 'aehi', 'fghi'],
4: [E]}
M = CircuitClosuresMatroid(groundset=E, circuit_closures=CC)
M.rename('R9B: ' + repr(M))
NSC = ['abde', 'bcdf', 'aceg', 'abch', 'befh', 'cdgh', 'bcei', 'adfi',
'abgi', 'degi', 'bdhi', 'aehi', 'fghi']
M = Matroid(groundset='abcdefghi', rank=4, nonspanning_circuits=NSC)
M.rename("R9B: " + repr(M))
return M


Expand All @@ -4791,22 +4765,20 @@ def Block_9_4():
EXAMPLES::
sage: M = matroids.catalog.Block_9_4()
sage: M.is_valid() # long time
sage: M = matroids.catalog.Block_9_4(); M
Block(9, 4): Matroid of rank 4 on 9 elements with 18 nonspanning
circuits
sage: M.is_valid() and M.is_paving()
True
sage: BD = BlockDesign(M.groundset(), M.nonspanning_circuits())
sage: BD.is_t_design(return_parameters=True)
(True, (2, 9, 4, 3))
"""
E = 'abcdefghi'
CC = {
3: ['abcd', 'acef', 'bdef', 'cdeg', 'abfg', 'adeh', 'bcfh', 'acgh',
'begh', 'dfgh', 'abei', 'cdfi', 'bcgi', 'adgi', 'efgi', 'bdhi',
'cehi', 'afhi'],
4: [E]
}
M = CircuitClosuresMatroid(groundset=E, circuit_closures=CC)
M.rename('Block(9, 4): ' + repr(M))
NSC = ['abcd', 'acef', 'bdef', 'cdeg', 'abfg', 'adeh', 'bcfh', 'acgh',
'begh', 'dfgh', 'abei', 'cdfi', 'bcgi', 'adgi', 'efgi', 'bdhi',
'cehi', 'afhi']
M = Matroid(groundset='abcdefghi', rank=4, nonspanning_circuits=NSC)
M.rename("Block(9, 4): " + repr(M))
return M


Expand All @@ -4819,22 +4791,19 @@ def TicTacToe():
EXAMPLES::
sage: M = matroids.catalog.TicTacToe()
sage: M.is_valid() # long time
sage: M = matroids.catalog.TicTacToe(); M
TicTacToe: Matroid of rank 5 on 9 elements with 8 nonspanning circuits
sage: M.is_valid() and M.is_paving()
True
REFERENCES:
[Hoc]_
"""
E = 'abcdefghi'
CC = {
4: ['abcdg', 'adefg', 'abceh', 'abcfi', 'cdefi', 'adghi',
'beghi', 'cfghi'],
5: [E]
}
M = CircuitClosuresMatroid(groundset=E, circuit_closures=CC)
M.rename('TicTacToe: ' + repr(M))
NSC = ['abcdg', 'adefg', 'abceh', 'abcfi', 'cdefi', 'adghi', 'beghi',
'cfghi']
M = Matroid(groundset='abcdefghi', rank=5, nonspanning_circuits=NSC)
M.rename("TicTacToe: " + repr(M))
return M


Expand Down Expand Up @@ -4876,25 +4845,23 @@ def Block_10_5():
EXAMPLES::
sage: M = matroids.catalog.Block_10_5()
sage: M.is_valid() # long time
sage: M = matroids.catalog.Block_10_5(); M
Block(10, 5): Matroid of rank 5 on 10 elements with 36 nonspanning
circuits
sage: M.is_valid() and M.is_paving()
True
sage: BD = BlockDesign(M.groundset(), M.nonspanning_circuits())
sage: BD.is_t_design(return_parameters=True)
(True, (3, 10, 5, 3))
"""
E = 'abcdefghij'
CC = {
4: ['abcde', 'acdfg', 'bdefg', 'bcdfh', 'abefh', 'abcgh', 'adegh',
'cefgh', 'bcefi', 'adefi', 'bcdgi', 'acegi', 'abfgi', 'abdhi',
'cdehi', 'acfhi', 'beghi', 'dfghi', 'abdfj', 'acefj', 'abegj',
'cdegj', 'bcfgj', 'acdhj', 'bcehj', 'defhj', 'bdghj', 'afghj',
'abcij', 'bdeij', 'cdfij', 'adgij', 'efgij', 'aehij', 'bfhij',
'cghij'],
5: [E]
}
M = CircuitClosuresMatroid(groundset=E, circuit_closures=CC)
M.rename('Block(10, 5): ' + repr(M))
NSC = ['abcde', 'acdfg', 'bdefg', 'bcdfh', 'abefh', 'abcgh', 'adegh',
'cefgh', 'bcefi', 'adefi', 'bcdgi', 'acegi', 'abfgi', 'abdhi',
'cdehi', 'acfhi', 'beghi', 'dfghi', 'abdfj', 'acefj', 'abegj',
'cdegj', 'bcfgj', 'acdhj', 'bcehj', 'defhj', 'bdghj', 'afghj',
'abcij', 'bdeij', 'cdfij', 'adgij', 'efgij', 'aehij', 'bfhij',
'cghij']
M = Matroid(groundset='abcdefghij', rank=5, nonspanning_circuits=NSC)
M.rename("Block(10, 5): " + repr(M))
return M


