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expand and explain doctest of _preprocess_intertwining_relations #39310

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expand and explain doctest of _preprocess_intertwining_relations #39310

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expand and explain doctest of _preprocess_intertwining_relations
mantepse Jan 10, 2025
7d53e28
correct backticks
mantepse Jan 17, 2025
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21 changes: 16 additions & 5 deletions src/sage/combinat/bijectionist.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2124,11 +2124,6 @@
In particular, if `P` consists only if singletons, this
method has no effect.

.. TODO::

create one test with one and one test with two
intertwining relations

.. TODO::

it is not clear whether this method makes sense
Expand All @@ -2144,6 +2139,17 @@
sage: bij._P
{{'a'}, {'b'}, {'c'}, {'d'}}

However, adding that ``'a'`` and ``'c'`` are in the same block,
we can infer that also ``'b'`` and ``'d'`` are in the same
block::

sage: bij.set_constant_blocks([['a', 'c']])
sage: bij._P
{{'a', 'c'}, {'b'}, {'d'}}
sage: bij._preprocess_intertwining_relations()
sage: bij._P
{{'a', 'c'}, {'b', 'd'}}

Let a group act on permutations::

sage: A = B = Permutations(3)
Expand All @@ -2152,6 +2158,11 @@
sage: bij._preprocess_intertwining_relations()
sage: bij._P
{{[1, 2, 3]}, {[1, 3, 2]}, {[2, 1, 3]}, {[2, 3, 1]}, {[3, 1, 2]}, {[3, 2, 1]}}

Thus, in this case we do not detect the constant blocks::

sage: bij.constant_blocks(optimal=True)
{{[1, 2, 3], [3, 2, 1]}, {[1, 3, 2], [2, 3, 1]}, {[2, 1, 3], [3, 1, 2]}}
"""
A = self._A
P = self._P
Expand Down Expand Up @@ -3119,7 +3130,7 @@
sage: bij = Bijectionist(sum(As, []), sum(Bs, []))
sage: bij.set_statistics((lambda x: x[0], lambda x: x[0]))
sage: bij.set_intertwining_relations((2, c1, c1), (1, c2, c2))
sage: l = list(bij.solutions_iterator()); len(l) # long time -- (2.7 seconds with SCIP on AMD Ryzen 5 PRO 3500U w/ Radeon Vega Mobile Gfx)

Check warning on line 3133 in src/sage/combinat/bijectionist.py

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GitHub Actions / test-long (src/sage/[a-f]*)

Warning: slow doctest: 

slow doctest:
64

A brute force check would be difficult::
Expand Down Expand Up @@ -3147,7 +3158,7 @@
sage: A = sum(As, [])
sage: respects_c1 = lambda s: all(c1(a1, a2) not in A or s[c1(a1, a2)] == c1(s[a1], s[a2]) for a1 in A for a2 in A)
sage: respects_c2 = lambda s: all(c2(a1) not in A or s[c2(a1)] == c2(s[a1]) for a1 in A)
sage: l2 = [s for s in it if respects_c1(s) and respects_c2(s)] # long time -- (17 seconds on AMD Ryzen 5 PRO 3500U w/ Radeon Vega Mobile Gfx)

Check warning on line 3161 in src/sage/combinat/bijectionist.py

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Warning: slow doctest: 

slow doctest:
sage: sorted(l1, key=lambda s: tuple(s.items())) == l2 # long time
True

Expand Down
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