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sagemath#39287: fix doctest in sage/matroids/chow_ring.py
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‎src/sage/matroids/chow_ring.py‎

Lines changed: 40 additions & 37 deletions
Original file line numberDiff line numberDiff line change
@@ -245,12 +245,14 @@ def lefschetz_element(self):
245245
....: basis_deg[deg].append(b)
246246
....:
247247
sage: basis_deg
248-
{0: [1], 1: [A02, A12, A01, A012, A03, A13, A013, A23, A023,
249-
A123, A04, A14, A014, A24, A024, A124, A34, A034, A134, A234,
250-
A01234], 2: [A02*A01234, A12*A01234, A01*A01234, A012^2,
251-
A03*A01234, A13*A01234, A013^2, A23*A01234, A023^2, A123^2,
252-
A04*A01234, A14*A01234, A014^2, A24*A01234, A024^2, A124^2,
253-
A34*A01234, A034^2, A134^2, A234^2, A01234^2], 3: [A01234^3]}
248+
{0: [1],
249+
1: [A01, A12, A02, A012, A23, A13, A123, A03, A013, A023, A34, A24,
250+
A234, A14, A124, A134, A04, A014, A024, A034, A01234],
251+
2: [A01*A01234, A12*A01234, A02*A01234, A012^2, A23*A01234,
252+
A13*A01234, A123^2, A03*A01234, A013^2, A023^2, A34*A01234,
253+
A24*A01234, A234^2, A14*A01234, A124^2, A134^2, A04*A01234,
254+
A014^2, A024^2, A034^2, A01234^2],
255+
3: [A01234^3]}
254256
sage: g_eq_maps = {}
255257
sage: lefschetz_el = ch.lefschetz_element(); lefschetz_el
256258
-2*A01 - 2*A02 - 2*A03 - 2*A04 - 2*A12 - 2*A13 - 2*A14 - 2*A23
@@ -262,37 +264,38 @@ def lefschetz_element(self):
262264
....: g_eq_maps[deg].extend([i*lefschetz_el for i in basis_deg[deg]])
263265
....:
264266
sage: g_eq_maps
265-
{0: [-2*A01 - 2*A02 - 2*A03 - 2*A04 - 2*A12 - 2*A13 - 2*A14
266-
- 2*A23 - 2*A24 - 2*A34 - 6*A012 - 6*A013 - 6*A014 - 6*A023
267-
- 6*A024 - 6*A034 - 6*A123 - 6*A124 - 6*A134 - 6*A234
268-
- 20*A01234], 1: [2*A012^2 + 2*A023^2 + 2*A024^2
269-
- 10*A02*A01234 + 2*A01234^2, 2*A012^2 + 2*A123^2 + 2*A124^2
270-
- 10*A12*A01234 + 2*A01234^2, 2*A012^2 + 2*A013^2 + 2*A014^2
271-
- 10*A01*A01234 + 2*A01234^2, -6*A012^2 + 2*A01*A01234
272-
+ 2*A02*A01234 + 2*A12*A01234, 2*A013^2 + 2*A023^2 + 2*A034^2
273-
- 10*A03*A01234 + 2*A01234^2, 2*A013^2 + 2*A123^2 + 2*A134^2
274-
- 10*A13*A01234 + 2*A01234^2, -6*A013^2 + 2*A01*A01234
275-
+ 2*A03*A01234 + 2*A13*A01234, 2*A023^2 + 2*A123^2 + 2*A234^2
276-
- 10*A23*A01234 + 2*A01234^2, -6*A023^2 + 2*A02*A01234
277-
+ 2*A03*A01234 + 2*A23*A01234, -6*A123^2 + 2*A12*A01234
278-
+ 2*A13*A01234 + 2*A23*A01234, 2*A014^2 + 2*A024^2 + 2*A034^2
279-
- 10*A04*A01234 + 2*A01234^2, 2*A014^2 + 2*A124^2 + 2*A134^2
280-
- 10*A14*A01234 + 2*A01234^2, -6*A014^2 + 2*A01*A01234
281-
+ 2*A04*A01234 + 2*A14*A01234, 2*A024^2 + 2*A124^2 + 2*A234^2
282-
- 10*A24*A01234 + 2*A01234^2, -6*A024^2 + 2*A02*A01234
283-
+ 2*A04*A01234 + 2*A24*A01234, -6*A124^2 + 2*A12*A01234
284-
+ 2*A14*A01234 + 2*A24*A01234, 2*A034^2 + 2*A134^2 + 2*A234^2
285-
