Add and document new function DirectProductFamily

[ssiccha]

lib: add operation DirectProductFamily

This declares the new operation DirectProductFamily and installs a
method for it. Also adds documentation and tests.

In the reference manual, the section "IsDirectProductElement (Filter)"
is renamed into "Direct Products and their Elements" to also accomodate
the documentation of DirectProductFamily and future categories and
operations.

UnderlyingRelation is adapted to use the new method, which makes it
easier to read.

[ssiccha]

I have added the release notes not needed tag since this function is not documented. Or should I document it?

[DominikBernhardt]

Several tests failed due to a No method found error. You should check that.

[codecov]

Codecov Report

Merging #3455 into master will increase coverage by 0.22%.
The diff coverage is 100%.

@@            Coverage Diff             @@
##           master    #3455      +/-   ##
==========================================
+ Coverage    85.4%   85.63%   +0.22%     
==========================================
  Files         696      646      -50     
  Lines      344610   319019   -25591     
==========================================
- Hits       294327   273203   -21124     
+ Misses      50283    45816    -4467

Impacted Files	Coverage Δ
lib/mapping.gi	89.78% <100%> (-0.02%)	⬇️
lib/tuples.gi	95.72% <100%> (+0.12%)	⬆️
lib/tuples.gd	100% <100%> (ø)	⬆️
src/libgap-api.c	0% <0%> (-64.54%)	⬇️
lib/random.g	66.66% <0%> (-30.56%)	⬇️
src/compiler.c	67.44% <0%> (-21.21%)	⬇️
src/error.c	67.87% <0%> (-20.35%)	⬇️
lib/read2.g	85.71% <0%> (-14.29%)	⬇️
lib/read1.g	85.36% <0%> (-13.42%)	⬇️
lib/session.g	57.69% <0%> (-12.83%)	⬇️
... and 174 more

[ssiccha]

Thanks for the heads-up.

I fixed the issue. The filter IsCollection was (in hindsight obviously) too restrictive.

[coveralls]

Coverage increased (+0.0007%) to 85.232% when pulling 4ea0738 on ssiccha:ss/add-DirectProductFamily into f71497d on gap-system:master.

[ChrisJefferson]

Do you want to be able to call this in your own code? If so, we should document it, so we know what it is supposed to do.

[DominikBernhardt]

Tests for DirectProductFamily checking your added code would be nice.

[DominikBernhardt]

It would be good to document your code, I don't see any reason against it?

[stevelinton]

In documenting this, (and DirectProductElement) it is probably worth pointing out that not all direct products are made this way. For instance:

gap> g := SymmetricGroup(4);
Sym( [ 1 .. 4 ] )
gap> DirectProduct(g,g);    
Group([ (1,2,3,4), (1,2), (5,6,7,8), (5,6) ])

Arguably, perhaps they should be, with IsomorphismPermGroup available to those who want a nicer form, but that's a question for another time.

[ssiccha]

Good point! Thanks

[ssiccha]

I was thinking about doing a function DirectProductGroupInProductAction. But that's low priority for me atm.

[ssiccha]

I've updated the PR!

[ssiccha]

Added the method to hpcgap/lib/tuples.gi

[fingolfin]

Seems plausible to me.

[DominikBernhardt]

Looks good to me.

[ssiccha]

I rebased onto master and put the new changes into a separate commit. Once this PR is accepted I'll squash everything into a single commit.

[ssiccha]

Squashed.

[fingolfin]

Thank you, this looks pretty good now! Unfortunately there is one issue left, but that should be easy to fix: changes to lib/mapping.gi also need to be applied to hpcgap/lib/mapping.gi.