Document precisely which methods are implemented *and* used

[fingolfin]

We already made some progress on this by adding comments to source files that give references to papers that are implemented in the file (resp. where we think they are implemented -- some TODO comments here need to be resolved, grep for "probably based on").

But I would like this to be in the code itself -- for each recognition method we install, we should also have a record member that indicates the algorithm implemented there, via a string describing the source (for some of the most basic ones, that could of course be a simple string like "folklore").

Once we have that, we then insert this information automatically into the manual.

• [ ] create a list of algorithms which are implemented; in particular proper citation and a bibliography (in the code, and also the manual; ideally generate the list in the manual from the code) (edit by @ssiccha:) split up the list into reduction and constructive recognition algorithms.
• [ ] similar, a list of algorithms that are not yet there, but which should be implemented! These include:
  • [ ] constructive recognition of orthogonal and symplectic groups (in all variations, i.e. natural and non-natural representations; for matrix, permutation, black box groups; ...)
  • [ ] constructive recognition of exceptional groups (in all variations)
  • [ ] constructive recognition of sporadic groups (???)
• [ ] besides this "technical" overview, we should also approach this from a mathematical angle:
  • [ ] which (families of) groups are currently supported, which are not?
  • [ ] note that sometimes groups are recognized, but only because they were small enough to be handled by some fallback method. E.g. small orthogonal groups "work" because recog can fallback to an isomorphism with a permutation group, and then applies Schreier-Sims. So, for families, it's a good idea to test multiple members, and in particular large ones
• [ ] determine whether all Aschbacher classes are correctly covered
  • [ ] generate test inputs for which the structure is known, and then test whether recog handles
  • [ ] Frank Lübeck and und Jürgen Müller provided examples, which are bundled with recog as examples/example*.g; these show some problem areas.
  • [ ] Frank has the tools to generate these and more...

[fingolfin]

A good way to produce lots of nice test cases is to take the atlasrep package, then iterate over all the groups in there, and for each group, iterate over its maximal subgroups; and then try recognition on the maximal subgroups. This covers lots of interesting cases and we also have data about the expected isomorphism type resp. the size of those maximal subgroups.

Work on this was started during the GAP Days by @ChrisJefferson et all, and this resulted in RECOG.testAllMaximalSubgroupsOfAtlasGroup. It reveals many, many problems. Before we pursue this further, we need to address some of them, and most importantly, implement mandarins (see issue #85)