Enh/matrix actions

[kalmarek]

here's the first try;

Note that the action (ex_C2_linear.jl) is not given by

x → x+y
y → x-y

but rather normalized (or rather: orthonormalized)

x → (x+y)/√2
y → (x-y)/√2

This nicely extends to an actual action on larger basis (modulo numerics).

I see several problems arising here: if features/their images are not orthogonal (whatever that means) this code has no chance of working in general (or so I think);

should we then vectors when we compute their action?

there are a few more things I guess, but I'm too tired now, and will be arriving home in 30 minutes, so time to wrap it up ;)

@tweisser @blegat

[codecov[bot]]

Codecov Report

Merging #32 (0970d4e) into master (0fefd3c) will decrease coverage by 0.72%. The diff coverage is 87.27%.

@@            Coverage Diff             @@
##           master      #32      +/-   ##
==========================================
- Coverage   89.83%   89.10%   -0.73%     
==========================================
  Files           9        9              
  Lines         472      505      +33     
==========================================
+ Hits          424      450      +26     
- Misses         48       55       +7     

Flag	Coverage Δ
unittests	89.10% <87.27%> (-0.73%)	:arrow_down:

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

Impacted Files	Coverage Δ
src/actions.jl	82.60% <83.72%> (-11.15%)	:arrow_down:
src/characters.jl	77.89% <100.00%> (ø)
src/projections.jl	84.74% <100.00%> (+0.53%)	:arrow_up:
src/eigenspacedecomposition.jl	95.23% <0.00%> (+0.03%)	:arrow_up:

---

Continue to review full report at Codecov.

Legend - Click here to learn more Δ = absolute <relative> (impact), ø = not affected, ? = missing data Powered by Codecov. Last update 0fefd3c...0970d4e. Read the comment docs.

[kalmarek]

@blegat I should note that I simplified somehow the API compared to what we discussed yesterday, but of course this is just a first try ;)

[blegat]

I fixed the issue with Julia v1.0. I guess it's important that the basis is linearly independent. It probably also needs to be orthogonal, not sure.

[kalmarek]

thanks for those fixes; but it seems that either we should drop this InducedActionHomomorphism, or replace those type methods by functions.

I'll try to play with the dihedral group later in the evening

[kalmarek]

@blegat I tried to fix DihedralAction in SOS, but I ran into some trouble. Could you have a look at my branch?

[kalmarek]

ok, I'll create a testset based on the C2 example and once coverage is high enough i'll merge

[kalmarek]

@blegat ready to register?

[blegat]

Almost, one last detail :)