Expand Down Expand Up @@ -4949,20 +4916,19 @@ def BetsyRoss():
EXAMPLES::
sage: M = matroids.catalog.BetsyRoss()
sage: M = matroids.catalog.BetsyRoss(); M
BetsyRoss: Matroid of rank 3 on 11 elements with 25 nonspanning
circuits
sage: len(M.circuit_closures()[2])
10
sage: M.is_valid() # long time
sage: M.is_valid()
True
"""
E = 'abcdefghijk'
CC = {
2: ['acfg', 'bdgh', 'cehi', 'befj', 'adij', 'dfk',
'egk', 'ahk', 'bik', 'cjk'],
3: [E]
}
M = CircuitClosuresMatroid(groundset=E, circuit_closures=CC)
M.rename('BetsyRoss: ' + repr(M))
NSC = ['acf', 'acg', 'adi', 'adj', 'afg', 'ahk', 'aij', 'bdg', 'bdh',
'bef', 'bej', 'bfj', 'bgh', 'bik', 'ceh', 'cei', 'cfg', 'chi',
'cjk', 'dfk', 'dgh', 'dij', 'efj', 'egk', 'ehi']
M = Matroid(groundset='abcdefghijk', rank=3, nonspanning_circuits=NSC)
M.rename("BetsyRoss: " + repr(M))
return M


Expand Down
6 changes: 1 addition & 5 deletions src/sage/matroids/dual_matroid.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -382,11 +382,7 @@ def dual(self):
sage: N.rank()
3
sage: N
Pappus: Matroid of rank 3 on 9 elements with circuit-closures
{2: {{'a', 'b', 'c'}, {'a', 'e', 'i'}, {'a', 'f', 'h'},
{'b', 'd', 'i'}, {'b', 'f', 'g'}, {'c', 'd', 'h'},
{'c', 'e', 'g'}, {'d', 'e', 'f'}, {'g', 'h', 'i'}},
3: {{'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i'}}}
Pappus: Matroid of rank 3 on 9 elements with 9 nonspanning circuits
"""
return self._matroid

Expand Down
13 changes: 2 additions & 11 deletions src/sage/matroids/matroid.pyx
View file
Original file line number Diff line number Diff line change
Expand Up @@ -3987,12 +3987,7 @@ cdef class Matroid(SageObject):
sage: N.rank()
6
sage: N
Dual of 'Pappus: Matroid of rank 3 on 9 elements with
circuit-closures
{2: {{'a', 'b', 'c'}, {'a', 'e', 'i'}, {'a', 'f', 'h'},
{'b', 'd', 'i'}, {'b', 'f', 'g'}, {'c', 'd', 'h'},
{'c', 'e', 'g'}, {'d', 'e', 'f'}, {'g', 'h', 'i'}},
3: {{'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i'}}}'
Dual of 'Pappus: Matroid of rank 3 on 9 elements with 9 nonspanning circuits'
"""
from sage.matroids import dual_matroid
return dual_matroid.DualMatroid(self)
Expand Down Expand Up @@ -8189,11 +8184,7 @@ cdef class Matroid(SageObject):
sage: N = matroids.catalog.Fano().direct_sum(M); N
Matroid of rank 6 on 16 elements as matroid sum of
Binary matroid of rank 3 on 7 elements, type (3, 0)
Matroid of rank 3 on 9 elements with circuit-closures
{2: {{'a', 'b', 'c'}, {'a', 'e', 'i'}, {'a', 'f', 'h'},
{'b', 'd', 'i'}, {'b', 'f', 'g'}, {'c', 'd', 'h'},
{'c', 'e', 'g'}, {'d', 'e', 'f'}, {'g', 'h', 'i'}},
3: {{'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i'}}}
Matroid of rank 3 on 9 elements with 9 nonspanning circuits
sage: len(N.independent_sets())
6897
sage: len(N.bases())
Expand Down

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