EventDeduplication.md

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"EventDeduplication"

Some rules can match the same set of inputs in different ways. For example, consider the rule {{a, b}, {a, c}} -> {{b, c}} starting with an initial condition {{1, 2}, {1, 3}}. There are two possible ways to match it: <|a -> 1, b -> 2, c -> 3|> and <|a -> 1, b -> 3, c -> 2|>. In this case, these matches yield different results, {2, 3} and {3, 2} respectively:

In[] := WolframModel[{{a, b}, {a, c}} -> {{b, c}}, {{1, 2}, {1, 3}},
  "EventSelectionFunction" ->
   "MultiwaySpacelike"]["ExpressionsEventsGraph",
 VertexLabels -> Automatic]

In the case above the outputs are different, however sometimes they are the same (more precisely, isomorphic):

In[] := WolframModel[{{a, b}, {a, c}} -> {{b, c}, {c, b}}, {{1, 2}, {1, 3}},
  "EventSelectionFunction" ->
   "MultiwaySpacelike"]["ExpressionsEventsGraph",
 VertexLabels -> Automatic]

EventDeduplication option can be used in a case like this to combine these two identical events into one:

In[] := WolframModel[{{a, b}, {a, c}} -> {{b, c}, {c, b}}, {{1, 2}, {1, 3}},
  "EventSelectionFunction" -> "MultiwaySpacelike",
  "EventDeduplication" -> "SameInputSetIsomorphicOutputs"]["ExpressionsEventsGraph",
 VertexLabels -> Automatic]

The outputs of the rule need not be identical, but should be isomorphic with respect to renaming of new atoms:

In[] := WolframModel[{{a, b}, {a, c}} -> {{b, d}, {c, d}}, {{1, 2}, {1, 3}},
  "EventSelectionFunction" -> "MultiwaySpacelike",
  "EventDeduplication" -> "SameInputSetIsomorphicOutputs"]["ExpressionsEventsGraph",
 VertexLabels -> Automatic]