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Implement correct iteration through disjoint enumerated set for infinite set #39443

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Implement correct iteration through disjoint enumerated set for infinite set #39443

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9ec9af8
Implement correct iteration through disjoint enumerated set for infin…
user202729 Feb 4, 2025
2dd9b21
Handle the case where is_finite is not available
user202729 Feb 4, 2025
8a91beb
Fix tests
user202729 Feb 4, 2025
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2 changes: 1 addition & 1 deletion src/sage/categories/modules_with_basis.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2560,7 +2560,7 @@ def _an_element_(self):
B[()] + B[(1,2)] + 3*B[(1,2,3)] + 2*B[(1,3,2)]
sage: ABA = cartesian_product((A, B, A))
sage: ABA.an_element() # indirect doctest
2*B[(0, word: )] + 2*B[(0, word: a)] + 3*B[(0, word: b)]
2*B[(0, word: )] + 2*B[(1, ())] + 3*B[(1, (1,3,2))]
"""
from .cartesian_product import cartesian_product
return cartesian_product([module.an_element() for module in self.modules])
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18 changes: 9 additions & 9 deletions src/sage/combinat/root_system/root_lattice_realizations.py
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Original file line number Diff line number Diff line change
Expand Up @@ -694,14 +694,14 @@ def positive_roots(self, index_set=None):
sage: [PR.unrank(i) for i in range(10)] # needs sage.graphs
[alpha[1],
alpha[2],
alpha[0] + alpha[1] + alpha[2] + alpha[3],
alpha[3],
2*alpha[0] + 2*alpha[1] + 2*alpha[2] + 2*alpha[3],
alpha[1] + alpha[2],
3*alpha[0] + 3*alpha[1] + 3*alpha[2] + 3*alpha[3],
alpha[2] + alpha[3],
alpha[1] + alpha[2] + alpha[3],
alpha[0] + 2*alpha[1] + alpha[2] + alpha[3],
alpha[0] + alpha[1] + 2*alpha[2] + alpha[3],
alpha[0] + alpha[1] + alpha[2] + 2*alpha[3],
alpha[0] + 2*alpha[1] + 2*alpha[2] + alpha[3]]
4*alpha[0] + 4*alpha[1] + 4*alpha[2] + 4*alpha[3],
alpha[1] + alpha[2] + alpha[3]]
"""
if self.cartan_type().is_affine():
from sage.sets.disjoint_union_enumerated_sets \
Expand Down Expand Up @@ -798,18 +798,18 @@ def positive_real_roots(self):
sage: [PR.unrank(i) for i in range(5)] # needs sage.graphs
[alpha[1],
alpha[2],
2*alpha[0] + 2*alpha[1] + alpha[2],
alpha[1] + alpha[2],
2*alpha[1] + alpha[2],
alpha[0] + alpha[1] + alpha[2]]
4*alpha[0] + 4*alpha[1] + 2*alpha[2]]

sage: Q = RootSystem(['D',3,2]).root_lattice()
sage: PR = Q.positive_roots() # needs sage.graphs
sage: [PR.unrank(i) for i in range(5)] # needs sage.graphs
[alpha[1],
alpha[2],
alpha[0] + alpha[1] + alpha[2],
alpha[1] + 2*alpha[2],
alpha[1] + alpha[2],
alpha[0] + alpha[1] + 2*alpha[2]]
2*alpha[0] + 2*alpha[1] + 2*alpha[2]]
"""
if self.cartan_type().is_finite():
return tuple(RecursivelyEnumeratedSet(self.simple_roots(),
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126 changes: 112 additions & 14 deletions src/sage/sets/disjoint_union_enumerated_sets.py
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Original file line number Diff line number Diff line change
Expand Up @@ -392,32 +392,130 @@
"""
TESTS::

sage: from itertools import islice
sage: U4 = DisjointUnionEnumeratedSets(
....: Family(NonNegativeIntegers(), Permutations))
sage: it = iter(U4)
sage: [next(it), next(it), next(it), next(it), next(it), next(it)]
sage: list(islice(iter(U4), 6))
[[], [1], [1, 2], [2, 1], [1, 2, 3], [1, 3, 2]]

sage: # needs sage.combinat
sage: U4 = DisjointUnionEnumeratedSets(
....: Family(NonNegativeIntegers(), Permutations),
....: keepkey=True, facade=False)
sage: it = iter(U4)
sage: [next(it), next(it), next(it), next(it), next(it), next(it)]
[(0, []), (1, [1]), (2, [1, 2]), (2, [2, 1]), (3, [1, 2, 3]), (3, [1, 3, 2])]
sage: el = next(it); el.parent() == U4
True
sage: el.value == (3, Permutation([2,1,3]))
sage: l = list(islice(iter(U4), 7)); l
[(0, []), (1, [1]), (2, [1, 2]), (2, [2, 1]), (3, [1, 2, 3]), (3, [1, 3, 2]), (3, [2, 1, 3])]
sage: l[-1].parent() is U4
True

