Implement hyperbolic Cartan types

[tscrim]

They are a important class of indeterminate Cartan types. They will be given in terms of the table given in Classification of hyperbolic Dynkin diagrams, root lengths, and Weyl group orbits by Carbone, Chung, Cobbs, McRae, Nandi, Naqvi, and Penta (​http://arxiv.org/abs/1003.0564), as well as in some of the other notations specified in the aforementioned paper.

[tscrim]

Current WIP version (I'm not guaranteeing anything to really work, nor for the structure to not change).

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Last 10 new commits:

​59c49b4	Refactoring hyperbolic types and added Lorentzian types.
​a920566	More work on Lorentzian Cartan types.
​ca06d90	Moved type E Lorentzian to separate file, started rank 3 hyperbolic types.
​9a07193	More work on hyperbolic root systems.
​d65fb76	Merge branch 'develop' into public/combinat/root_systems/hyperbolic-15974
​c655d51	Implemented marked Cartan types and refactored common code.
​80684be	Fixed last doctests and added to full coverage.
​612db21	Fixed last failing doctest.
​964d8ac	Merge branch 'public/combinat/root_systems/marked_types-15948' into public/combinat/root_systems/hyperbolic-15974
​cd15134	Merge branch 'develop' into public/combinat/root_systems/hyperbolic-15974

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​ae6d01c

Merge branch 'develop' into public/combinat/root_systems/hyperbolic-15974

[nthiery]

Hi Travis!

Just a quick suggestion for less duplication in the code and a better isolation of the "database" part. Make:

if index == 1:
    dd = CartanType_Rank3Cycle._construct_dynkin_diagram((1,1,2))
elif index == 2:
    dd = CartanType_Rank3Cycle._construct_dynkin_diagram((1,1,-22))
elif index == 3:
   dd = CartanType_Rank3Cycle._construct_dynkin_diagram((1,1,3))
...

Into, at the start of the file and with a more specific name than data if possible:

    data = (None, (1,1,2), (1,1,-22), (1,1,3), ...)

And in the constructor:

    dd = CartanType_Rank3Cycle._construct_dynkin_diagram(data[i])

Cheers,

Nicolas

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​a807b5f	Merge branch 'public/combinat/root_systems/hyperbolic-15974' of trac.sagemath.org:sage into public/combinat/root_systems/hyperbolic-15974
​8748c79	Merge branch 'develop' into public/combinat/root_systems/hyperbolic-15974
​d170a57	Replaced Lorentzian with hyperbolic.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​be1375d

Merge branch 'public/combinat/root_systems/hyperbolic-15974' of trac.sagemath.org:sage into public/combinat/root_systems/hyperbolic-15974