private ExploreChildNodesResult ExploreChildNodes <TVertex>(
QuiverWithPotential <TVertex> qp,
TransformationRuleTreeNode <TVertex> transformationRuleTree,
AnalysisStateForSingleStartingVertexOld <TVertex> state,
SearchTreeNodeOld <TVertex> parentNode,
QPAnalysisSettings settings)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
bool pathHasNonzeroExtension = false; // Path has no nonzero extension until proven otherwise
// Explore every child node (determine its equivalence class)
foreach (var nextVertex in qp.Quiver.AdjacencyLists[parentNode.Vertex])
{
var result = ExploreChildNode(transformationRuleTree, state, parentNode, nextVertex, settings);
switch (result)
{
case ExploreChildNodeResult.NotZeroEquivalent:
pathHasNonzeroExtension = true;
break;
case ExploreChildNodeResult.NonCancellativityDetected:
return(ExploreChildNodesResult.NonCancellativityDetected);
case ExploreChildNodeResult.TooLongPath:
return(ExploreChildNodesResult.TooLongPath);
}
}
return(pathHasNonzeroExtension ? ExploreChildNodesResult.PathHasNonzeroExtension : ExploreChildNodesResult.PathHasNoNonzeroExtension);
}
/// <summary>
/// Computes the equivalence class of the specified node.
/// </summary>
/// <typeparam name="TVertex">The type of the vertices in the quiver.</typeparam>
/// <param name="node">The node whose equivalence class to determine.</param>
/// <param name="state">The state of the computation.</param>
/// <param name="transformationRuleTree">The transformation rule tree.</param>
/// <param name="settings">The computation settings.</param>
/// <returns><see cref="EquivalenceClassResult.TooLongPath"/> if
/// <paramref name="settings"/> has <see cref="AnalysisSettings.UseMaxLength"/> equal to
/// <see langword="true"/> and a path of length (in arrows) strictly greater than
/// <see cref="AnalysisSettings.MaxPathLength"/> of <paramref name="settings"/> is
/// encountered during the equivalence class search. Otherwise,
/// <see cref="EquivalenceClassResult.Zero"/> if the equivalence class is the zero
/// class, and <see cref="EquivalenceClassResult.Nonzero"/> if the equivalence class is not
/// the zero class.</returns>
/// <remarks>
/// <para>This method may modify the
/// <see cref="AnalysisStateForSingleStartingVertex{TVertex}.SearchTree"/>,
/// <see cref="AnalysisStateForSingleStartingVertex{TVertex}.EquivalenceClasses"/>, and
/// <see cref="AnalysisStateForSingleStartingVertex{TVertex}.LongestPathEncounteredNode"/>
/// properties of the <paramref name="state"/> argument.</para>
/// </remarks>
private EquivalenceClassResult ComputeEquivalenceClass <TVertex>(
SearchTreeNode <TVertex> startNode,
AnalysisStateForSingleStartingVertex <TVertex> state,
TransformationRuleTreeNode <TVertex> transformationRuleTree,
MaximalNonzeroEquivalenceClassRepresentativeComputationSettings settings)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
// The stack or queue of nodes to process
var equivClassStack = new Stack <SearchTreeNode <TVertex> >();
equivClassStack.Push(startNode);
startNode.HasBeenDiscoveredDuringEquivalenceClassComputation = true;
while (equivClassStack.Count > 0)
{
var node = equivClassStack.Pop();
var result = ExploreNodeForEquivalenceClassSearch(node, equivClassStack, state, transformationRuleTree, settings);
if (result == EquivalenceClassResult.TooLongPath)
{
return(EquivalenceClassResult.TooLongPath); // If too long, return "too long".
