WIP lib: add SetAsDomain

[ssiccha]

TODO

• move new code into domain.g?
• add tests!!
• text for release notes

Description

Currently there is no filter that specifies explicitly that a domain is created as a set with no operational structure. This PR introduces the filter IsSetAsDomain. The motivation is to be able to use e.g. SetAsDomain([1..n]) as a domain for MappingByFunction:

gap> MappingByFunction(SetAsDomain([1..5]), SetAsDomain([1..5]), x -> x);
MappingByFunction( SetAsDomain([ 1 .. 5 ]), SetAsDomain([ 1 .. 5 ]), function( x ) ... end )
gap> Image(last);
[ 1, 2, 3, 4, 5 ]

One thing that is not entirely clear to me yet: As IsPermGroup already implies IsDomain, should it also imply IsSetAsDomain or not? I think it should. Methods for e.g. IsPermGroup would then outrank methods for IsSetAsDomain anyways.

[coveralls]

Coverage decreased (-0.003%) to 85.159% when pulling 069366b on ssiccha:ss/add-SetAsDomain into 7162a59 on gap-system:master.

[codecov]

Codecov Report

Merging #3460 into master will decrease coverage by <.01%.
The diff coverage is 51.51%.

@@            Coverage Diff             @@
##           master    #3460      +/-   ##
==========================================
- Coverage   85.34%   85.33%   -0.01%     
==========================================
  Files         699      699              
  Lines      346471   346505      +34     
==========================================
+ Hits       295681   295699      +18     
- Misses      50790    50806      +16

Impacted Files	Coverage Δ
lib/set.gd	100% <100%> (ø)	⬆️
lib/set.gi	61.37% <48.38%> (-3.23%)	⬇️

[fingolfin]

Something is wrong with this PR, with it it seems GAP cannot even start (looking at Travis logs here).

To be honest, I am not quite sure what the point of this is. In the end, all it seems to add is a print method, and only for domains who are defined on a GAP "set". But that does not seem to be very compelling to me. I can already do everything else in GAP right now, can't I?

gap> d:=Domain([1,2,3,1]);
<object>
gap> d!.GeneratorsOfDomain;
[ 1, 2, 3, 1 ]
gap> AsSet(d);
[ 1, 2, 3 ]
gap> 1 in d;
true
gap> 4 in d;
false

[fingolfin]

But IsSetAsDomain is merely a synonym for IsDomain; so now you really have installed a generic \in method for arbitrary domains, which tries to use AsList. That makes me a bit nervous, though I can't put my finger on it right now.

[fingolfin]

Don't you need a different function for empty domains?

[ssiccha]

Oh sorry. This was a bit chaotic since I also had like 5 other PRs going on. I first thought I would introduce a new Category IsSetAsDomain. Then I decided against that and unfortunately left the PR in a broken state which doesn't make any sense.

Here are my current thoughts on what I actually want to do:
For constructing the normalisers of socles of primitive groups I want to use the IsMapping objects in GAP. If I define a mapping of "sets" in the current master though I get

gap> MappingByFunction(Domain([1..5]), Domain([1..5]), x -> x);
MappingByFunction( <object>, <object>, function( x ) ... end )

which I find very ugly. At the very least I want users to be able to see for a map that I defined what its domain and range are. So I think there are basically two options

1. Install a PrintObj method for IsDomain and HasGeneratorsOfDomain
2. Create a new category IsSetAsDomain which models that our domain is an actual set. After all a collection of families could also be turned into a domain and this is neither a set in the mathematical sense nor in the IsSSortedList sense.

While I'm not sure whether there are people who would find 2. useful I'm gonna go with 1. atm since that's also a lot less effort.