Is there a good computer program for doing calculations in A-infinity categories?
Explicit calculations in A-infinity categories are an important, useful, yet very tedious task. One has to keep track of horrific signs and the combinatorics of trees is lurking always in the background. Examples of such calculations include:
- Minimal A-infinity structures on e.g. Ext-algebras of quiver representations.
- Morphism spaces between A-infinity modules.
- Multiplications on twisted complexes.
Doing this explicit calculation is merely a book-keeping problem and therefore calls for some computer support. Is there a good solution for that problem?
At best I would like to have a well documented SAGE library - but this is apparently too much to ask. Here are my Google searches results:
In Paul Seidel's proof of Mirror Symmetry for the Quartic K3 surface, he uses a python script to do calculations in A-infinity categories.
Mikael Vejdemo-Johansson has written a thesis on Computation of A-inifinity algebras in group cohomology. He gives some code in Haskell, there is an MAGMA implementation for the A-infinity strucures on group cohomology, here. Thanks to mt for the reference!
Marc Nieper-Wißkirchen and Samuel Boissier use the MAUDE rewriting system to make explicit computation in cohomology rings of the Hilbert-Scheme of points in Generating series in the cohomology of Hilbert schemes of points on surfaces. Maybe similar methods have been used for A-infinity calculations?
