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Decouple tuple #35812

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merged 8 commits into from
Jul 9, 2023
Merged

Decouple tuple #35812

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e057b27
Mind the GAP
deinst Jun 22, 2023
aba3954
Finish decoupling tuple.py from GAP.
deinst Jun 22, 2023
5702830
Added testcases to Tuples for undelying lists with duplicates
deinst Jun 23, 2023
dffe683
Have tuple.py return tuples instead of lists
deinst Jun 25, 2023
14e7540
Switch tuple to list in projective_space.py
deinst Jun 25, 2023
f40c739
Merge branch 'develop' into decouple_tuple
deinst Jun 26, 2023
660653c
Change dict to set
deinst Jun 26, 2023
f79c0d0
Merge tag '10.1.beta5' into decouple_tuple
mkoeppe Jul 2, 2023
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88 changes: 39 additions & 49 deletions src/sage/combinat/tuple.py
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Original file line number Diff line number Diff line change
Expand Up @@ -16,12 +16,12 @@
# https://www.gnu.org/licenses/
# ****************************************************************************

from sage.libs.gap.libgap import libgap
from sage.arith.misc import binomial
from sage.rings.integer_ring import ZZ
from sage.structure.parent import Parent
from sage.structure.unique_representation import UniqueRepresentation
from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets

from itertools import product, combinations_with_replacement

class Tuples(Parent, UniqueRepresentation):
"""
Expand All @@ -35,23 +35,23 @@ class Tuples(Parent, UniqueRepresentation):

sage: S = [1,2]
sage: Tuples(S,3).list()
[[1, 1, 1], [2, 1, 1], [1, 2, 1], [2, 2, 1], [1, 1, 2],
[2, 1, 2], [1, 2, 2], [2, 2, 2]]
[(1, 1, 1), (2, 1, 1), (1, 2, 1), (2, 2, 1), (1, 1, 2),
(2, 1, 2), (1, 2, 2), (2, 2, 2)]
sage: mset = ["s","t","e","i","n"]
sage: Tuples(mset,2).list()
[['s', 's'], ['t', 's'], ['e', 's'], ['i', 's'], ['n', 's'],
['s', 't'], ['t', 't'], ['e', 't'], ['i', 't'], ['n', 't'],
['s', 'e'], ['t', 'e'], ['e', 'e'], ['i', 'e'], ['n', 'e'],
['s', 'i'], ['t', 'i'], ['e', 'i'], ['i', 'i'], ['n', 'i'],
['s', 'n'], ['t', 'n'], ['e', 'n'], ['i', 'n'], ['n', 'n']]
[('s', 's'), ('t', 's'), ('e', 's'), ('i', 's'), ('n', 's'),
('s', 't'), ('t', 't'), ('e', 't'), ('i', 't'), ('n', 't'),
('s', 'e'), ('t', 'e'), ('e', 'e'), ('i', 'e'), ('n', 'e'),
('s', 'i'), ('t', 'i'), ('e', 'i'), ('i', 'i'), ('n', 'i'),
('s', 'n'), ('t', 'n'), ('e', 'n'), ('i', 'n'), ('n', 'n')]

::

sage: K.<a> = GF(4, 'a') # optional - sage.rings.finite_rings
sage: mset = [x for x in K if x != 0] # optional - sage.rings.finite_rings
sage: Tuples(mset,2).list() # optional - sage.rings.finite_rings
[[a, a], [a + 1, a], [1, a], [a, a + 1], [a + 1, a + 1], [1, a + 1],
[a, 1], [a + 1, 1], [1, 1]]
[(a, a), (a + 1, a), (1, a), (a, a + 1), (a + 1, a + 1), (1, a + 1),
(a, 1), (a + 1, 1), (1, 1)]
"""
@staticmethod
def __classcall_private__(cls, S, k):
Expand All @@ -75,7 +75,7 @@ def __init__(self, S, k):
"""
self.S = S
self.k = k
self._index_list = [S.index(s) for s in S]
self._index_list = list(set(S.index(s) for s in S))
category = FiniteEnumeratedSets()
Parent.__init__(self, category=category)

Expand All @@ -94,33 +94,21 @@ def __iter__(self):

sage: S = [1,2]
sage: Tuples(S,3).list()
[[1, 1, 1], [2, 1, 1], [1, 2, 1], [2, 2, 1], [1, 1, 2],
[2, 1, 2], [1, 2, 2], [2, 2, 2]]
[(1, 1, 1), (2, 1, 1), (1, 2, 1), (2, 2, 1), (1, 1, 2),
(2, 1, 2), (1, 2, 2), (2, 2, 2)]
sage: mset = ["s","t","e","i","n"]
sage: Tuples(mset,2).list()
[['s', 's'], ['t', 's'], ['e', 's'], ['i', 's'], ['n', 's'],
['s', 't'], ['t', 't'], ['e', 't'], ['i', 't'],
['n', 't'], ['s', 'e'], ['t', 'e'], ['e', 'e'], ['i', 'e'],
['n', 'e'], ['s', 'i'], ['t', 'i'], ['e', 'i'],
['i', 'i'], ['n', 'i'], ['s', 'n'], ['t', 'n'], ['e', 'n'],
['i', 'n'], ['n', 'n']]
"""
S = self.S
k = self.k
import copy
if k <= 0:
yield []
return
if k == 1:
for x in S:
yield [x]
return

