Enh/action character

[kalmarek]

• reworked real projections using frobenius-schur indicator
• I guess we don't need VirtualCharacters now
• added action_character and use orthogonality of characters to figure out its constituents : no unnecessary(=zero) projection will be ever computed
• when calling symmetry_adapted_basis(G, basis, action) the user provides the action as a function action(b, g) → b' for b,b'∈ basis and g ∈ G. No need to extend/pirate anything, closing #22 ? with this method a call for polynomial basis is structured as

  permuted(exponent::AbstractVector, p::Perm) =
  [exponent[i^p] for i in eachindex(exponent)]
  sa = symmetry_adapted_basis(G, monomial_basis, permuted)

• the action function (permuted) is stored in ExtensionHomomorphism, which hopefully will allow us to use it for other actions than permutation ones ;)

[codecov[bot]]

Codecov Report

Merging #25 (e84e826) into master (98e56d0) will decrease coverage by 2.63%. The diff coverage is 83.33%.

@@            Coverage Diff             @@
##           master      #25      +/-   ##
==========================================
- Coverage   91.17%   88.53%   -2.64%     
==========================================
  Files          10       10              
  Lines         442      445       +3     
==========================================
- Hits          403      394       -9     
- Misses         39       51      +12     

Flag	Coverage Δ
unittests	88.53% <83.33%> (-2.64%)	:arrow_down:

Flags with carried forward coverage won't be shown. Click here to find out more.

Impacted Files	Coverage Δ
src/SymbolicWedderburn.jl	100.00% <ø> (ø)
src/characters_arith.jl	25.00% <0.00%> (-46.43%)	:arrow_down:
src/characters.jl	75.51% <67.64%> (+1.43%)	:arrow_up:
src/actions.jl	91.66% <100.00%> (ø)
src/dixon.jl	98.18% <100.00%> (+0.03%)	:arrow_up:
src/eigenspacedecomposition.jl	93.87% <100.00%> (-0.07%)	:arrow_down:
src/gf.jl	94.02% <100.00%> (ø)
src/projections.jl	84.21% <100.00%> (-10.24%)	:arrow_down:

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[kalmarek]

@blegat I'll merge this but it'd be best to meet and chat about ScaledPerm etc. ;)