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Free band elements by graph representation #689

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@reiniscirpons reiniscirpons commented Jul 7, 2020

This PR adds some functions for creating and manipulating free band elements in a graph representation. This representation has benefits in comparison to the current tree based rep, and even a possible word based one.

  • Actually describe what the structure and algorithms are
  • Come up with representation description
    • Make structure mutable
    • Allow reusing memory
    • Make the graph irredundant (each node represents a single free band element)
  • Add methods to initialize FreeBandElementByGraph
    • Initialize from word
    • Initialize from tree-rep
    • Initialize from graph
  • Multiplication
    • Multiply by single letter
    • Figure out how to multiply two elements in graph-rep
  • Equality checking
  • Canonical word
  • Making a copy (to support immutable operations)
  • DotString for visualizing the structure
  • Iterators (?)
  • Collections of elements
    • Reuse element code to make collection, redefine elements be specified by a collection and node in collection
  • Write up a proof for certain results
    • V <= |A|*N where V is the number of vertices of the graph, N is the length of the shortest word representation and |A| is the size of the alphabet
    • The right multiplication by letter algorithm is correct
    • The canonical word algorithm actually produces the shortest possible word

@reiniscirpons reiniscirpons added do not merge Label for PR that should not be merged WIP Label for PRs that are Works In Progress (WIP) enhancement A label for issues or PRs that offer an enhancement to existing functionality labels Jul 7, 2020
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