Macaulay2 » Documentation
Packages » ThinSincereQuivers > coneSystem

next | previous | forward | backward | up | index | toc

coneSystem -- compute the chamber decomposition of weights

Synopsis

Usage:

coneSystem Q
Inputs:
- Q, an instance of the type ToricQuiver,
Outputs:
- L, a list, of Cones

Description

The set of weights th for which the polytope (Q,th) is nonempty lies in a fan CQ. This fan is partitioned into cones by the walls of the toric quiver Q, and for each partition there exists a unique flow polytope. For a detailed discussion see Lutz Hille "Quivers, cones and polytopes", Linear algebra and its applications 365 (2003): 215-237.

i1 : Q = toricQuiver {{0,1},{0,2},{0,3},{1,2},{1,3},{2,3}};

i2 : CS = coneSystem Q

o2 = {Cone{...1...}, Cone{...1...}, Cone{...1...}, Cone{...1...},
     ------------------------------------------------------------------------
     Cone{...1...}, Cone{...1...}, Cone{...1...}}

o2 : List

See also

flowPolytopeVertices -- generate the polytope associated to a toric quiver

For the programmer

The object coneSystem is a function closure.