Allow giving, and make use of, a known subgroup of the answer

[ChrisJefferson]

This should be particularly useful for computing normalisers.

This should result in better performance.

[wilfwilson]

There are three aspects to this:

1. What should the interface be (easiest part!)
2. Mathematically, what is possible to do?
3. The implementation of 1. and 2.

In reference to 1, I think that partially it should be done automatically where possible (e.g. if we ask Vole for the symmetric normaliser of a group G, we shouldn't need to have to explicitly tell Vole that it should use that the result contains G), and at least in the first instance, I think a specific partial answer should be given by another ValueOption, e.g.:

VoleFind.Group(con1, con2, con3 : partial := G);

In reference to 2, I'm not sure yet!

[Munsee]

At least for now, I do not require it to be automatic. We probably want it to be protected for now though.
Mathematically it allows us to search in the coset of the known subgroup. Is that what you're asking?
Since we are skipping using known answers anyway, implementation should not be too hard? There may be something I'm completely missing.

[wilfwilson]

Yes you're right, we simply get a 'head start' on the search. I wondered if there was anything deeper that we could use, but surely not?