}}}
{{{id=39|
MC = S33.b_matrix_class(); MC
///
WARNING: Output truncated!
full_output.txt
\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left(\begin{array}{rrrrrr}
0 & 0 & 0 & 0 & 1 & 1 \\
0 & 0 & 0 & 1 & 0 & 1 \\
0 & 0 & 0 & 1 & 1 & 0 \\
0 & -1 & -1 & 0 & 0 & 0 \\
-1 & 0 & -1 & 0 & 0 & 0 \\
-1 & -1 & 0 & 0 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrrr}
0 & 0 & 0 & 1 & 1 & 0 \\
0 & 0 & 1 & 0 & 1 & 0 \\
0 & -1 & 0 & 0 & 0 & 1 \\
-1 & 0 & 0 & 0 & 0 & 1 \\
-1 & -1 & 0 & 0 & 0 & 0 \\
0 & 0 & -1 & -1 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrrr}
0 & 0 & 0 & 0 & 1 & 1 \\
0 & 0 & 1 & 1 & 0 & 0 \\
0 & -1 & 0 & 0 & 0 & 1 \\
0 & -1 & 0 & 0 & 1 & 0 \\
-1 & 0 & 0 & -1 & 0 & 0 \\
-1 & 0 & -1 & 0 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrrr}
0 & 0 & 1 & 0 & 0 & 1 \\
0 & 0 & 0 & -1 & 1 & 1 \\
-1 & 0 & 0 & 0 & 1 & 0 \\
0 & 1 & 0 & 0 & -1 & 0 \\
0 & -1 & -1 & 1 & 0 & 0 \\
-1 & -1 & 0 & 0 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrrr}
0 & 0 & 0 & 1 & 1 & 0 \\
0 & 0 & 0 & 0 & -1 & 1 \\
0 & 0 & 0 & -1 & 0 & 1 \\
-1 & 0 & 1 & 0 & 0 & 0 \\
-1 & 1 & 0 & 0 & 0 & 0 \\
0 & -1 & -1 & 0 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrrr}
0 & 0 & 0 & 0 & 1 & 1 \\
0 & 0 & 0 & -1 & 1 & 0 \\
0 & 0 & 0 & 1 & 0 & -1 \\
0 & 1 & -1 & 0 & 0 & 1 \\
-1 & -1 & 0 & 0 & 0 & 0 \\
-1 & 0 & 1 & -1 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrrr}
0 & 0 & 0 & 1 & 1 & 0 \\
0 & 0 & 0 & -1 & 0 & 1 \\
0 & 0 & 0 & 0 & 1 & -1 \\
-1 & 1 & 0 & 0 & 0 & 0 \\
-1 & 0 & -1 & 0 & 0 & 1 \\
0 & -1 & 1 & 0 & -1 & 0
\end{array}\right), \left(\begin{array}{rrrrrr}
0 & 0 & 0 & -1 & 1 & 1 \\
0 & 0 & -1 & 0 & 1 & 1 \\
0 & 1 & 0 & 0 & 0 & -1 \\
1 & 0 & 0 & 0 & 0 & -1 \\
-1 & -1 & 0 & 0 & 0 & 0 \\
-1 & -1 & 1 & 1 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrrr}
0 & 0 & -1 & 0 & 0 & 1 \\
0 & 0 & 0 & -1 & 1 & 0 \\
...
