# Computer calculations in A_infinity categories?

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:

1. Minimal A-infinity structures on e.g. Ext-algebras of quiver representations.
2. Morphism spaces between A-infinity modules.
3. 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:

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I know that Laurent Bartholdi has spent some time making a program that computes minimal A-inf structures on Ext-algebras (mainly in the context of group cohomology). The problem is that this A-inf structure is highly non-unique, and that once you have it in front of you, there are still a bunch of questions that you can't really answer. –  André Henriques Mar 21 '12 at 11:09
The Magma implementation of $A_\infty$ structures on group cohomology is described in the Magma documentation here magma.maths.usyd.edu.au/magma/handbook/text/904 –  M T Mar 21 '12 at 12:18
Thx @mt for the reference. I have edited the question accordingly. @Andre, do you know if Laurent Barholdi published his code somewhere? I think that the non-uniqueness makes it even more desireable to not do the computations by hand ;) –  Heinrich Hartmann Mar 22 '12 at 17:11
for me the relevant section of Magma handbook is strangely this one: magma.maths.usyd.edu.au/magma/handbook/text/937 (the one you link says "Construction of Subalgebras, Ideals and Quotient Rings") –  Vladimir Dotsenko Jan 23 '13 at 8:15