File:Set partitions with complement relation between blocks.svg
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Summary
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Set partitions with a complement relationship between the blocks of equivalent elements Blocks mare marked with thick black rectangles. Complementary blocks are connected by red lines. The equations on the left describe the change that turns the last object into the next one. Such an object can be used to save equality and complement relationships between variables in Boolean algebra. The image illustrates the following test of such an object in Python. spc = SetPartComp([[3, 4], [5, 6, 7], [8, 9], [20, 30]], {(1, 2), (3, 8), (10, 11)})
spc.set_equal(2, 4)
assert spc == SetPartComp([[1, 8, 9], [2, 3, 4], [5, 6, 7], [20, 30]], {(1, 2), (10, 11)})
spc.set_comp(11, 20)
assert spc == SetPartComp([[1, 8, 9], [2, 3, 4], [5, 6, 7], [10, 20, 30]], {(1, 2), (10, 11)})
spc.set_comp(12, 30)
assert spc == SetPartComp([[1, 8, 9], [2, 3, 4], [5, 6, 7], [10, 20, 30], [11, 12]], {(1, 2), (10, 11)})
spc.set_equal(6, 13)
assert spc == SetPartComp([[1, 8, 9], [2, 3, 4], [5, 6, 7, 13], [10, 20, 30], [11, 12]], {(1, 2), (10, 11)})
spc.set_comp(3, 30)
assert spc == SetPartComp([[1, 8, 9, 10, 20, 30], [2, 3, 4, 11, 12], [5, 6, 7, 13]], {(1, 2)})
spc.set_comp(40, 50)
assert spc == SetPartComp([[1, 8, 9, 10, 20, 30], [2, 3, 4, 11, 12], [5, 6, 7, 13]], {(1, 2), (40, 50)})
spc.set_equal(60, 70)
assert spc == SetPartComp([[1, 8, 9, 10, 20, 30], [2, 3, 4, 11, 12], [5, 6, 7, 13], [60, 70]], {(1, 2), (40, 50)})
spc.set_comp(0, 70)
assert spc == SetPartComp([[1, 8, 9, 10, 20, 30], [2, 3, 4, 11, 12], [5, 6, 7, 13], [60, 70]], {(1, 2), (40, 50), (0, 60)})
spc.set_comp(0, 40)
assert spc == SetPartComp([[0, 50], [1, 8, 9, 10, 20, 30], [2, 3, 4, 11, 12], [5, 6, 7, 13], [40, 60, 70]], {(1, 2), (0, 40)})
spc.set_equal(0, 1)
assert spc == SetPartComp([[0, 1, 8, 9, 10, 20, 30, 50], [2, 3, 4, 11, 12, 40, 60, 70], [5, 6, 7, 13]], {(0, 2)})
spc.set_equal(2, 5)
assert spc == SetPartComp([[0, 1, 8, 9, 10, 20, 30, 50], [2, 3, 4, 5, 6, 7, 11, 12, 13, 40, 60, 70]], {(0, 2)})
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 16:14, 25 August 2020 | | 853 × 1,291 (728 KB) | Watchduck | Uploaded own work with UploadWizard |
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