/// <summary>
/// Returns a boolean value indicating whether the specified results indicate that the QP
/// is self-injective.
/// </summary>
/// <param name="results">The results.</param>
/// <returns><see langword="true"/> if <paramref name="results"/> indicates that the QP is
/// self-injective. <see langword="false"/> otherwise.</returns>
/// <remarks>
/// <para>This method uses strong cancellativity instead of weak cancellativity to ensure
/// that the socles of the indecomposable projective modules are spanned by the
/// corresponding maximal nonzero equivalence classes.</para>
/// <para>If the analysis settings dictate that cancellativity should not be checked,
/// the underlying bound quiver could fail to be cancellative without
/// <paramref name="results"/> indicating this. In that case, the bound quiver algebra could
/// fail to be self-injective but this method could still return <see langword="true"/>.</para>
/// </remarks>
public static bool IndicatesSelfInjectivityUsingStrongCancellativity(this QuiverInPlaneAnalysisMainResults results)
{
return(results.HasFlag(QuiverInPlaneAnalysisMainResults.Success) &&
!results.HasFlag(QuiverInPlaneAnalysisMainResults.QPIsNotCancellative) &&
!results.HasFlag(QuiverInPlaneAnalysisMainResults.SomeVertexHasMultipleMaximalNonzeroClasses) &&
!results.HasFlag(QuiverInPlaneAnalysisMainResults.TentativeNakayamaPermutationIsNonInjective));
}
/// <summary>
/// Initializes a new instance of the <see cref="QuiverInPlaneAnalysisResults{TVertex}"/> class.
/// </summary>
/// <param name="mainResults">The main result.</param>
/// <param name="maximalPathRepresentatives">A dictionary mapping every vertex of the
/// quiver to a collection of representatives of all maximal non-zero equivalence classes
/// of paths starting at the vertex, or <see langword="null"/> depending on whether the
/// analysis was successful.</param>
/// <param name="nakayamaPermutation">The Nakayama permutation for the induced QP or
/// <see langword="null"/>, depending on whether the analysis was successful and the
/// induced QP has a Nakayama permutation.</param>
/// <param name="longestPathEncountered">A path of maximal length of the paths encountered
/// during the analysis.</param>
public QuiverInPlaneAnalysisResults(
QuiverInPlaneAnalysisMainResults mainResults,
IReadOnlyDictionary <TVertex, IEnumerable <Path <TVertex> > > maximalPathRepresentatives,
NakayamaPermutation <TVertex> nakayamaPermutation,
Path <TVertex> longestPathEncountered)
: base(mainResults, maximalPathRepresentatives, nakayamaPermutation, longestPathEncountered)
{
if (mainResults.HasFlag(QuiverInPlaneAnalysisMainResults.Success) && maximalPathRepresentatives is null)
{
throw new ArgumentNullException(nameof(maximalPathRepresentatives));
}
if (mainResults.IndicatesSelfInjectivity() && nakayamaPermutation is null)
{
throw new ArgumentNullException(nameof(nakayamaPermutation));
}
}