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SetReplace.md

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Symbols and Functions >

SetReplace*

SetReplace (and related SetReplaceList, SetReplaceAll, SetReplaceFixedPoint and SetReplaceFixedPointList) are the functions the package is named after. They are quite simple, and perform replacement operations either one-at-a-time (as in the case of SetReplace), to all non-overlapping subsets (SetReplaceAll), or until no more matches can be made (SetReplaceFixedPoint). A suffix *List implies the function returns a list of sets after each step instead of just the final result.

These functions are good for their simplicity and can be primarily used to obtain replacement results. WolframModel is an advanced version of these functions and incorporates all of their features plus more sophisticated analysis capabilities.

As was mentioned previously, SetReplace performs a single iteration if called with two arguments:

In[] := SetReplace[set, rule]

For example,

In[] := SetReplace[{1, 2, 5, 3, 6}, {a_, b_} :> {a + b}]
Out[] = {5, 3, 6, 3}

It can be supplied a third argument specifying the number of replacements (the same can be achieved using Nest):

In[] := SetReplace[{1, 2, 5, 3, 6}, {a_, b_} :> {a + b}, 2]
Out[] = {6, 3, 8}

If the number of replacements is set to Infinity calling SetReplace is equivalent to SetReplaceFixedPoint:

In[] := SetReplace[{1, 2, 5, 3, 6}, {a_, b_} :> {a + b}, Infinity]
Out[] = {17}

It is possible to use multiple rules (here the replacements {1, 5} -> {5} and {2, 6} -> {8} are made):

In[] := SetReplace[{1, 2, 5, 3, 6},
 {{a_?EvenQ, b_?EvenQ} :> {a + b}, {a_?OddQ, b_?OddQ} :> {a b}}, 2]
Out[] = {3, 5, 8}

SetReplaceList can be used to see the set after each replacement (here a list is omitted on the right-hand side of the rule, which can be done if the subset only contains a single element). Similar to SetReplace, if the number of steps is Infinity, it's equivalent to SetReplaceFixedPointList:

In[] := SetReplaceList[{1, 2, 5, 3, 6}, {a_, b_} :> a + b, Infinity]
Out[] = {{1, 2, 5, 3, 6}, {5, 3, 6, 3}, {6, 3, 8}, {8, 9}, {17}}

SetReplaceAll replaces all non-overlapping subsets:

In[] := SetReplaceAll[{1, 2, 5, 3, 6}, {a_, b_} :> a + b]
Out[] = {6, 3, 8}

SetReplaceFixedPoint and SetReplaceFixedPointList perform replacements for as long as possible as previously mentioned:

In[] := SetReplaceFixedPoint[{1, 2, 5, 3, 6}, {a_, b_} :> a + b]
Out[] = {17}
In[] := SetReplaceFixedPointList[{1, 2, 5, 3, 6}, {a_, b_} :> a + b]
Out[] = {{1, 2, 5, 3, 6}, {5, 3, 6, 3}, {6, 3, 8}, {8, 9}, {17}}

All of these functions have Method , TimeConstraint and "EventOrderingFunction" options. TimeConstraint is self-explanatory. The other two work the same way as they do in WolframModel, and we describe them further in the WolframModel section.