0 & 1 & 1 & 0 & -1 & -1 \\
-1 & 0 & -1 & 1 & 0 & 0 \\
-1 & -1 & 0 & 1 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrrr}
0 & 0 & 0 & 0 & -1 & 0 \\
0 & 0 & -1 & 0 & 0 & 1 \\
0 & 1 & 0 & -1 & 0 & 0 \\
0 & 0 & 1 & 0 & -1 & 1 \\
1 & 0 & 0 & 1 & 0 & -1 \\
0 & -1 & 0 & -1 & 1 & 0
\end{array}\right), \left(\begin{array}{rrrrrr}
0 & 0 & 0 & -1 & 0 & 0 \\
0 & 0 & -1 & 0 & 1 & 0 \\
0 & 1 & 0 & 0 & -1 & 1 \\
1 & 0 & 0 & 0 & 1 & -1 \\
0 & -1 & 1 & -1 & 0 & 1 \\
0 & 0 & -1 & 1 & -1 & 0
\end{array}\right), \left(\begin{array}{rrrrrr}
0 & 0 & 0 & -1 & 0 & 0 \\
0 & 0 & 0 & 0 & 1 & -1 \\
0 & 0 & 0 & -1 & 1 & 1 \\
1 & 0 & 1 & 0 & 0 & -1 \\
0 & -1 & -1 & 0 & 0 & 1 \\
0 & 1 & -1 & 1 & -1 & 0
\end{array}\right), \left(\begin{array}{rrrrrr}
0 & 0 & 0 & 0 & 0 & 1 \\
0 & 0 & 1 & -1 & 1 & 0 \\
0 & -1 & 0 & 1 & 0 & 0 \\
0 & 1 & -1 & 0 & 1 & -1 \\
0 & -1 & 0 & -1 & 0 & 1 \\
-1 & 0 & 0 & 1 & -1 & 0
\end{array}\right), \left(\begin{array}{rrrrrr}
0 & 0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 0 & -1 & 1 \\
0 & 0 & 0 & -1 & 1 & 1 \\
-1 & 0 & 1 & 0 & -1 & 0 \\
0 & 1 & -1 & 1 & 0 & -1 \\
0 & -1 & -1 & 0 & 1 & 0
\end{array}\right), \left(\begin{array}{rrrrrr}
0 & 0 & 0 & 1 & 1 & -2 \\
0 & 0 & 0 & 0 & -1 & 0 \\
0 & 0 & 0 & -1 & 0 & 0 \\
-1 & 0 & 1 & 0 & 0 & 1 \\
-1 & 1 & 0 & 0 & 0 & 1 \\
2 & 0 & 0 & -1 & -1 & 0
\end{array}\right), \left(\begin{array}{rrrrrr}
0 & 0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 & 1 & -2 \\
0 & -1 & -1 & 0 & 0 & 1 \\
-1 & 0 & -1 & 0 & 0 & 1 \\
0 & 0 & 2 & -1 & -1 & 0
\end{array}\right), \left(\begin{array}{rrrrrr}
0 & 0 & 0 & 0 & 1 & 0 \\
0 & 0 & 1 & 0 & 1 & -2 \\
0 & -1 & 0 & 1 & 0 & 1 \\
0 & 0 & -1 & 0 & 0 & 0 \\
-1 & -1 & 0 & 0 & 0 & 1 \\
0 & 2 & -1 & 0 & -1 & 0
\end{array}\right)\right]
}}}
{{{id=40|
B = MC[5]; B
///
\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrr}
0 & 0 & 0 & 0 & 1 & 1 \\
0 & 0 & 0 & -1 & 1 & 0 \\
0 & 0 & 0 & 1 & 0 & -1 \\
0 & 1 & -1 & 0 & 0 & 1 \\
-1 & -1 & 0 & 0 & 0 & 0 \\
-1 & 0 & 1 & -1 & 0 & 0
\end{array}\right)
}}}
{{{id=41|
Snew = ClusterSeed(B); Snew; Snew.show()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\verb|A|\phantom{x}\verb|seed|\phantom{x}\verb|for|\phantom{x}\verb|a|\phantom{x}\verb|cluster|\phantom{x}\verb|algebra|\phantom{x}\verb|of|\phantom{x}\verb|rank|\phantom{x}\verb|6|
}}}
{{{id=42|
Snew2 = Snew.principal_extension(); Snew2; Snew2.show()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\verb|A|\phantom{x}\verb|seed|\phantom{x}\verb|for|\phantom{x}\verb|a|\phantom{x}\verb|cluster|\phantom{x}\verb|algebra|\phantom{x}\verb|of|\phantom{x}\verb|rank|\phantom{x}\verb|6|\phantom{x}\verb|with|\phantom{x}\verb|6|\phantom{x}\verb|frozen|\phantom{x}\verb|variables|
}}}
{{{id=43|
Snew2.mutation_type()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\verb|['A',|\phantom{x}\verb|[3,|\phantom{x}\verb|3],|\phantom{x}\verb|1]|
}}}
{{{id=44|
Snew2
///
\newcommand{\Bold}[1]{\mathbf{#1}}\verb|A|\phantom{x}\verb|seed|\phantom{x}\verb|for|\phantom{x}\verb|a|\phantom{x}\verb|cluster|\phantom{x}\verb|algebra|\phantom{x}\verb|of|\phantom{x}\verb|rank|\phantom{x}\verb|6|\phantom{x}\verb|of|\phantom{x}\verb|type|\phantom{x}\verb|['A',|\phantom{x}\verb|[3,|\phantom{x}\verb|3],|\phantom{x}\verb|1]|\phantom{x}\verb|with|\phantom{x}\verb|6|\phantom{x}\verb|frozen|\phantom{x}\verb|variables|
}}}
{{{id=45|
QuiverMutationType?