for s in S:
for x in Tuples(S, k - 1):
y = copy.copy(x)
y.append(s)
yield y
[('s', 's'), ('t', 's'), ('e', 's'), ('i', 's'), ('n', 's'),
('s', 't'), ('t', 't'), ('e', 't'), ('i', 't'), ('n', 't'),
('s', 'e'), ('t', 'e'), ('e', 'e'), ('i', 'e'), ('n', 'e'),
('s', 'i'), ('t', 'i'), ('e', 'i'), ('i', 'i'), ('n', 'i'),
('s', 'n'), ('t', 'n'), ('e', 'n'), ('i', 'n'), ('n', 'n')]
sage: Tuples((1,1,2),3).list()
[(1, 1, 1), (2, 1, 1), (1, 2, 1), (2, 2, 1), (1, 1, 2),
(2, 1, 2), (1, 2, 2), (2, 2, 2)]
"""
for p in product(self._index_list, repeat=self.k):
yield tuple(self.S[i] for i in reversed(p))

def cardinality(self):
"""
Expand All @@ -133,7 +121,7 @@ def cardinality(self):
sage: Tuples(S,2).cardinality() # optional - sage.libs.gap
25
"""
return ZZ(libgap.NrTuples(self._index_list, ZZ(self.k)))
return ZZ(len(self._index_list)).__pow__(self.k)


Tuples_sk = Tuples
Expand All @@ -151,10 +139,10 @@ class UnorderedTuples(Parent, UniqueRepresentation):

sage: S = [1,2]
sage: UnorderedTuples(S,3).list()
[[1, 1, 1], [1, 1, 2], [1, 2, 2], [2, 2, 2]]
[(1, 1, 1), (1, 1, 2), (1, 2, 2), (2, 2, 2)]
sage: UnorderedTuples(["a","b","c"],2).list()
[['a', 'a'], ['a', 'b'], ['a', 'c'], ['b', 'b'], ['b', 'c'],
['c', 'c']]
[('a', 'a'), ('a', 'b'), ('a', 'c'), ('b', 'b'), ('b', 'c'),
('c', 'c')]
"""
@staticmethod
def __classcall_private__(cls, S, k):
Expand All @@ -178,7 +166,7 @@ def __init__(self, S, k):
"""
self.S = S
self.k = k
self._index_list = [S.index(s) for s in S]
self._index_list = list(set(S.index(s) for s in S))
category = FiniteEnumeratedSets()
Parent.__init__(self, category=category)

Expand All @@ -191,19 +179,21 @@ def __repr__(self):
"""
return "Unordered tuples of %s of length %s" % (self.S, self.k)

def list(self):
def __iter__(self):
"""
EXAMPLES::

sage: S = [1,2]
sage: UnorderedTuples(S,3).list()
[[1, 1, 1], [1, 1, 2], [1, 2, 2], [2, 2, 2]]
[(1, 1, 1), (1, 1, 2), (1, 2, 2), (2, 2, 2)]
sage: UnorderedTuples(["a","b","c"],2).list()
[['a', 'a'], ['a', 'b'], ['a', 'c'], ['b', 'b'], ['b', 'c'],
['c', 'c']]
[('a', 'a'), ('a', 'b'), ('a', 'c'), ('b', 'b'), ('b', 'c'),
('c', 'c')]
sage: UnorderedTuples([1,1,2],3).list()
[(1, 1, 1), (1, 1, 2), (1, 2, 2), (2, 2, 2)]
"""
ans = libgap.UnorderedTuples(self._index_list, ZZ(self.k))
return [[self.S[i] for i in l] for l in ans]
for ans in combinations_with_replacement(self._index_list, self.k):
yield tuple(self.S[i] for i in ans)

def cardinality(self):
"""
Expand All @@ -213,7 +203,7 @@ def cardinality(self):
sage: UnorderedTuples(S,2).cardinality() # optional - sage.libs.gap
15
"""
return ZZ(libgap.NrUnorderedTuples(self._index_list, ZZ(self.k)))
return binomial(len(self._index_list) + self.k - 1, self.k)


UnorderedTuples_sk = UnorderedTuples
4 changes: 2 additions & 2 deletions src/sage/schemes/projective/projective_space.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2068,7 +2068,7 @@ def subscheme_from_Chow_form(self, Ch, dim):
L1 = []
for t in UnorderedTuples(list(range(n + 1)), dim + 1):
if all(t[i] < t[i + 1] for i in range(dim)):
L1.append(t)
L1.append(list(t))
# create the dual brackets
L2 = []
signs = []
Expand Down Expand Up @@ -2374,7 +2374,7 @@ def rational_points(self, bound=0):
for ai in R:
P[i] = ai
for tup in S[i - 1]:
if gcd([ai] + tup) == 1:
if gcd((ai,) + tup) == 1:
for j in range(i):
P[j] = tup[j]
pts.append(self(P))
Expand Down