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Matthias Koeppe
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‎src/sage/combinat/designs/database.py

Lines changed: 7 additions & 8 deletions
Original file line numberDiff line numberDiff line change
@@ -768,8 +768,8 @@ def OA_9_120():
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sage: from sage.combinat.designs.designs_pyx import is_orthogonal_array
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sage: from sage.combinat.designs.database import OA_9_120
771-
sage: OA = OA_9_120() # optional - sage.modules
772-
sage: is_orthogonal_array(OA,9,120,2) # optional - sage.modules
771+
sage: OA = OA_9_120() # optional - sage.modules sage.schemes
772+
sage: is_orthogonal_array(OA,9,120,2) # optional - sage.modules sage.schemes
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True
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The design is available from the general constructor::
@@ -828,8 +828,7 @@ def OA_9_135():
828828
As this orthogonal array requires a `(273,17,1)` cyclic difference set, we check that
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it is available::
830830
831-
sage: G,D = designs.difference_family(273,17,1)
832-
sage: G
831+
sage: G,D = designs.difference_family(273,17,1); G # optional - sage.libs.pari
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Ring of integers modulo 273
834833
"""
835834
from .bibd import BIBD_from_difference_family
@@ -1837,7 +1836,7 @@ def OA_14_524():
18371836
18381837
The design is available from the general constructor::
18391838
1840-
sage: designs.orthogonal_arrays.is_available(14,524)
1839+
sage: designs.orthogonal_arrays.is_available(14,524) # optional - sage.schemes
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True
18421841
"""
18431842
return OA_520_plus_x(4)
@@ -2432,7 +2431,7 @@ def QDM_57_9_1_1_8():
24322431
sage: from sage.combinat.designs.database import QDM_57_9_1_1_8
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sage: from sage.combinat.designs.designs_pyx import is_quasi_difference_matrix
24342433
sage: G,M = QDM_57_9_1_1_8()
2435-
sage: is_quasi_difference_matrix(M,G,9,1,1,8)
2434+
sage: is_quasi_difference_matrix(M,G,9,1,1,8) # optional - sage.schemes
24362435
True
24372436
"""
24382437
from sage.rings.finite_rings.integer_mod_ring import IntegerModRing as G
@@ -3271,7 +3270,7 @@ def DM_28_6_1():
32713270
32723271
Can be obtained from the constructor::
32733272
3274-
sage: _ = designs.difference_matrix(28,6) # optional - sage.modules
3273+
sage: _ = designs.difference_matrix(28,6) # optional - sage.libs.pari sage.modules
32753274
"""
32763275
z=2
32773276
M = [
@@ -3388,7 +3387,7 @@ def DM_36_9_1():
33883387
33893388
Can be obtained from the constructor::
33903389
3391-
sage: _ = designs.difference_matrix(36,9) # optional - sage.modules
3390+
sage: _ = designs.difference_matrix(36,9) # optional - sage.libs.pari sage.modules
33923391
"""
33933392
M = [
33943393
[(0,0,0,0), (0,0,0,0), (0,0,0,0), (0,0,0,0), (0,0,0,0), (0,0,0,0), (0,0,0,0), (0,0,0,0), (0,0,0,0), (0,0,0,0), (0,0,0,0), (0,0,0,0)],

