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Andrzej Mrůz - homepage

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  1. Bigraph Congruences. Environment for computing strong and weak Gram congruences between bigraphs and graphs and their isotropy groups. Implementation (as a collection of Maple packages) of algorithmic solutions from the articles [Congruences of edge-bipartite graphs... I & II, Fund. Inform. (2016)], describing applications to a variant of Grothendieck group recognition problem. Download packages (with instructions and examples - eng.):
    (ZIP 634kB)
    • New: added package InflationsPositive: better implementation of inflations + nondeterministic positive definiteness test for integral matrices (see the fourth pic).

    Nakayama Bigraph Dynkin graph Congruences Maple wild Nakayama algebra piecewise hereditary quiver type Isotropy Group D4 Dynkin Maple positive definite test Dynkin Maple
    [Click on the pics to enlarge]

  2. Inflations. Implementation of a variant of inflation algorithm for bigraphs, that is, for edge-bipartite graphs (implementation in C++ for Windows in two versions: text and graphic with WinAPI 32). Download package (both versions, with instructions - eng.): (ZIP 543kB)
    • Added in ver. 0.9: new randomized algorithms and shape recognition for resulting (bi)graphs.

    Inflations Bigraph Graphic Inflations Bigraph Nakayama Inflations edge-bipartite graph Nakayama wild star graph E10 wild quiver

  3. DegOrderFiniteType. GAP package - a framework for computing degeneration order for modules over finite type algebras. This is a separated subpackage of QPA - see below. Download package (with instruction and examples of usage - eng.): (ZIP 26kB)
  4. Improved Bongartz's algorithm. GAP codes, description and tests of the original algorithm and my improvement.
  5. QPA. Large open source GAP package for computations in representation theory of algebras (quivers with relations). Download package from: SourceForge or GitHub.
  6. Exceptional. Maple package containing the procedures for construction of modules from exceptional tubes over tubular canonical algebras. This is an implementation of the algorithms from the [An algorithm..., J. Algebra 323 (2010) 2710-2734]. Download package (with instruction and examples of usage - eng.): (ZIP 38kB)
  7. Homogeneous Tubular. Maple package containing the procedures for generating bimodules parametrizing all homogeneous modules (of integral slopes) over tubular canonical algebras, constructed in the [Parametrizations...., Algebr Represent Theor (2014) 17:321-356]. Additional procedures compute the specialisations of bimodules, homomorphism spaces... Download package (with instruction and examples of usage - eng.): (ZIP 14kB)
  8. Special biserial trees. Java application which determines and presents (graphically) the indecomposable modules over the special biserial trees. It also computes and presents canonical subrepresentations, quotients, almost split sequences, DTr and Auslander-Reiten matrix. Download software (with instruction - eng.): (ZIP 628kB) or see the screenshots (click to enlarge):

    Special biserial trees 1 Special biserial trees 2 Special biserial trees 3

  9. Bielitskii's algorithm. Brief description with an example (PDF 353kB)
    • Representation of a poset - four subspaces - sum of exceptional representations (PDF 130kB);
    • Representation of a poset - four subspaces - representation without selfextensions (PDF 93kB);
    • Representation of a quiver (of a wild type) (PDF 183kB).

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Last updated on: 6 September 2016.