LieAlgebras: Constructions for module homs

[lgoettgens]

This builds upon #2644 and thus includes that PR. Once #2644 gets merged, I will rebase this PR.

Introduces new constructions for Lie algebra module homs:

• injections/projections for direct sums
• hom_tensor
• hom_direct_sum
• lift hom $V \to W$ to $T^k V \to T^k W$
• lift hom $V \to W$ to $\bigwedge^k V \to \bigwedge^k W$
• lift hom $V \to W$ to $S^k V \to S^k W$

While doing that, refactor the constructions of the modules and put more helpful stuff in attribute storage:

• direct sum
• tensor product
• tensor power
• exterior power
• symmetric power

More changes:

• add is_welldefined to be able to check that even if using check=false in the hom constructor
• add zero_map
• change the internals of modules to use right multiplication with a matrix as the action

Missing:

• Handle 0-th powers

[codecov]

Codecov Report

Merging #2753 (3d4a213) into master (d42af1a) will increase coverage by 0.33%.
Report is 48 commits behind head on master.
The diff coverage is 77.73%.

@@            Coverage Diff             @@
##           master    #2753      +/-   ##
==========================================
+ Coverage   73.26%   73.60%   +0.33%     
==========================================
  Files         450      455       +5     
  Lines       63973    64675     +702     
==========================================
+ Hits        46872    47604     +732     
+ Misses      17101    17071      -30     

Files Changed	Coverage
experimental/LieAlgebras/src/LieAlgebras.jl	ø
...rimental/LieAlgebras/test/LieAlgebraModule-test.jl	ø
experimental/LieAlgebras/src/LieAlgebraModule.jl	70.77%
...xperimental/LieAlgebras/src/LieAlgebraModuleHom.jl	81.72%
...xperimental/LieAlgebras/test/LieAlgebraHom-test.jl	96.00%
experimental/LieAlgebras/src/LieAlgebraHom.jl	100.00%

[fieker]

is there any reason to not bind hom_tensor and hom_direct_sum to hom as well? As in
hom(M, N, V) for M and N being tensor products: call hom_tensor, for both being ...?

[lgoettgens]

is there any reason to not bind hom_tensor and hom_direct_sum to hom as well? As in hom(M, N, V) for M and N being tensor products: call hom_tensor, for both being ...?

I am not sure if I understand you correctly. Are you proposing to add hom_tensor (and hom_direct_sum) instead as methods to hom?
As similar functions (hom_tensor and hom_product) already exist for ModuleFP, I would keep it here for the time being as is, and then discuss your proposal in a new issue for both ModuleFP and LieAlgebraModule.

[lgoettgens]

There is a little bit of cleanup possible once thofma/Hecke.jl#1196 is available.

[fingolfin]

Looks good to me, thanks