In [1]:
load("SimpleGroup.sage")
load("GIT.sage")
In [2]:
# Example 
# Cubics in P2
Phi = WeylCharacterRing("A2")
representation= Phi(3,0,0)
P=GITProblem(representation,label="Plane quartics")
P.solve_non_stable(Weyl_optimisation=True)
P.print_solution_nonstable()


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SOLUTION TO GIT PROBLEM: NONSTABLE LOCI
***************************************
Group: A2
Representation  A2(3,0,0)
Set of maximal non-stable states:
(1) 1-PS = (1, 1, -2) yields a state with 7 characters
Maximal nonstable state={ (1, 2, 0), (2, 1, 0), (1, 1, 1), (0, 2, 1), (0, 3, 0), (2, 0, 1), (3, 0, 0) }
(2) 1-PS = (1, -1/2, -1/2) yields a state with 6 characters
Maximal nonstable state={ (1, 2, 0), (1, 0, 2), (2, 1, 0), (1, 1, 1), (2, 0, 1), (3, 0, 0) }
In [3]:
P.solve_unstable(Weyl_optimisation=True)
P.print_solution_unstable()


**************************************
SOLUTION TO GIT PROBLEM: UNSTABLE LOCI
**************************************
Group: A2
Representation  A2(3,0,0)
Set of maximal unstable states:
(1) 1-PS = (1, 1/4, -5/4) yields a state with 5 characters
Maximal unstable state={ (1, 2, 0), (2, 1, 0), (0, 3, 0), (2, 0, 1), (3, 0, 0) }
In [4]:
P.solve_strictly_polystable()
P.print_solution_strictly_polystable()


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SOLUTION TO GIT PROBLEM: STRICTLY POLYSTABLE LOCI
*************************************************************
Group: A2
Representation  A2(3,0,0)
Set of strictly T-polystable states:
(1) A state with 1 characters
Strictly polystable state={ (1, 1, 1) }
(2) A state with 3 characters
Strictly polystable state={ (0, 2, 1), (2, 0, 1), (1, 1, 1) }
In [ ]: