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shorter doctests in finite monoids #35257

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Apr 1, 2023
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shorter doctests in finite monoids #35257

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20 changes: 10 additions & 10 deletions src/sage/categories/finite_monoids.py
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Original file line number Diff line number Diff line change
Expand Up @@ -144,20 +144,18 @@ def nerve(self):
sage: len(BSigma3.n_cells(3))
125

sage: BC3.homology(range(5), base_ring=GF(3))
sage: BC3.homology(range(4), base_ring=GF(3))
{0: Vector space of dimension 0 over Finite Field of size 3,
1: Vector space of dimension 1 over Finite Field of size 3,
2: Vector space of dimension 1 over Finite Field of size 3,
3: Vector space of dimension 1 over Finite Field of size 3,
4: Vector space of dimension 1 over Finite Field of size 3}
3: Vector space of dimension 1 over Finite Field of size 3}

sage: BC5 = groups.permutation.Cyclic(5).nerve()
sage: BC5.homology(range(5), base_ring=GF(5))
sage: BC5.homology(range(4), base_ring=GF(5))
{0: Vector space of dimension 0 over Finite Field of size 5,
1: Vector space of dimension 1 over Finite Field of size 5,
2: Vector space of dimension 1 over Finite Field of size 5,
3: Vector space of dimension 1 over Finite Field of size 5,
4: Vector space of dimension 1 over Finite Field of size 5}
3: Vector space of dimension 1 over Finite Field of size 5}
"""
from sage.topology.simplicial_set_examples import Nerve
return Nerve(self)
Expand Down Expand Up @@ -209,7 +207,7 @@ def rhodes_radical_congruence(self, base_ring=None):
res = []
for m in self:
for n in self:
if (m == n) or ((n, m) in res):
if m == n or (n, m) in res:
continue
try:
kSrad.retract(kS(m) - kS(n))
Expand All @@ -222,7 +220,7 @@ def rhodes_radical_congruence(self, base_ring=None):
class ElementMethods:
def pseudo_order(self):
r"""
Returns the pair `[k, j]` with `k` minimal and `0\leq j <k` such
Return the pair `[k, j]` with `k` minimal and `0\leq j <k` such
that ``self^k == self^j``.

Note that `j` is uniquely determined.
Expand Down Expand Up @@ -256,8 +254,10 @@ def pseudo_order(self):
sage: x.pseudo_order()
[2, 0]

TODO: more appropriate name? see, for example, Jean-Eric Pin's
lecture notes on semigroups.
.. TODO::

more appropriate name? see, for example, Jean-Eric Pin's
lecture notes on semigroups.
"""
self_powers = {self.parent().one(): 0}
k = 1
Expand Down