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-- Author: Lily Silverstein
doc ///
Key
sublists
(sublists, VisibleList, Function, Nothing)
(sublists, VisibleList, Function, Function, Function)
(sublists, VisibleList, Function)
(sublists, VisibleList, Function, Function)
(sublists, VisibleList, Function, Function, Nothing)
(sublists, VisibleList, Function, Nothing, Function)
(sublists, VisibleList, Function, Nothing, Nothing)
Headline
process interspersed subsequences of a visible list
Usage
sublists(L, f, g, h)
Inputs
L:VisibleList
f:Function
returning Boolean values
g:Function
which acts on VisibleLists,
applied to sublists of {\tt L} with {\tt f(i)} true for each {\tt i} in the sublist
h:Function
which acts on elements of {\tt L},
applied to the elements {\tt i} of {\tt L} with {\tt f(i)} false
Outputs
:List
the result obtained by applying {\tt g} to each of the
maximal nonempty sequences of consecutive elements with {\tt f} true,
and applying {\tt h} to the other elements
Description
Text
In the first example, consecutive odd elements are grouped
into sublists, while each even element is negated.
Example
L = {1,2,3,5,7,8,10,12,13,17,18,20,21};
sublists(L, odd, toList, minus)
Text
If {\tt g} or {\tt h} is omitted, the @TO identity@ function is
used in its place.
Example
sublists(L, odd, toList)
sublists(L, odd)
Text
The sublists will belong to the same class as {\tt L}.
Example
L = (1,2,3,5,7,8,10,12,13,17,18,20,21);
sublists(L, isPrime, , e -> 0)
Text
Note that {\tt g} acts on the {\em sublists}, not their elements.
Example
sublists(L, isPrime, plus, e -> 0)
Text
Because of the grouping of consecutive elements that return {\tt true} when input to {\tt f},
{\tt sublists(L, f, g, h)} is NOT the same as applying {\tt g} to elements returning {\tt true},
and applying {\tt h} to elements returning false. This could be achieved with a simple
@TO "if"@-then-else loop, or with @TO apply@.
Example
a = for l in L list if isPrime l then l else -10*l
b = apply(L, l -> if isPrime l then l else -10*l)
Text
On the other hand, if we want to group both "true" and "false" elements into sublists, we
can achieve this with a second call to {\tt sublists}, selecting those elements not already
grouped by the first {\tt sublists} command, {\em as long as the original list was not nested}.
Example
X = {1, 3, 5, 2, 4, 7, 1, 3, 4, 4, 5, 4, 7, 9, 13};
sublists(sublists(X, odd), i -> not instance(i, List))
SeeAlso
apply
partition
positions
select
"lists and sequences"
///
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