}
else if (result == EquivalenceClassResult.Zero)
{
return(EquivalenceClassResult.Zero); // If definitely zero-equivalent, return "zero"
}
}
return(EquivalenceClassResult.Nonzero);
}
/// <summary>
///
/// </summary>
/// <typeparam name="TVertex">The type of the vertices in the quiver.</typeparam>
/// <param name="quiver">The quiver.</param>
/// <param name="startingVertex">The starting vertex of the paths to look at.</param>
/// <param name="transformationRuleTree"></param>
/// <returns>The state of the search after it is done.</returns>
private AnalysisStateForSingleStartingVertex <TVertex> DoSearchInPathTree <TVertex>(
Quiver <TVertex> quiver,
TVertex startingVertex,
TransformationRuleTreeNode <TVertex> transformationRuleTree,
MaximalNonzeroEquivalenceClassRepresentativeComputationSettings settings)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
// Set up for analysis/graph search
var state = new AnalysisStateForSingleStartingVertex <TVertex>(startingVertex);
// Analysis/graph search
// Keep a stack of "recently equivalence-class-computed" nodes
// In every iteration, pop a node from the stack and determine the equivalence classes
// of its child nodes.
// It would be cleaner to in every iteration determine the equivalence class of the
// *current* node and enqueue its child nodes (in other words, to have the queue
// contain nodes whose equivalence classes to explore), but this makes it non-trivial
// to keep track of the maximal nonzero equivalence classes
while (state.Stack.Count > 0)
{
var node = state.Stack.Pop();
bool isMaximalNonzero = true;
foreach (var nextVertex in quiver.AdjacencyLists[node.Vertex])
{
var child = state.GetInsertChildNode(node, nextVertex);
if (DoPathLengthCheck(child, state, settings) == PathLengthCheckResult.TooLongPath)
{
state.TooLongPathEncountered = true;
return(state);
}
var equivClassResult = DetermineEquivalenceClass(child, state, transformationRuleTree, settings);
if (equivClassResult == EquivalenceClassResult.Nonzero)
{
isMaximalNonzero = false;
state.Stack.Push(child);
}
else if (equivClassResult == EquivalenceClassResult.TooLongPath)
{
state.TooLongPathEncountered = true;
return(state);
}
}
if (isMaximalNonzero)
{
var representative = state.EquivalenceClasses.FindSet(node);
if (!state.maximalPathRepresentatives.Contains(representative))
{
state.maximalPathRepresentatives.Add(representative);
}
}
}
return(state);
}
// After figuring out the use cases (high performance?) for these methods and figuring out
// whether to change the interface, implement the counterparts of the methods in
// SemimonomialUnboundQuiverAnalyzer and have the public methods of this class just be a
// wrapper for said methods in SemimonomialUnboundQuiverAnalyzer (like the Analyze method
// is right now).
#region Code to refactor
public AnalysisResultsForSingleStartingVertexOld <TVertex> AnalyzeWithStartingVertex <TVertex>(
QuiverWithPotential <TVertex> qp,
TVertex startingVertex,
TransformationRuleTreeNode <TVertex> transformationRuleTree,
QPAnalysisSettings settings)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
// Parameter validation
if (qp == null)
{
throw new ArgumentNullException(nameof(qp));
}
if (!qp.Quiver.Vertices.Contains(startingVertex))
{
throw new ArgumentException($"The QP does not contain the starting vertex {startingVertex}.");
}
// Set up for analysis/graph search
var state = new AnalysisStateForSingleStartingVertexOld <TVertex>(startingVertex);
bool cancellativityFailed = false;
bool tooLongPathEncountered = false;
// Analysis/graph search
// Keep a stack of "recently explored" nodes
// In every iteration, pop a recently explored node from the stack and explore (determine
// the equivalence classes of) its child nodes.
// It would be cleaner to in every iteration explore the current node (determine its equivalence class)
// and discover its child nodes (push new equivalence class representatives (which may overlap?) onto
// the stack for future iterations, but this makes it non-trivial to keep track of the maximal nonzero
// equivalence classes
while (state.Stack.Count > 0)
{
var node = state.Stack.Pop();
var result = ExploreChildNodes(qp, transformationRuleTree, state, node, settings);
if (result == ExploreChildNodesResult.PathHasNoNonzeroExtension)
{
state.maximalPathRepresentatives.Add(node);
}
else if (result == ExploreChildNodesResult.NonCancellativityDetected)
{
cancellativityFailed = true;
break;
}
else if (result == ExploreChildNodesResult.TooLongPath)
{
tooLongPathEncountered = true;
break;
}
}
// Return results
var results = new AnalysisResultsForSingleStartingVertexOld <TVertex>(state, cancellativityFailed, tooLongPathEncountered);
return(results);
}
/// <summary>
/// Essentially <see cref="ComputeMaximalNonzeroEquivalenceClassRepresentativesStartingAt"/>
/// but with a more detailed, implementation-specific return value.