- 10*A34*A01234 + 2*A01234^2, -6*A034^2 + 2*A03*A01234
286-
+ 2*A04*A01234 + 2*A34*A01234, -6*A134^2 + 2*A13*A01234
287-
+ 2*A14*A01234 + 2*A34*A01234, -6*A234^2 + 2*A23*A01234
288-
+ 2*A24*A01234 + 2*A34*A01234, -2*A01*A01234 - 2*A02*A01234
289-
- 2*A03*A01234 - 2*A04*A01234 - 2*A12*A01234 - 2*A13*A01234
290-
- 2*A14*A01234 - 2*A23*A01234 - 2*A24*A01234 - 2*A34*A01234
291-
- 20*A01234^2], 2: [2*A01234^3, 2*A01234^3, 2*A01234^3,
292-
6*A01234^3, 2*A01234^3, 2*A01234^3, 6*A01234^3, 2*A01234^3,
293-
6*A01234^3, 6*A01234^3, 2*A01234^3, 2*A01234^3, 6*A01234^3,
294-
2*A01234^3, 6*A01234^3, 6*A01234^3, 2*A01234^3, 6*A01234^3,
295-
6*A01234^3, 6*A01234^3, -20*A01234^3], 3: [0]}
267+
{0: [-2*A01 - 2*A02 - 2*A03 - 2*A04 - 2*A12 - 2*A13 - 2*A14 - 2*A23
268+
- 2*A24 - 2*A34 - 6*A012 - 6*A013 - 6*A014 - 6*A023 - 6*A024
269+
- 6*A034 - 6*A123 - 6*A124 - 6*A134 - 6*A234 - 20*A01234],
270+
1: [2*A012^2 + 2*A013^2 + 2*A014^2 - 10*A01*A01234 + 2*A01234^2,
271+
2*A012^2 + 2*A123^2 + 2*A124^2 - 10*A12*A01234 + 2*A01234^2,
272+
2*A012^2 + 2*A023^2 + 2*A024^2 - 10*A02*A01234 + 2*A01234^2,
273+
-6*A012^2 + 2*A01*A01234 + 2*A02*A01234 + 2*A12*A01234,
274+
2*A023^2 + 2*A123^2 + 2*A234^2 - 10*A23*A01234 + 2*A01234^2,
275+
2*A013^2 + 2*A123^2 + 2*A134^2 - 10*A13*A01234 + 2*A01234^2,
276+
-6*A123^2 + 2*A12*A01234 + 2*A13*A01234 + 2*A23*A01234,
277+
2*A013^2 + 2*A023^2 + 2*A034^2 - 10*A03*A01234 + 2*A01234^2,
278+
-6*A013^2 + 2*A01*A01234 + 2*A03*A01234 + 2*A13*A01234,
279+
-6*A023^2 + 2*A02*A01234 + 2*A03*A01234 + 2*A23*A01234,
280+
2*A034^2 + 2*A134^2 + 2*A234^2 - 10*A34*A01234 + 2*A01234^2,
281+
2*A024^2 + 2*A124^2 + 2*A234^2 - 10*A24*A01234 + 2*A01234^2,
282+
-6*A234^2 + 2*A23*A01234 + 2*A24*A01234 + 2*A34*A01234,
283+
2*A014^2 + 2*A124^2 + 2*A134^2 - 10*A14*A01234 + 2*A01234^2,
284+
-6*A124^2 + 2*A12*A01234 + 2*A14*A01234 + 2*A24*A01234,
285+
-6*A134^2 + 2*A13*A01234 + 2*A14*A01234 + 2*A34*A01234,
286+
2*A014^2 + 2*A024^2 + 2*A034^2 - 10*A04*A01234 + 2*A01234^2,
287+
-6*A014^2 + 2*A01*A01234 + 2*A04*A01234 + 2*A14*A01234,
288+
-6*A024^2 + 2*A02*A01234 + 2*A04*A01234 + 2*A24*A01234,
289+
-6*A034^2 + 2*A03*A01234 + 2*A04*A01234 + 2*A34*A01234,
290+
-2*A01*A01234 - 2*A02*A01234 - 2*A03*A01234 - 2*A04*A01234
291+
- 2*A12*A01234 - 2*A13*A01234 - 2*A14*A01234 - 2*A23*A01234
292+
- 2*A24*A01234 - 2*A34*A01234 - 20*A01234^2],
293+
2: [2*A01234^3, 2*A01234^3, 2*A01234^3, 6*A01234^3, 2*A01234^3,
294+
2*A01234^3, 6*A01234^3, 2*A01234^3, 6*A01234^3, 6*A01234^3,
295+
2*A01234^3, 2*A01234^3, 6*A01234^3, 2*A01234^3, 6*A01234^3,
296+
6*A01234^3, 2*A01234^3, 6*A01234^3, 6*A01234^3, 6*A01234^3,
297+
-20*A01234^3],
298+
3: [0]}
296299
"""
297300
w = sum(len(F) * (len(self.matroid().groundset()) - len(F)) * gen
298301
for F, gen in self.defining_ideal().flats_to_generator_dict().items())

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