‎src/sage/combinat/designs/difference_family.py

Lines changed: 20 additions & 20 deletions
Original file line numberDiff line numberDiff line change
@@ -5,7 +5,7 @@
55
This module gathers everything related to difference families. One can build a
66
difference family (or check that it can be built) with :func:`difference_family`::
77
8-
sage: G,F = designs.difference_family(13,4,1) # optional - sage.modules
8+
sage: G,F = designs.difference_family(13,4,1) # optional - sage.libs.pari sage.modules
99
1010
It defines the following functions:
1111
@@ -1564,15 +1564,15 @@ def is_relative_difference_set(R, G, H, params, verbose=False):
15641564
sage: from sage.combinat.designs.difference_family import _get_submodule_of_order, relative_difference_set_from_m_sequence, is_relative_difference_set
15651565
sage: q, N = 5, 2
15661566
sage: params = ((q^N-1) // (q-1), q - 1, q^(N-1), q^(N-2))
1567-
sage: G, R = relative_difference_set_from_m_sequence(q, N, return_group=True) # optional - sage.modules
1568-
sage: H = _get_submodule_of_order(G, q - 1) # optional - sage.modules
1569-
sage: is_relative_difference_set(R, G, H, params) # optional - sage.modules
1567+
sage: G, R = relative_difference_set_from_m_sequence(q, N, return_group=True) # optional - sage.libs.pari sage.modules
1568+
sage: H = _get_submodule_of_order(G, q - 1) # optional - sage.libs.pari sage.modules
1569+
sage: is_relative_difference_set(R, G, H, params) # optional - sage.libs.pari sage.modules
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True
15711571
15721572
If we pass the ``verbose`` argument, the function will explain why it failed::
15731573
1574-
sage: R2 = [G[1], G[2], G[3], G[5], G[6]] # optional - sage.modules
1575-
sage: is_relative_difference_set(R2, G, H, params, verbose=True) # optional - sage.modules
1574+
sage: R2 = [G[1], G[2], G[3], G[5], G[6]] # optional - sage.libs.pari sage.modules
1575+
sage: is_relative_difference_set(R2, G, H, params, verbose=True) # optional - sage.libs.pari sage.modules
15761576
There is a value in the difference set which is not repeated d times
15771577
False
15781578
"""
@@ -1741,7 +1741,7 @@ def supplementary_difference_set_from_rel_diff_set(q, existence=False, check=Tru
17411741
EXAMPLES::
17421742
17431743
sage: from sage.combinat.designs.difference_family import supplementary_difference_set_from_rel_diff_set
1744-
sage: supplementary_difference_set_from_rel_diff_set(17) #random
1744+
sage: supplementary_difference_set_from_rel_diff_set(17) #random # optional - sage.libs.pari
17451745
(Additive abelian group isomorphic to Z/16,
17461746
[[(1), (5), (6), (7), (9), (13), (14), (15)],
17471747
[(0), (2), (3), (5), (6), (10), (11), (13), (14)],
@@ -1750,39 +1750,39 @@ def supplementary_difference_set_from_rel_diff_set(q, existence=False, check=Tru
17501750
17511751
If ``existence=True``, the function returns a boolean::
17521752
1753-
sage: supplementary_difference_set_from_rel_diff_set(7, existence=True)
1753+
sage: supplementary_difference_set_from_rel_diff_set(7, existence=True) # optional - sage.libs.pari
17541754
False
1755-
sage: supplementary_difference_set_from_rel_diff_set(17, existence=True)
1755+
sage: supplementary_difference_set_from_rel_diff_set(17, existence=True) # optional - sage.libs.pari
17561756
True
17571757
17581758
TESTS::
17591759
17601760
sage: from sage.combinat.designs.difference_family import is_supplementary_difference_set
1761-
sage: G, sets = supplementary_difference_set_from_rel_diff_set(17, check=False)
1762-
sage: is_supplementary_difference_set(sets, lmbda=16, G=G)
1761+
sage: G, sets = supplementary_difference_set_from_rel_diff_set(17, check=False) # optional - sage.libs.pari
1762+
sage: is_supplementary_difference_set(sets, lmbda=16, G=G) # optional - sage.libs.pari
17631763
True
1764-
sage: G, sets = supplementary_difference_set_from_rel_diff_set(9, check=False)
1765-
sage: is_supplementary_difference_set(sets, lmbda=8, G=G)
1764+
sage: G, sets = supplementary_difference_set_from_rel_diff_set(9, check=False) # optional - sage.libs.pari
1765+
sage: is_supplementary_difference_set(sets, lmbda=8, G=G) # optional - sage.libs.pari
17661766
True
1767-
sage: supplementary_difference_set_from_rel_diff_set(7)
1767+
sage: supplementary_difference_set_from_rel_diff_set(7) # optional - sage.libs.pari
17681768
Traceback (most recent call last):
17691769
...
17701770
ValueError: There is no s for which m-1 is an odd prime power
1771-
sage: supplementary_difference_set_from_rel_diff_set(8)
1771+
sage: supplementary_difference_set_from_rel_diff_set(8) # optional - sage.libs.pari
17721772
Traceback (most recent call last):
17731773
...
17741774
ValueError: q must be an odd prime power
1775-
sage: supplementary_difference_set_from_rel_diff_set(8, existence=True)
1775+
sage: supplementary_difference_set_from_rel_diff_set(8, existence=True) # optional - sage.libs.pari
17761776
False
1777-
sage: supplementary_difference_set_from_rel_diff_set(7, existence=True)
1777+
sage: supplementary_difference_set_from_rel_diff_set(7, existence=True) # optional - sage.libs.pari
17781778
False
1779-
sage: supplementary_difference_set_from_rel_diff_set(1, existence=True)
1779+
sage: supplementary_difference_set_from_rel_diff_set(1, existence=True) # optional - sage.libs.pari
17801780
False
17811781
17821782
Check that the function works even when s > 1::
17831783
1784-
sage: G, sets = supplementary_difference_set_from_rel_diff_set(353, check=False) #long time
1785-
sage: is_supplementary_difference_set(sets, lmbda=352, G=G) #long time
1784+
sage: G, sets = supplementary_difference_set_from_rel_diff_set(353, check=False) # long time, optional - sage.libs.pari
1785+
sage: is_supplementary_difference_set(sets, lmbda=352, G=G) # long time, optional - sage.libs.pari
17861786
True
17871787
17881788
.. SEEALSO::

‎src/sage/combinat/designs/incidence_structures.py

Lines changed: 7 additions & 6 deletions
Original file line numberDiff line numberDiff line change
@@ -458,14 +458,15 @@ def is_isomorphic(self, other, certificate=False):
458458
incidentally computes their canonical label (if necessary). Thus,
459459
subsequent calls to :meth:`is_isomorphic` will be faster::
460460
461-
sage: IS1 = designs.projective_plane(3)
462-
sage: IS2 = IS1.relabel(Permutations(IS1.ground_set()).random_element(), inplace=False)
463-
sage: IS2 = IncidenceStructure(IS2.blocks())
464-
sage: IS1._canonical_label is None and IS2._canonical_label is None
461+
sage: IS1 = designs.projective_plane(3) # optional - sage.schemes
462+
sage: IS2 = IS1.relabel(Permutations(IS1.ground_set()).random_element(), # optional - sage.schemes
463+
....: inplace=False)
464+
sage: IS2 = IncidenceStructure(IS2.blocks()) # optional - sage.schemes
465+
sage: IS1._canonical_label is None and IS2._canonical_label is None # optional - sage.schemes
465466
True
466-
sage: IS1.is_isomorphic(IS2)
467+
sage: IS1.is_isomorphic(IS2) # optional - sage.schemes
467468
True
468-
sage: IS1._canonical_label is None or IS2._canonical_label is None
469+
sage: IS1._canonical_label is None or IS2._canonical_label is None # optional - sage.schemes
469470
False
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471472
"""

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