/// </summary>
/// <typeparam name="TVertex"></typeparam>
/// <param name="quiver"></param>
/// <param name="startingVertex"></param>
/// <param name="transformationRuleTree"></param>
/// <param name="settings"></param>
/// <returns></returns>
private AnalysisResultsForSingleStartingVertex <TVertex> AnalyzeWithStartingVertex <TVertex>(
Quiver <TVertex> quiver,
TVertex startingVertex,
TransformationRuleTreeNode <TVertex> transformationRuleTree,
MaximalNonzeroEquivalenceClassRepresentativeComputationSettings settings)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
// Parameter validation
if (quiver is null)
{
throw new ArgumentNullException(nameof(quiver));
}
if (!quiver.Vertices.Contains(startingVertex))
{
throw new ArgumentException($"The quiver does not contain the starting vertex {startingVertex}.");
}
if (transformationRuleTree is null)
{
throw new ArgumentNullException(nameof(transformationRuleTree));
}
if (settings is null)
{
throw new ArgumentNullException(nameof(settings));
}
// Do search in the tree of all paths starting at startingVertex
AnalysisStateForSingleStartingVertex <TVertex> state = DoSearchInPathTree(quiver, startingVertex, transformationRuleTree, settings);
// Do cancellativity check
bool shouldDoCancellativityFailureDetection = settings.DetectCancellativityFailure && !state.TooLongPathEncountered;
bool cancellativityFailureDetected = shouldDoCancellativityFailureDetection ? DetectFailureOfCancellativity(state) : false;
bool shouldDoWeakCancellativityFailureDetection = settings.DetectWeakCancellativityFailure && !state.TooLongPathEncountered;
bool weakCancellativityFailureDetected = shouldDoWeakCancellativityFailureDetection ? DetectFailureOfWeakCancellativity(state) : false;
var cancellativityFailuresDetected = CancellativityTypes.None;
if (cancellativityFailureDetected)
{
cancellativityFailuresDetected |= CancellativityTypes.Cancellativity;
}
if (weakCancellativityFailureDetected)
{
cancellativityFailuresDetected |= CancellativityTypes.WeakCancellativity;
}
// Return results
var results = new AnalysisResultsForSingleStartingVertex <TVertex>(state, cancellativityFailuresDetected);
return(results);
}
/// <summary>
/// Determines the equivalence class of the specified node.
