MultiwayQ property (#503)

## Changes * Adds a new `WolframModelEvolutionObject` property, `"MultiwayQ"`, which checks if any expressions were destroyed by multiple events. ## Examples * Check that a particular system does not branch: ```wl In[] := WolframModel[{{1, 2}} -> {{1, 3}, {3, 2}}, {{1, 1}}, 2, "EventSelectionFunction" -> "MultiwaySpacelike"]["MultiwayQ"] Out[] = False ```
maxitg · Nov 2, 2020 · 8986200 · 8986200
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diff --git a/Documentation/Images/MultiwayExpressionsEventsGraphEchoed.png b/Documentation/Images/MultiwayExpressionsEventsGraphEchoed.png
diff --git a/Documentation/Images/SinglewayExpressionsEventsGraphEchoed.png b/Documentation/Images/SinglewayExpressionsEventsGraphEchoed.png
diff --git a/...AndFunctions/WolframModelAndWolframModelEvolutionObject/Properties/MultiwayQ.md b/...AndFunctions/WolframModelAndWolframModelEvolutionObject/Properties/MultiwayQ.md
@@ -0,0 +1,33 @@
+###### [Symbols and Functions](/README.md#symbols-and-functions) > [WolframModel and WolframModelEvolutionObject](../WolframModelAndWolframModelEvolutionObject.md) > [Properties](../WolframModelAndWolframModelEvolutionObject.md#properties) >
+
+# MultiwayQ
+
+**`"MultiwayQ"`** checks if a given evolution contains multiway branching, i.e., there is an expression used in multiple events.
+
+```wl
+In[] := EchoFunction[#["ExpressionsEventsGraph"] &][
+  WolframModel[{{1, 2}, {2, 3}} -> {{1, 2}, {2, 3}, {3, 4}},
+               {{1, 2}, {2, 3}, {3, 4}},
+               1,
+               "EventSelectionFunction" -> "MultiwaySpacelike"]]["MultiwayQ"]
+```
+
+<img src="/Documentation/Images/MultiwayExpressionsEventsGraphEchoed.png" width="451">
+
+```wl
+Out[] = True
+```
+
+Note that even if [`"EventSelectionFunction"`](/Documentation/WolframModelAndWolframModelEvolutionObject/Options/EventSelectionFunction.md) is set to allow multiway branching, the system might still be singleway if no overlapping matches occurred:
+
+
+```wl
+In[] := EchoFunction[#["ExpressionsEventsGraph"] &][WolframModel[
+  {{1, 2}} -> {{1, 3}, {3, 2}}, {{1, 1}}, 2, "EventSelectionFunction" -> "MultiwaySpacelike"]]["MultiwayQ"]
+```
+
+<img src="/Documentation/Images/SinglewayExpressionsEventsGraphEchoed.png" width="415">
+
+```wl
+Out[] = False
+```
diff --git a/...delAndWolframModelEvolutionObject/WolframModelAndWolframModelEvolutionObject.md b/...delAndWolframModelEvolutionObject/WolframModelAndWolframModelEvolutionObject.md
@@ -333,6 +333,7 @@ Currently, it's equivalent to `<|"MaxEvents" -> 5000, "MaxVertices" -> 200|>`, s
 - [Creator and Destroyer Events](Properties/CreatorAndDestroyerEvents.md)
 - [Causal Graphs](Properties/CausalGraphs.md)
 - [Expression Separations](Properties/ExpressionSeparations.md)
+- [MultiwayQ](Properties/MultiwayQ.md)
 - [Rule Indices for Events](Properties/RuleIndicesForEvents.md)
 - [Edge and Event Generations](Properties/EdgeAndEventGenerations.md)
 - [Termination Reason](Properties/TerminationReason.md)

diff --git a/Kernel/WolframModelEvolutionObject.m b/Kernel/WolframModelEvolutionObject.m
@@ -134,6 +134,7 @@
     "EdgeDestroyerEventIndices" -> {0, 0},
     "EdgeGenerationsList" -> {0, 0},
     "ExpressionsSeparation" -> {2, 2},
+    "MultiwayQ" -> {0, 0},
     "Properties" -> {0, 0}|>,
   Association[# -> {0, 0} & /@ Keys[$accessorProperties]]];
 
@@ -920,6 +921,13 @@ connecting them if the same event is a creator and a destroyer for the same expr
   If[Length[boundaryExpressions] =!= 0, "Branchlike", "Spacelike"]
 ]
 
+propertyEvaluate[True, includeBoundaryEventsPattern][
+    obj : WolframModelEvolutionObject[_ ? evolutionDataQ],
+    caller_,
+    "MultiwayQ"] := ModuleScope[
+  Max[Length /@ propertyEvaluate[True, None][obj, caller, "EdgeDestroyerEventsIndices"]] > 1
+]
+
 (* Public properties call *)
 
 $masterOptions = {

diff --git a/README.md b/README.md
@@ -145,6 +145,7 @@ We have a [Discord server](https://discord.setreplace.org). If you would like to
     - [Creator and Destroyer Events](Documentation/SymbolsAndFunctions/WolframModelAndWolframModelEvolutionObject/Properties/CreatorAndDestroyerEvents.md)
     - [Causal Graphs](Documentation/SymbolsAndFunctions/WolframModelAndWolframModelEvolutionObject/Properties/CausalGraphs.md)
     - [Expression Separations](Documentation/SymbolsAndFunctions/WolframModelAndWolframModelEvolutionObject/Properties/ExpressionSeparations.md)
+    - [MultiwayQ](Documentation/SymbolsAndFunctions/WolframModelAndWolframModelEvolutionObject/Properties/MultiwayQ.md)
     - [Rule Indices for Events](Documentation/SymbolsAndFunctions/WolframModelAndWolframModelEvolutionObject/Properties/RuleIndicesForEvents.md)
     - [Edge and Event Generations](Documentation/SymbolsAndFunctions/WolframModelAndWolframModelEvolutionObject/Properties/EdgeAndEventGenerations.md)
     - [Termination Reason](Documentation/SymbolsAndFunctions/WolframModelAndWolframModelEvolutionObject/Properties/TerminationReason.md)

diff --git a/Tests/WolframModelEvolutionObject.wlt b/Tests/WolframModelEvolutionObject.wlt
@@ -1945,6 +1945,27 @@
             Infinity,
             "EventSelectionFunction" -> None]["ExpressionsSeparation", -2, -1],
           "Spacelike"
+        ],
+
+        (* MultiwayQ *)
+
+        VerificationTest[
+          WolframModel[{{1}} -> {{1}}, {{1}}, 0]["MultiwayQ"],
+          False
+        ],
+
+        VerificationTest[
+          WolframModel[{{1, 2}, {2, 3}} -> {{1, 2}, {2, 3}, {3, 4}}, {{1, 2}, {2, 3}, {3, 4}}, 1]["MultiwayQ"],
+          False
+        ],
+
+        VerificationTest[
+          WolframModel[{{1, 2}, {2, 3}} -> {{1, 2}, {2, 3}, {3, 4}},
+                       {{1, 2}, {2, 3}, {3, 4}},
+                       1,
+                       "EventSelectionFunction" -> "MultiwaySpacelike"][
+                       "MultiwayQ"],
+          True
         ]
       }]
     }]