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src/sage/sets/recursively_enumerated_set.pyx

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@@ -22,8 +22,7 @@ AUTHORS:
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EXAMPLES:
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No hypothesis on the structure
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------------------------------
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.. RUBRIC:: No hypothesis on the structure
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What we mean by "no hypothesis" is that the set is not known
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to be a forest, symmetric, or graded. However, it may have other
@@ -50,8 +49,7 @@ Depth first search::
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sage: [next(it) for _ in range(10)]
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[0, 3, 6, 9, 12, 15, 18, 21, 24, 27]
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Symmetric structure
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-------------------
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.. RUBRIC:: Symmetric structure
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The origin ``(0, 0)`` as seed and the upper, lower, left and right lattice
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point as successor function. This function is symmetric since `p` is a
@@ -86,8 +84,7 @@ Levels (elements of given depth)::
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sage: sorted(C.graded_component(2))
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[(-2, 0), (-1, -1), (-1, 1), (0, -2), (0, 2), (1, -1), (1, 1), (2, 0)]
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Graded structure
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----------------
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.. RUBRIC:: Graded structure
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Identity permutation as seed and ``permutohedron_succ`` as successor
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function::
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sage: sorted(R.graded_component(10))
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[[5, 4, 3, 2, 1]]
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Forest structure
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----------------
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.. RUBRIC:: Forest structure [Ex 1]
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.. RUBRIC:: Forest structure (Example 1)
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The set of words over the alphabet `\{a,b\}` can be generated from the
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empty word by appending the letter `a` or `b` as a successor function. This set
@@ -175,20 +169,20 @@ classes being very similar):
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.. MATH::
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\begin{array}{ccc}
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& ``\," \\
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& \emptyset \\
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\hfil\swarrow & \downarrow & \searrow\hfil\\
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``a" & ``b" & ``c" \\
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a & b & c \\
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\begin{array}{ccc}
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\swarrow & \downarrow & \searrow \\
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``aa" & ``ab" & ``ac" \\
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aa & ab & ac \\
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\end{array} &
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\begin{array}{ccc}
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\swarrow & \downarrow & \searrow \\
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``ba" & ``bb" & ``bc" \\
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ba & bb & bc \\
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\end{array} &
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\begin{array}{ccc}
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\swarrow & \downarrow & \searrow \\
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``ca" & ``cb" & ``cc" \\
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ca & cb & cc \\
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\end{array}
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\end{array}
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@@ -230,7 +224,7 @@ or::
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sage: S.list()
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['', 'a', 'aa', 'ab', 'ac', 'b', 'ba', 'bb', 'bc', 'c', 'ca', 'cb', 'cc']
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.. RUBRIC:: Forest structure [Ex 2]
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.. RUBRIC:: Forest structure (Example 2)
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This example was provided by Florent Hivert.
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