/// </summary>
/// <typeparam name="TVertex">The type of the vertices in the quiver.</typeparam>
/// <param name="node">The node whose equivalence class to determine.</param>
/// <param name="state">The state of the computation.</param>
/// <param name="transformationRuleTree">The transformation rule tree.</param>
/// <param name="settings">The computation settings.</param>
/// <returns><see cref="EquivalenceClassResult.TooLongPath"/> if the equivalence class has
/// not been computed before, <paramref name="settings"/> has
/// <see cref="AnalysisSettings.UseMaxLength"/> equal to <see langword="true"/>, and a path
/// of length (in arrows) strictly greater than
/// <see cref="AnalysisSettings.MaxPathLength"/> of <paramref name="settings"/> is
/// encountered during the equivalence class search. Otherwise,
/// <see cref="EquivalenceClassResult.Zero"/> if the equivalence class is the zero
/// class, and <see cref="EquivalenceClassResult.Nonzero"/> if the equivalence class is
/// not the zero class.</returns>
/// <remarks>
/// <para>This method may modify the
/// <see cref="AnalysisStateForSingleStartingVertex{TVertex}.SearchTree"/>,
/// <see cref="AnalysisStateForSingleStartingVertex{TVertex}.EquivalenceClasses"/>, and
/// <see cref="AnalysisStateForSingleStartingVertex{TVertex}.LongestPathEncounteredNode"/>
/// properties of the <paramref name="state"/> argument.</para>
/// </remarks>
private EquivalenceClassResult DetermineEquivalenceClass <TVertex>(
SearchTreeNode <TVertex> node,
AnalysisStateForSingleStartingVertex <TVertex> state,
TransformationRuleTreeNode <TVertex> transformationRuleTree,
MaximalNonzeroEquivalenceClassRepresentativeComputationSettings settings)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
if (node.EquivalenceClassIsComputed)
{
return(state.NodeIsZeroEquivalent(node) ? EquivalenceClassResult.Zero : EquivalenceClassResult.Nonzero);
}
return(ComputeEquivalenceClass(node, state, transformationRuleTree, settings));
}
public MaximalNonzeroEquivalenceClassRepresentativesResults <TVertex> ComputeMaximalNonzeroEquivalenceClassRepresentativesStartingAt <TVertex>(
QuiverWithPotential <TVertex> qp,
TVertex startingVertex,
TransformationRuleTreeNode <TVertex> transformationRuleTree,
QPAnalysisSettings settings)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
var bogusPath = new Path <TVertex>(qp.Quiver.Vertices.First());
var analysisResults = AnalyzeWithStartingVertex(qp, startingVertex, transformationRuleTree, settings);
var outputResults = new MaximalNonzeroEquivalenceClassRepresentativesResults <TVertex>(
analysisResults.NonCancellativityDetected ? CancellativityTypes.Cancellativity : CancellativityTypes.None,
analysisResults.TooLongPathEncountered,
analysisResults.MaximalPathRepresentatives.Select(node => node.Path),
longestPathEncountered: bogusPath); // bogus path because this is an old method and the longest path feature is new
return(outputResults);
}
/// <summary>
/// Creates a transformation rule tree for a <see cref="SemimonomialUnboundQuiver{TVertex}"/>.
/// </summary>
/// <typeparam name="TVertex">The type of the vertices of the quiver.</typeparam>
/// <param name="unboundQuiver">The unbound quiver.</param>
/// <returns>A transformation rule tree for <paramref name="semimonomialIdeal"/>.</returns>
/// <exception cref="ArgumentNullException"><paramref name="semimonomialIdeal"/> is <see langword="null"/>.</exception>
/// <exception cref="NotSupportedException"><paramref name="semimonomialIdeal"/> has two
/// distinct non-monomial generators <c>p1 - q1</c> and <c>p2 - q2</c> where
/// <c>p1, q1, p2, q2</c> are not all distinct.</exception>
/// <exception cref="ArgumentException"><paramref name="semimonomialIdeal"/> has a
/// non-monomial generator <c>p - q</c> where the paths <c>p</c> and <c>q</c> do not have
/// the same endpoints.</exception>
public TransformationRuleTreeNode <TVertex> CreateTransformationRuleTree <TVertex>(SemimonomialIdeal <TVertex> semimonomialIdeal)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
var root = new TransformationRuleTreeNode <TVertex>(false, null, null);
// Monomial generators (kill rules)
foreach (var path in semimonomialIdeal.Paths)
{
var node = GetOrInsertDefaultNode(path, root);
node.CanBeKilled = true;
}
// Non-monomial generators (replace rules)
foreach (var difference in semimonomialIdeal.DifferencesOfPaths)
{
// Replacement rules where the paths have different starting or ending points are disallowed
if (!difference.Minuend.StartingPoint.Equals(difference.Subtrahend.StartingPoint) || !difference.Minuend.EndingPoint.Equals(difference.Subtrahend.EndingPoint))