Check when both the set of keys and each element set is finite::

sage: list(DisjointUnionEnumeratedSets(
....: Family({1: FiniteEnumeratedSet([1,2,3]),
....: 2: FiniteEnumeratedSet([4,5,6])})))
[1, 2, 3, 4, 5, 6]

Check when the set of keys is finite but each element set is infinite::

sage: list(islice(DisjointUnionEnumeratedSets(
....: Family({1: NonNegativeIntegers(),
....: 2: NonNegativeIntegers()}), keepkey=True), 0, 10))
[(1, 0), (1, 1), (2, 0), (1, 2), (2, 1), (1, 3), (2, 2), (1, 4), (2, 3), (1, 5)]

Check when the set of keys is infinite but each element set is finite::

sage: list(islice(DisjointUnionEnumeratedSets(
....: Family(NonNegativeIntegers(), lambda x: FiniteEnumeratedSet(range(x))),
....: keepkey=True), 0, 20))
[(1, 0), (2, 0), (2, 1), (3, 0), (3, 1), (3, 2), (4, 0), (4, 1), (4, 2), (4, 3),
(5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (6, 0), (6, 1), (6, 2), (6, 3), (6, 4)]

Check when some element sets are empty (note that if there are infinitely many sets
but only finitely many elements in total, the iteration will hang)::

sage: list(DisjointUnionEnumeratedSets(
....: Family({1: FiniteEnumeratedSet([]),
....: 2: FiniteEnumeratedSet([]),
....: 3: FiniteEnumeratedSet([]),
....: 4: FiniteEnumeratedSet([]),
....: 5: FiniteEnumeratedSet([1,2,3]),
....: 6: FiniteEnumeratedSet([4,5,6])})))
[1, 2, 3, 4, 5, 6]

Check when there's one infinite set and infinitely many finite sets::

sage: list(islice(DisjointUnionEnumeratedSets(
....: Family(NonNegativeIntegers(), lambda x: FiniteEnumeratedSet([]) if x else NonNegativeIntegers())),
....: 0, 10))
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

The following cannot be determined to be finite, but the first elements can still be retrieved::

sage: U = DisjointUnionEnumeratedSets(
....: Family(NonNegativeIntegers(), lambda x: FiniteEnumeratedSet([] if x >= 2 else [1, 2])),
....: keepkey=True)
sage: list(U) # not tested
sage: list(islice(iter(U), 5)) # not tested, hangs
sage: list(islice(iter(U), 4))
[(0, 1), (0, 2), (1, 1), (1, 2)]
"""
for k in self._family.keys():
for el in self._family[k]:
def wrap_element(el, k):
nonlocal self
if self._keepkey:
el = (k, el)
if self._facade:
return el
else:
return self.element_class(self, el) # Bypass correctness tests

keys_iter = iter(self._family.keys())
if self._keepkey:
seen_keys = []
el_iters = []
while keys_iter is not None or el_iters:
if keys_iter is not None:
try:
k = next(keys_iter)
except StopIteration:
keys_iter = None
if keys_iter is not None:
el_set = self._family[k]
try:
is_finite = el_set.is_finite()
except (AttributeError, NotImplementedError):
is_finite = False
if is_finite:
for el in el_set:
yield wrap_element(el, k)
else:
el_iters.append(iter(el_set))
if self._keepkey:
seen_keys.append(k)
any_stopped = False
for i, obj in enumerate(zip(seen_keys, el_iters) if self._keepkey else el_iters):
if self._keepkey:
k, el_iter = obj
else:
k = None
el_iter = obj
try:
el = next(el_iter)
except StopIteration:
el_iters[i] = None
any_stopped = True
continue

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yield wrap_element(el, k)
if any_stopped:
if self._keepkey:
el = (k, el)
if self._facade:
yield el
filtered = [*zip(

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*[(k, el_iter) for k, el_iter in zip(seen_keys, el_iters) if el_iter is not None])]
if filtered:
seen_keys = list(filtered[0])
el_iters = list(filtered[1])

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else:
seen_keys = []
el_iters = []

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else:
yield self.element_class(self, el) # Bypass correctness tests
el_iters = [el_iter for el_iter in el_iters if el_iter is not None]

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def an_element(self):
"""
Expand Down
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