///
File: /Users/sage/sage/local/lib/python2.6/site-packages/sage/combinat/cluster_algebra_quiver/quiver_mutation_type.py
Type: <class ‘sage.combinat.cluster_algebra_quiver.quiver_mutation_type.QuiverMutationTypeFactory’>
Definition: QuiverMutationType(*args)
Docstring:
Quiver mutation types can be seen as a slight generalization of generalized Cartan types.
Background on generalized Cartan types can be found at
http://en.wikipedia.org/wiki/Generalized_Cartan_matrix
For the compendium on the cluster algebra and quiver package in Sage see
http://arxiv.org/abs/1102.4844
A B-matrix is a skew-symmetrizable ( n x n )-matrix M. I.e., there exists an invertible diagonal matrix D such that DM is skew-symmetric. M can be encoded as a quiver by having a directed edge from vertex i to vertex j with label (a,b) if a = M_{i,j} > 0 and b = M_{j,i} < 0. We consider quivers up to mutation equivalence.
In particular, to a quiver mutation type we can associate a generalized Cartan type by sending M to the generalized Cartan matrix C(M) obtained by replacing all positive entries by their negatives and adding 2‘s on the main diagonal.
It appears that C(M) and C(M') are isomorphic Cartan types for mutation equivalent skew-symmetrizable matrices M and M'. Thus, all generalized Cartan types appear as well as quiver mutation types.
- AUTHOR:
- – Gregg Musiker – Christian Stump
Constructs a quiver mutation type object. For the possible different types, please see the compendium. Kac’s classification types can also be used as input.
INPUT:
- letter, rank – letter is one of ‘A’,’B’,’C’,’D’,’E’,’F’,’G’ and rank is an integer
- letter, rank, twist – letter is one of ‘A’,’BB’,’CC’,’D’,’E’,’F’,’G’, ‘BC’, ‘BD’, ‘CD’, and rank is a tuple (b,c) or an integer and twist is an integer
- object – a quiver mutation type
EXAMPLES:
Finite types:
sage: QuiverMutationType('A',1)
['A', 1]
sage: QuiverMutationType('A',5)
['A', 5]
sage: QuiverMutationType('B',2)
['B', 2]
sage: QuiverMutationType('B',5)
['B', 5]
sage: QuiverMutationType('C',2)
['B', 2]
sage: QuiverMutationType('C',5)
['C', 5]
sage: QuiverMutationType('D',2)
[ ['A', 1], ['A', 1] ]
sage: QuiverMutationType('D',3)
['A', 3]
sage: QuiverMutationType('D',4)
['D', 4]
sage: QuiverMutationType('E',6)
['E', 6]
sage: QuiverMutationType('E',7)
['E', 7]
sage: QuiverMutationType('E',8)
['E', 8]
sage: QuiverMutationType('F',4)
['F', 4]
sage: QuiverMutationType('G',2)
['G', 2]
Affine types:
sage: QuiverMutationType('A',(1,1),1)
['A', [1, 1], 1]
sage: QuiverMutationType('A',(2,4),1)
['A', [2, 4], 1]
sage: QuiverMutationType('BB',1,1)
['A', [1, 1], 1]
sage: QuiverMutationType('BB',2,1)
['BB', 2, 1]
sage: QuiverMutationType('BB',4,1)
['BB', 4, 1]
sage: QuiverMutationType('CC',1,1)
['A', [1, 1], 1]
sage: QuiverMutationType('CC',2,1)
['CC', 2, 1]
sage: QuiverMutationType('CC',4,1)
['CC', 4, 1]
sage: QuiverMutationType('BC',1,1)
['BC', 1, 1]
sage: QuiverMutationType('BC',5,1)
['BC', 5, 1]
sage: QuiverMutationType('BD',3,1)
['BD', 3, 1]
sage: QuiverMutationType('BD',5,1)
['BD', 5, 1]
sage: QuiverMutationType('CD',3,1)
['CD', 3, 1]
sage: QuiverMutationType('CD',5,1)
['CD', 5, 1]
sage: QuiverMutationType('D',4,1)
['D', 4, 1]