{
throw new NotSupportedException("Ideals with a non-monomial generator whose two paths have different starting points or ending points are not supported.");
}
InsertReplacementRule(difference.Minuend, difference.Subtrahend);
InsertReplacementRule(difference.Subtrahend, difference.Minuend);
}
void InsertReplacementRule(Path <TVertex> originalPath, Path <TVertex> replacementPath)
{
var node = GetOrInsertDefaultNode(originalPath, root);
if (node.ReplacementPath != null)
{
// Shouldn't be too much work to add support for this imo
throw new NotSupportedException("Ideals with a path occurring in more than one non-monomial generator are not supported.");
}
node.ReplacementPath = replacementPath;
}
return(root);
}
/// <inheritdoc/>
public MaximalNonzeroEquivalenceClassRepresentativesResults <TVertex> ComputeMaximalNonzeroEquivalenceClassRepresentativesStartingAt <TVertex>(
Quiver <TVertex> quiver,
TVertex startingVertex,
TransformationRuleTreeNode <TVertex> transformationRuleTree,
MaximalNonzeroEquivalenceClassRepresentativeComputationSettings settings)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
var analysisResults = AnalyzeWithStartingVertex(quiver, startingVertex, transformationRuleTree, settings);
// The .ToList() call to eagerly evaluate the maximal path representatives is really
// important here; otherwise, the MaximalPathRepresentatives property of the
// MaximalNonzeroEquivalenceClassRepresentativesResult prevents the entire search tree
// of analysisResults from being freed.
var maximalPathRepresentatives = analysisResults.MaximalPathRepresentatives.Select(node => node.Path).ToList();
var outputResults = new MaximalNonzeroEquivalenceClassRepresentativesResults <TVertex>(
analysisResults.CancellativityFailuresDetected,
analysisResults.TooLongPathEncountered,
maximalPathRepresentatives,
analysisResults.LongestPathEncountered);
return(outputResults);
}
/// <remarks>This method should be made obsolete (prefer converting the QP to a
/// semimonomial unbound quiver, and analyzing that instead (or at least creating the
/// transformation rule tree for that instead).</remarks>
public TransformationRuleTreeNode <TVertex> CreateTransformationRuleTree <TVertex>(QuiverWithPotential <TVertex> qp)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
if (qp is null)
{
throw new ArgumentNullException(nameof(qp));
}
var root = new TransformationRuleTreeNode <TVertex>(false, null, null);
foreach (var arrow in qp.Quiver.Arrows)
{
var linComb = new LinearCombination <Path <TVertex> >();
foreach (var(cycle, coefficient) in qp.Potential.LinearCombinationOfCycles.ElementToCoefficientDictionary)
{
linComb = linComb.Add(cycle.DifferentiateCyclically(arrow).Scale(coefficient));
}
AddRulesFromSingleLinearCombination(linComb, root);
}
return(root);
}
/// <returns>A boolean value indicating whether the node was found to be zero-equivalent.
/// That is, the returned value is <see langword="true"/> <em>only</em> if the node is
/// zero-equivalent but may be <see langword="false"/> even if the node is zero-equivalent.</returns>
/// <remarks>A node is found to be zero-equivalent either if its path can be killed or if
/// the path is equivalent to (up to replacement) to a path that has previously been
/// determined to be zero-equivalent.</remarks>
private static bool EquivClassExploreNode <TVertex>(
TransformationRuleTreeNode <TVertex> transformationRuleTree,
SearchTreeNodeOld <TVertex> node,
AnalysisStateForSingleStartingVertexOld <TVertex> state,
Stack <SearchTreeNodeOld <TVertex> > equivClassStack,
SearchTreeNodeOld <TVertex> origin)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
node.Explored = true;
var trailingVertexPath = new List <TVertex>(); // In reversed order
foreach (var endingNode in node.ReversePathOfNodes) // The last vertex of endingNode is the last vertex in the subpath
{
var transformationNode = transformationRuleTree;
foreach (var startingNode in endingNode.ReversePathOfNodes) // The last vertex of startingNode is the first vertex in the subpath
{
var pathVertex = startingNode.Vertex;
if (!transformationNode.Children.TryGetValue(pathVertex, out transformationNode))
{
break;
}
if (transformationNode.CanBeKilled)
{
state.EquivalenceClasses.Union(node, state.ZeroDummyNode);
return(true);
}
// If replacement is possible, do the replacement on the subpath
// and add a search tree node for the entire resulting path
if (transformationNode.CanBeReplaced)
{
// Add search tree nodes for replacement path
// This doesn't work when pathNode is the root ...
