sublists -- process interspersed subsequences of a visible list

Usage:

sublists(L, f, g, h)
Inputs:
- L, a visible list,
- f, a function, returning Boolean values
- g, a function, which acts on VisibleLists, applied to sublists of L with f(i) true for each i in the sublist
- h, a function, which acts on elements of L, applied to the elements i of L with f(i) false
Outputs:
- a list, the result obtained by applying g to each of the maximal nonempty sequences of consecutive elements with f true, and applying h to the other elements

Description

In the first example, consecutive odd elements are grouped into sublists, while each even element is negated.

i1 : L = {1,2,3,5,7,8,10,12,13,17,18,20,21};

i2 : sublists(L, odd, toList, minus)

o2 = {{1}, -2, {3, 5, 7}, -8, -10, -12, {13, 17}, -18, -20, {21}}

o2 : List

If g or h is omitted, the identity function is used in its place.

i3 : sublists(L, odd, toList)

o3 = {{1}, 2, {3, 5, 7}, 8, 10, 12, {13, 17}, 18, 20, {21}}

o3 : List

i4 : sublists(L, odd)

o4 = {{1}, 2, {3, 5, 7}, 8, 10, 12, {13, 17}, 18, 20, {21}}

o4 : List

The sublists will belong to the same class as L.

i5 : L = (1,2,3,5,7,8,10,12,13,17,18,20,21);

i6 : sublists(L, isPrime, , e -> 0)

o6 = {0, (2, 3, 5, 7), 0, 0, 0, (13, 17), 0, 0, 0}

o6 : List

Note that g acts on the sublists, not their elements.

i7 : sublists(L, isPrime, plus, e -> 0)

o7 = {0, 17, 0, 0, 0, 30, 0, 0, 0}

o7 : List

Because of the grouping of consecutive elements that return true when input to f, sublists(L, f, g, h) is NOT the same as applying g to elements returning true, and applying h to elements returning false. This could be achieved with a simple if-then-else loop, or with apply.

i8 : a = for l in L list if isPrime l then l else -10*l

o8 = {-10, 2, 3, 5, 7, -80, -100, -120, 13, 17, -180, -200, -210}

o8 : List

i9 : b = apply(L, l -> if isPrime l then l else -10*l)

o9 = (-10, 2, 3, 5, 7, -80, -100, -120, 13, 17, -180, -200, -210)

o9 : Sequence

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 sublists, selecting those elements not already grouped by the first sublists command, as long as the original list was not nested.

i10 : X = {1, 3, 5, 2, 4, 7, 1, 3, 4, 4, 5, 4, 7, 9, 13};

i11 : sublists(sublists(X, odd), i -> not instance(i, List))

o11 = {{1, 3, 5}, {2, 4}, {7, 1, 3}, {4, 4}, {5}, {4}, {7, 9, 13}}

o11 : List

Ways to use sublists:

sublists(VisibleList,Function)
sublists(VisibleList,Function,Function)
sublists(VisibleList,Function,Function,Function)
sublists(VisibleList,Function,Function,Nothing)
sublists(VisibleList,Function,Nothing)
sublists(VisibleList,Function,Nothing,Function)
sublists(VisibleList,Function,Nothing,Nothing)

For the programmer

The object sublists is a method function.

The source of this document is in Macaulay2Doc/functions/sublists-doc.m2:76:0.

sublists -- process interspersed subsequences of a visible list

Description

See also

Ways to use sublists:

For the programmer