Opened 5 years ago
Last modified 5 years ago
#18000 new enhancement
Root multiplicities for symmetrizable KacMoody algebras
Reported by:  jonathan.judge  Owned by:  jonathan.judge 

Priority:  major  Milestone:  sage6.8 
Component:  combinatorics  Keywords:  days64 
Cc:  bump, bsalisbury1, khlee  Merged in:  
Authors:  Reviewers:  
Report Upstream:  N/A  Work issues:  
Branch:  u/jonathan.judge/root_multiplicities_for_symmetrizable_kac_moody_algebras (Commits)  Commit:  55d2f5269995e5ee42fbe765f657721257bf0c57 
Dependencies:  #18644, #18645  Stopgaps: 
Description
Add a method (probably in root_lattice_realizations) to compute the multiplicity of a given root. The algorithm is the Peterson recursive formula.
Change History (5)
comment:1 Changed 5 years ago by
 Branch set to u/jonathan.judge/root_multiplicities_for_symmetrizable_kac_moody_algebras
comment:2 Changed 5 years ago by
 Commit set to 4958ee0f2ebf0fe63dec7231b3111f2a4dd1d63d
 Owner changed from (none) to jonathan.judge
comment:3 Changed 5 years ago by
 Dependencies set to 18644, 18645
 Milestone changed from sage6.6 to sage6.8
comment:4 Changed 5 years ago by
 Dependencies changed from 18644, 18645 to #18644, #18645
comment:5 Changed 5 years ago by
 Commit changed from 4958ee0f2ebf0fe63dec7231b3111f2a4dd1d63d to 55d2f5269995e5ee42fbe765f657721257bf0c57
Branch pushed to git repo; I updated commit sha1. New commits:
d700a67  Merge branch 'develop' into t/18000/root_multiplicities_for_symmetrizable_kac_moody_algebras

77f1bf6  Added methods is_indefinite(), is_hyperbolic(), is_indecomposable(), and principal_submatrices() to the class CartanMatrix

2560229  Merge branch 't/18645/add_some_methods_to_cartanmatrix' into t/18000/root_multiplicities_for_symmetrizable_kac_moody_algebras

c7a1b37  Fixed element method is_real_root() in root_lattice_realizations.py

3cc6587  Merge branch 't/18645/add_some_methods_to_cartanmatrix' into t/18644/fix_method_is_real_root___in_root_lattice_realizations_py

6784229  Merge branch 't/18644/fix_method_is_real_root___in_root_lattice_realizations_py' into t/18000/root_multiplicities_for_symmetrizable_kac_moody_algebras

55d2f52  Rewrote multiplicity computation to take advantage of new and corrected methods in 18644 and 18645

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New commits:
Added a function multiplicity() on elements of a root lattice. The computation is done via Peterson's recurrent formula