// var lastUnreplacedNode = pathNode.Parent;
// var curNode = lastUnreplacedNode;
// ... so instead do the following (with Skip), which assumes that the replacement
// path has the same first vertex (which it does for the QPs under consideration)
var firstReplacementNode = startingNode;
var curNode = firstReplacementNode;
foreach (var vertex in transformationNode.ReplacementPath.Vertices.Skip(1))
{
curNode = state.GetInsertChildNode(curNode, vertex, origin);
}
// Add search tree nodes for the trailing path
foreach (var vertex in trailingVertexPath.Reversed())
{
curNode = state.GetInsertChildNode(curNode, vertex, origin);
}
var transformedNode = curNode;
if (state.NodeIsZeroEquivalent(transformedNode))
{
state.EquivalenceClasses.Union(node, transformedNode);
return(true);
}
// transformedNode.Explored may be true and is then a node that we have
// already encountered during the equivalence class search.
// (It cannot be an explored node of some *other* equivalence class,
// because then this current equivalence class search would not have
// started in the first place.)
//if (!transformedNode.Explored)
if (!state.EquivalenceClasses.FindSet(node).Equals(state.EquivalenceClasses.FindSet(transformedNode)))
{
state.EquivalenceClasses.Union(node, transformedNode);
equivClassStack.Push(transformedNode);
}
}
}
trailingVertexPath.Add(endingNode.Vertex);
}
return(false);
}
/// <returns>A boolean value indicating whether the path correspondings to the explored
/// child node is nonzero (up to equivalence).</returns>
private ExploreChildNodeResult ExploreChildNode <TVertex>(
TransformationRuleTreeNode <TVertex> transformationRuleTree,
AnalysisStateForSingleStartingVertexOld <TVertex> state,
SearchTreeNodeOld <TVertex> parentNode,
TVertex nextVertex,
QPAnalysisSettings settings)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
// Either the child node has not already been discovered, or the child node was
// discovered during an equivalence class search.
if (parentNode.Children.TryGetValue(nextVertex, out var childNode))
{
// The child node has already been discovered.
// Do a non-cancellativity check (if we are to detect non-cancellativity):
// If the child node is zero, everything is fine.
// If a different arrow was added to the origin than to the parent to get child node (i.e., origin and parent have different last vertices), things are fine.
// Else, make sure that the origin is equivalent to the parent
// (otherwise, the QP is not cancellative).
if (
settings.DetectCancellativityFailure &&
!state.NodeIsZeroEquivalent(childNode) &&
parentNode.Vertex.Equals(childNode.Origin.Vertex) &&
state.EquivalenceClasses.FindSet(parentNode) != state.EquivalenceClasses.FindSet(childNode.Origin))
{
return(ExploreChildNodeResult.NonCancellativityDetected);
}
}
else
{
// The child node has not been discovered, so let's discover it by inserting it
// into the search tree.
