@@ -2450,23 +2450,25 @@ def is_regular(self):
24502450
24512451 EXAMPLES:
24522452
2453- This is the mother of all examples, which is not regular (see Section
2454- 7.1.1 in [DLRS2010]_)::
2453+ This is the mother of all examples (see Section 7.1.1 in
2454+ [DLRS2010]_)::
2455+
2456+ sage: def mother(epsilon=0):
2457+ ....: rays = [(4-epsilon,epsilon,0),(0,4-epsilon,epsilon),(epsilon,0,4-epsilon),(2,1,1),(1,2,1),(1,1,2),(-1,-1,-1)]
2458+ ....: L = [(0,1,4),(0,3,4),(1,2,5),(1,4,5),(0,2,3),(2,3,5),(3,4,5),(6,0,1),(6,1,2),(6,2,0)]
2459+ ....: S1 = [Cone([rays[i] for i in indices]) for indices in L]
2460+ ....: return Fan(S1)
2461+
2462+ When epsilon=0, it is not regular::
24552463
24562464 sage: epsilon = 0
2457- sage: rays = [(4-epsilon,epsilon,0),(0,4-epsilon,epsilon),(epsilon,0,4-epsilon),(2,1,1),(1,2,1),(1,1,2),(-1,-1,-1)]
2458- sage: S1 = [Cone([rays[i] for i in indices]) for indices in [(0,1,4),(0,3,4),(1,2,5),(1,4,5),(0,2,3),(2,3,5),(3,4,5),(6,0,1),(6,1,2),(6,2,0)]]
2459- sage: mother = Fan(S1)
2460- sage: mother.is_regular()
2465+ sage: mother(epsilon).is_regular()
24612466 False
24622467
24632468 Doing a slight perturbation makes the same subdivision regular::
24642469
24652470 sage: epsilon = 1/2
2466- sage: rays = [(4-epsilon,epsilon,0),(0,4-epsilon,epsilon),(epsilon,0,4-epsilon),(2,1,1),(1,2,1),(1,1,2),(-1,-1,-1)]
2467- sage: S1 = [Cone([rays[i] for i in indices]) for indices in [(0,1,4),(0,3,4),(1,2,5),(1,4,5),(0,2,3),(2,3,5),(3,4,5),(6,0,1),(6,1,2),(6,2,0)]]
2468- sage: mother = Fan(S1)
2469- sage: mother.is_regular()
2471+ sage: mother(epsilon).is_regular()
24702472 True
24712473
24722474 .. SEEALSO::
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