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Partition representations: Difference between revisions
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Partition representations (view source)
Revision as of 14:47, 7 October 2020
, 14:47, 7 October 2020→Target indices: Add BQN link
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A more rigorous approach is to allow the left argument to specify the [[index]] of the division to which the corresponding element belongs. In order for this to produce a partition, the left argument must be a vector of non-decreasing non-negative integers (as with the division endpoint representation). Then for a left argument <source lang=apl inline>l</source> the number of divisions is <source lang=apl inline>⊃⌽l</source>. | A more rigorous approach is to allow the left argument to specify the [[index]] of the division to which the corresponding element belongs. In order for this to produce a partition, the left argument must be a vector of non-decreasing non-negative integers (as with the division endpoint representation). Then for a left argument <source lang=apl inline>l</source> the number of divisions is <source lang=apl inline>⊃⌽l</source>. BQN's [[Group (BQN)|Group]] uses an extension of this representation. | ||
<source lang=apl> | <source lang=apl> | ||
1 1 3 3 3 3 6 part 'abcdefg' | 1 1 3 3 3 3 6 part 'abcdefg' | ||
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Because it interleaves elements from a vector with dividers, partitioning is closely related to the [[Mesh]] operation. In fact, a partition can be used to produce a mesh by prepending an element to each division and [[Raze]]ing: | Because it interleaves elements from a vector with dividers, partitioning is closely related to the [[Mesh]] operation. In fact, a partition can be used to produce a mesh by prepending an element to each division and [[Raze]]ing: | ||
<source lang=apl> | <source lang=apl> | ||
⎕←P | |||
┌┬──┬┬────┬┬┬─┐ | ┌┬──┬┬────┬┬┬─┐ | ||
││ab││cdef│││g│ | ││ab││cdef│││g│ | ||
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</source> | </source> | ||
In the above functions, the only difference in code is exchanging 0 and 1, and the only difference in output is an extra trailing 0 when computed from the division lengths. The mesh representation makes the partition representation duality especially clear, as the dual representation can be obtained simply by [[Not|negating]] the mesh vector. | In the above functions, the only difference in code is exchanging 0 and 1, and the only difference in output is an extra trailing 0 when computed from the division lengths. The mesh representation makes the partition representation duality especially clear, as the dual representation can be obtained simply by [[Not|negating]] the mesh vector. | ||
[[Category:Essays]] | |||