mathtools.partition_integer_into_thirds — Abjad v1.1.1 documentation

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# mathtools.partition_integer_into_thirds

`abjad.tools.mathtools.` `partition_integer_into_thirds`(n, smallest='middle', biggest='middle')

  Partition positive integer n into `left, middle, right` parts.

  When `n % 3 == 0`, `left == middle == right`:

      abjad> mathtools.partition_integer_into_thirds(9)
      (3, 3, 3)

  When `n % 3 == 1`, set biggest part to biggest:

      abjad> maththools.partition_integer_into_thirds(10, biggest = 'left')
      (4, 3, 3)
      abjad> maththools.partition_integer_into_thirds(10, biggest = 'middle')
      (3, 4, 3)
      abjad> maththools.partition_integer_into_thirds(10, biggest = 'right')
      (3, 3, 4)

  When `n % 3 == 2`, set smallest part to smallest:

      abjad> maththools.partition_integer_into_thirds(11, smallest = 'left')
      (3, 4, 4)
      abjad> maththools.partition_integer_into_thirds(11, smallest = 'middle')
      (4, 3, 4)
      abjad> maththools.partition_integer_into_thirds(11, smallest = 'right')
      (4, 4, 3)

  Raise `TypeError` on noninteger n:

      abjad> mathtools.partition_integer_into_thirds(7.5)
      TypeError

  Raise `ValueError` on nonpositive n:

      abjad> mathtools.partition_integer_into_thirds(-1)
      ValueError

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