allow specifying index type for CachedExtensionHomomorphism

[kalmarek]

Problem:
No way to create CachedExtensionHomomorphism with specified index type. For large basis this could lead to hard to fix errors (without diving deep into the package).

Before:

julia> ehom = SymbolicWedderburn.CachedExtensionHomomorphism(G,action,words)
ERROR: "index type UInt16 is to small for basis of length 88572"
Stacktrace:
 [1] Basis
   @ ~/.julia/packages/StarAlgebras/0yFWh/src/bases.jl:9 [inlined]
 [2] ExtensionHomomorphism
   @ ~/.julia/dev/SymbolicWedderburn/src/ext_homomorphisms.jl:57 [inlined]
 [3] SymbolicWedderburn.CachedExtensionHomomorphism(::Type{Int16}, G::PermGroup{Perm{UInt16}, …}, action::OnLetters, basis::Vector{Word{Symbol}}; precompute::Bool)
   @ SymbolicWedderburn ~/.julia/dev/SymbolicWedderburn/src/ext_homomorphisms.jl:87
 [4] SymbolicWedderburn.CachedExtensionHomomorphism(::Type{Int16}, G::PermGroup{Perm{UInt16}, …}, action::OnLetters, basis::Vector{Word{Symbol}})
   @ SymbolicWedderburn ~/.julia/dev/SymbolicWedderburn/src/ext_homomorphisms.jl:80
 [5] top-level scope
   @ REPL[42]:1

After:

julia> ehom = SymbolicWedderburn.CachedExtensionHomomorphism(Int32, G,action,words);

julia> SW.induce(ehom, one(G))
()

julia> typeof(ans)
Perm{Int32}

CC: @laurentbartholdi

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (e710eda) 87.50% compared to head (01f4f03) 87.69%.
Report is 2 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #65      +/-   ##
==========================================
+ Coverage   87.50%   87.69%   +0.19%     
==========================================
  Files          20       20              
  Lines        1328     1333       +5     
==========================================
+ Hits         1162     1169       +7     
+ Misses        166      164       -2     

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unittests	87.69% <100.00%> (+0.19%)	⬆️

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[laurentbartholdi]

This works now fine for "CachedExtensionHomomorphism".

However, the all-in-one "sabasis = SymbolicWedderburn.symmetry_adapted_basis(UInt32, G, action, words)" does not work -- I suspect actually the "UInt32" is interpreted as a type for the scalars in the resulting basis, not a type for the permutations.

In fact, I can't see any situation in which UInt16 is better than UInt32 for permutations. If they fit in a UInt16, then unless you're programming a Commodore 64 you'll have plenty of free memory so UInt32 would also work. On the other hand there may be cases in which the user would like UInt64, but then leave it to them.

[kalmarek]

@laurentbartholdi The proper solution should be that the index type is inferrable from G and action.

[kalmarek]

Well, that's exactly what we need to do then ;)

@laurentbartholdi it's not only about the memory, but rather lookup (=hashing speed) in the dictionary

[laurentbartholdi]

The tests are broken, but the code itself seems very good to me.