childNode = state.InsertChildNode(parentNode, nextVertex, parentNode);
}
if (childNode.Explored)
{
return(state.NodeIsZeroEquivalent(childNode) ? ExploreChildNodeResult.ZeroEquivalent : ExploreChildNodeResult.NotZeroEquivalent);
}
// Code for equivalence class searching begins here
// Stack containing all the nodes to explore (by path transformation)
var equivClassStack = new Stack <SearchTreeNodeOld <TVertex> >(state.EquivalenceClasses.GetSet(childNode));
// This could happen with the current code, namely when the current childNode was encountered
// in a previous call to ExploreChildNodes (in EquivClassExploreNode, as transformationNode)
// and 'node' was found to be zero equivalent (in which case the search is cancelled
// before transformationNode is explored in EquivClassExploreNode)
// Thought: Would probably be good to have several Explored properties (or an
// enum-valued Explored property) containing information about the extent to which the
// node is explored (explored-as-in-encountered-in-EquivClassExploreNode would be
// useful here; more easily understood and maintained than this comment methinks)
if (equivClassStack.Count != 1)
{
return(ExploreChildNodeResult.ZeroEquivalent);
}
while (equivClassStack.Count > 0)
{
var equivalentNode = equivClassStack.Pop();
if (equivalentNode.Explored)
{
continue;
}
if (settings.UseMaxLength && equivalentNode.PathLengthInVertices > settings.MaxPathLength + 1)
{
return(ExploreChildNodeResult.TooLongPath);
}
var exploredNodeWasFoundZeroEquivalent = EquivClassExploreNode(transformationRuleTree, equivalentNode, state, equivClassStack, parentNode);
if (exploredNodeWasFoundZeroEquivalent)
{
return(ExploreChildNodeResult.ZeroEquivalent);
}
}
// Child node was not zero-equivalent
state.Stack.Push(childNode);
return(ExploreChildNodeResult.NotZeroEquivalent);
}
/// <summary>
/// Explores the specified node in the equivalence class search.
/// </summary>
/// <typeparam name="TVertex">The type of the vertices in the quiver.</typeparam>
/// <param name="node">The node to explore.</param>
/// <param name="equivClassStack">The stack or queue of nodes to explore.</param>
/// <param name="state">The state of the computation.</param>
/// <param name="transformationRuleTree">The transformation rule tree.</param>
/// <param name="settings">The computation settings.</param>
/// <returns>A value of the <see cref="EquivalenceClassResult"/> enum indicating whether
/// the node was <em>found</em> to be zero-equivalent. That is, the returned value is
/// <see cref="EquivalenceClassResult.Zero"/> <em>only</em> if the node is zero-equivalent
/// but may be <see cref="EquivalenceClassResult.Nonzero"/> even if the node is
/// zero-equivalent.
/// <remarks>
/// <para>A node is found to be zero-equivalent either if its path can be killed or if
/// the path is equivalent (up to replacement) to a path that has previously been
/// determined to be zero-equivalent.</para>
/// <para>This method may modify the
/// <see cref="AnalysisStateForSingleStartingVertex{TVertex}.SearchTree"/>,
/// <see cref="AnalysisStateForSingleStartingVertex{TVertex}.EquivalenceClasses"/>, and
/// <see cref="AnalysisStateForSingleStartingVertex{TVertex}.LongestPathEncounteredNode"/>
/// properties of the <paramref name="state"/> argument.</para>
/// </remarks>
private EquivalenceClassResult ExploreNodeForEquivalenceClassSearch <TVertex>(
SearchTreeNode <TVertex> node,
Stack <SearchTreeNode <TVertex> > equivClassStack,
AnalysisStateForSingleStartingVertex <TVertex> state,
TransformationRuleTreeNode <TVertex> transformationRuleTree,
MaximalNonzeroEquivalenceClassRepresentativeComputationSettings settings)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
// A list of the vertices that appear after the path being considered from transformation.
// The vertices are in reversed order.
var trailingVertexPath = new List <TVertex>();
foreach (var endingNode in node.ReversePathOfNodes) // The vertex (i.e., last vertex) of endingNode is the last vertex in the subpath
{
var transformationNode = transformationRuleTree;
foreach (var startingNode in endingNode.ReversePathOfNodes) // The vertex (i.e., last vertex) of startingNode is the first vertex in the subpath
{
var pathVertex = startingNode.Vertex;
if (!transformationNode.Children.TryGetValue(pathVertex, out transformationNode))
{
break;
}
if (transformationNode.CanBeKilled)
{
state.EquivalenceClasses.Union(node, state.ZeroDummyNode);
return(EquivalenceClassResult.Zero);
}
// If replacement is possible, do the replacement on the subpath
// and add a search tree node for the entire resulting path
if (transformationNode.CanBeReplaced)
{
// Add search tree nodes for replacement path
// This doesn't work when pathNode is the root ...
