When printing matrices, replace zeros by dots

[fingolfin]

This makes it easier to read many matrices, especially those which are relatively sparse.

Before:

julia> matrix(QQ, [42 0 0; 0 42 0; 0 0 42])
[42//1    0//1    0//1]
[ 0//1   42//1    0//1]
[ 0//1    0//1   42//1]

After:

julia> matrix(QQ, [42 0 0; 0 42 0; 0 0 42])
[42//1       .       .]
[    .   42//1       .]
[    .       .   42//1]

This is breaking in so far as it will require changes to a bunch of doctests in Oscar.jl and probably other packages.

I expect this will be somewhat controversial, but I wanted to at least put it out there. To me it is subjectively a major improvement but I realize others may have a quite different opinion. But I figured we could at least discuss it.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.67%. Comparing base (5170909) to head (cc58444).
⚠️ Report is 408 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1459      +/-   ##
==========================================
- Coverage   88.10%   86.67%   -1.43%     
==========================================
  Files         120      120              
  Lines       30045    30021      -24     
==========================================
- Hits        26470    26021     -449     
- Misses       3575     4000     +425     

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[thofma]

Hm, I have a different opinion. I don't like the dots.

I don't like the superfluous // either, but using Nemo/Oscar, it looks much better and I don't see a need for dots:

julia> matrix(QQ, [42 0 0; 0 42 0; 0 0 42])
[42    0    0]
[ 0   42    0]
[ 0    0   42]

[fingolfin]

For me the application are biggish matrices over finite fields where I can see the structure (e.g. block diagonal etc.) at a glance with the "." printing but not with integers, e.g. here an example over GF(11):

[1   8   2   0   0   0]
[7   1   8   0   8   0]
[0   1   1   0   0   0]
[0   0   0   1   2   3]
[0   0   0   9   8   0]
[0   0   0   0   7   8]

where I don't immediately see what's going on, but

[1   8   2   .   .   .]
[7   1   8   .   8   .]
[.   1   1   .   .   .]
[.   .   .   1   2   3]
[.   .   .   9   8   .]
[.   .   .   .   7   8]

makes it stand out.

[thofma]

I find

julia> zero_matrix(QQ, 2, 2)
[.   .]
[.   .]

rather obscure. To be honest, I am not too excited about this change.

Maybe we could hide it behind a preference?

[fingolfin]

Having a preferences for this sounds useful, just like for the unicode printing -- and just like for that, we should then have a way to temporarily turn it off, and also turn it off (or on, for testing the feature itself) in test suites