SegmentΒΆ

The Segment domain provides a generalized interval type.

Segments are created using the .. construct by indicating the (included) end points.

s := 3..10
  3..10
                           Type: Segment PositiveInteger

The first end point is called the lo and the second is called hi.

lo s
  3
                           Type: PositiveInteger

These names are used even though the end points might belong to an unordered set.

hi s
  10
                            Type: PositiveInteger

In addition to the end points, each segment has an integer “increment”. An increment can be specified using the “by” construct.

t := 10..3 by -2
  10..3 by - 2
                            Type: Segment PositiveInteger

This part can be obtained using the incr function.

incr s
  1
                            Type: PositiveInteger

Unless otherwise specified, the increment is 1.

incr t
  - 2
                            Type: Integer

A single value can be converted to a segment with equal end points. This happens if segments and single values are mixed in a list.

l := [1..3, 5, 9, 15..11 by -1]
  [1..3,5..5,9..9,15..11 by - 1]
                             Type: List Segment PositiveInteger

If the underlying type is an ordered ring, it is possible to perform additional operations. The expand operation creates a list of points in a segment.

expand s
  [3,4,5,6,7,8,9,10]
                             Type: List Integer

If k > 0, then expand(l..h by k) creates the list [l, l+k, ..., lN] where lN <= h < lN+k. If k < 0, then lN >= h > lN+k.

expand t
  [10,8,6,4]
                             Type: List Integer

It is also possible to expand a list of segments. This is equivalent to appending lists obtained by expanding each segment individually.

expand l
  [1,2,3,5,9,15,14,13,12,11]
                              Type: List Integer

See Also:

  • )help UniversalSegment
  • )help SegmentBinding
  • )show Segment

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