// var lastUnreplacedNode = pathNode.Parent;
// var curNode = lastUnreplacedNode;
// ... so instead do the following (with Skip), which assumes that the replacement
// path has the same first vertex (which it does for the semimonomial unbound
// quivers under consideration)
var firstNodeInTransformedPath = startingNode;
var curNode = firstNodeInTransformedPath;
foreach (var vertex in transformationNode.ReplacementPath.Vertices.Skip(1))
{
curNode = state.GetInsertChildNode(curNode, vertex);
}
// Add search tree nodes for the trailing path
foreach (var vertex in trailingVertexPath.Reversed())
{
curNode = state.GetInsertChildNode(curNode, vertex);
}
// We now have the node obtained by applying the replacement rule.
var transformedNode = curNode;
// Do stuff with its path length.
bool tooLong = DoPathLengthCheck(transformedNode, state, settings) == PathLengthCheckResult.TooLongPath;
if (tooLong)
{
return(EquivalenceClassResult.TooLongPath);
}
if (state.NodeIsZeroEquivalent(transformedNode))
{
state.EquivalenceClasses.Union(node, transformedNode); // Unioning with state.ZeroDummyNode would work equally well
return(EquivalenceClassResult.Zero);
}
// If transformedNode.HasBeenDiscoveredDuringEquivalenceClassComputation
// at this point, then it was discovered during this equivalence class
// search (not during an earlier search that ended with zero equivalence),
// and in this case, we should ignore it!
if (!transformedNode.HasBeenDiscoveredDuringEquivalenceClassComputation)
{
transformedNode.HasBeenDiscoveredDuringEquivalenceClassComputation = true;
state.EquivalenceClasses.Union(node, transformedNode);
equivClassStack.Push(transformedNode);
}
}
}
trailingVertexPath.Add(endingNode.Vertex);
}
return(EquivalenceClassResult.Nonzero);
}
/// <summary>
/// Gets a node according to a specified paths, inserting nodes without any transformation
/// data into the tree as necessary along the way.
/// </summary>
/// <typeparam name="TVertex">The type of the vertices.</typeparam>
/// <param name="path">The path according to which to get the node from the tree.</param>
/// <param name="root">The root node of the tree.</param>
/// <returns>The retrieved node.</returns>
/// <remarks>Additional nodes without any transformation data are inserted into the tree as
/// necessary between the root node and the node to insert.</remarks>
private TransformationRuleTreeNode <TVertex> GetOrInsertDefaultNode <TVertex>(Path <TVertex> path, TransformationRuleTreeNode <TVertex> root)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
var curNode = root;
foreach (var vertex in path.Vertices.Reverse())
{
if (!curNode.Children.ContainsKey(vertex))
{
curNode.children[vertex] = new TransformationRuleTreeNode <TVertex>(false, null, curNode);
}
curNode = curNode.Children[vertex];
}
return(curNode);
}
private void AddRulesFromSingleLinearCombination <TVertex>(LinearCombination <Path <TVertex> > linComb, TransformationRuleTreeNode <TVertex> root)
where TVertex : IEquatable <TVertex>, IComparable <TVertex>
{
switch (linComb.ElementToCoefficientDictionary.Count)
{
case 0: return;
case 1:
var path = linComb.Elements.Single();
var node = GetOrInsertDefaultNode(path, root);
node.CanBeKilled = true;
break;
case 2:
var coefficients = linComb.ElementToCoefficientDictionary.Values.ToList();
var paths = linComb.Elements.ToList(); // Could be in different order from the coefficients, but don't care
if (coefficients[1] == -coefficients[0])
{
GetOrInsertDefaultNode(paths[0], root).ReplacementPath = paths[1];
GetOrInsertDefaultNode(paths[1], root).ReplacementPath = paths[0];
}
else
{
throw new NotSupportedException("Linear combinations of length 2 with coefficients that are not the additive inverse of each other are not supported.");
}
break;
default:
throw new NotSupportedException("Linear combinations of length greater than 2 are not supported.");
}
}