sage: QuiverMutationType('D',6,1)
['D', 6, 1]
sage: QuiverMutationType('E',6,1)
['E', 6, 1]
sage: QuiverMutationType('E',7,1)
['E', 7, 1]
sage: QuiverMutationType('E',8,1)
['E', 8, 1]
sage: QuiverMutationType('F',4,1)
['F', 4, 1]
sage: QuiverMutationType('F',4,-1)
['F', 4, -1]
sage: QuiverMutationType('G',2,1)
['G', 2, 1]
sage: QuiverMutationType('G',2,-1)
['G', 2, -1]
Elliptic types:
sage: QuiverMutationType('E',6,[1,1])
['E', 6, [1, 1]]
sage: QuiverMutationType('E',7,[1,1])
['E', 7, [1, 1]]
sage: QuiverMutationType('E',8,[1,1])
['E', 8, [1, 1]]
Mutation finite types:
rank 2 cases:
sage: QuiverMutationType('R2',(1,1),2)
['A', 2]
sage: QuiverMutationType('R2',(1,2),2)
['B', 2]
sage: QuiverMutationType('R2',(1,3),2)
['G', 2]
sage: QuiverMutationType('R2',(1,4),2)
['BC', 1, 1]
sage: QuiverMutationType('R2',(1,5),2)
['R2', [1, 5], 2]
sage: QuiverMutationType('R2',(2,2),2)
['A', [1, 1], 1]
sage: QuiverMutationType('R2',(3,5),2)
['R2', [3, 5], 2]
exceptional quiver mutation types:
sage: QuiverMutationType('V',4,2)
['V', 4, 2]
sage: QuiverMutationType('W',4,2)
['W', 4, 2]
sage: QuiverMutationType('W',4,-2)
['W', 4, -2]
sage: QuiverMutationType('X',6,2)
['X', 6, 2]
sage: QuiverMutationType('Y',6,2)
['Y', 6, 2]
sage: QuiverMutationType('Z',6,2)
['Z', 6, 2]
sage: QuiverMutationType('Z',6,-2)
['Z', 6, -2]
Mutation infinite types:
infinite type E:
sage: QuiverMutationType('E',9,3)
['E', 8, 1]
sage: QuiverMutationType('E',10,3)
['E', 10, 3]
sage: QuiverMutationType('E',12,3)
['E', 12, 3]
sage: QuiverMutationType('AE',(1,1),3)
['AE', [1, 1], 3]
sage: QuiverMutationType('AE',(1,4),3)
['AE', [1, 4], 3]
sage: QuiverMutationType('BE',5,3)
['BE', 5, 3]
sage: QuiverMutationType('CE',5,3)
['CE', 5, 3]
sage: QuiverMutationType('DE',6,3)
['DE', 6, 3]
Grassmannian types:
sage: QuiverMutationType('GR',(2,4),3)
['A', 1]
sage: QuiverMutationType('GR',(2,6),3)
['A', 3]
sage: QuiverMutationType('GR',(3,6),3)
['D', 4]
sage: QuiverMutationType('GR',(3,7),3)
['E', 6]
sage: QuiverMutationType('GR',(3,8),3)
['E', 8]
sage: QuiverMutationType('GR',(3,10),3)
['GR', [3, 10], 3]
Triangular types:
sage: QuiverMutationType('TR',2,3)
['A', 3]
sage: QuiverMutationType('TR',3,3)
['D', 6]
sage: QuiverMutationType('TR',4,3)
['E', 8, [1, 1]]
sage: QuiverMutationType('TR',5,3)
['TR', 5, 3]
T types:
sage: QuiverMutationType('T',(1,1,1),3)
['A', 1]
sage: QuiverMutationType('T',(1,1,4),3)
['A', 4]
sage: QuiverMutationType('T',(1,4,4),3)
['A', 7]
sage: QuiverMutationType('T',(2,2,2),3)
['D', 4]
sage: QuiverMutationType('T',(2,2,4),3)
['D', 6]
sage: QuiverMutationType('T',(2,3,3),3)
['E', 6]
sage: QuiverMutationType('T',(2,3,4),3)
['E', 7]
sage: QuiverMutationType('T',(2,3,5),3)
['E', 8]
sage: QuiverMutationType('T',(2,3,6),3)
['E', 8, 1]
sage: QuiverMutationType('T',(2,3,7),3)
['E', 10, 3]
sage: QuiverMutationType('T',(3,3,3),3)
['E', 6, 1]
sage: QuiverMutationType('T',(3,3,4),3)
['T', [3, 3, 4], 3]
Reducible types:
sage: QuiverMutationType(['A',3],['B',4])
[ ['A', 3], ['B', 4] ]
}}}
{{{id=136|
Gr.is_mutation_finite()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\mathrm{False}
}}}
{{{id=137|
Gr2 = ClusterSeed(['GR',[4,8],3]); Gr2;
///
\newcommand{\Bold}[1]{\mathbf{#1}}\verb|A|\phantom{x}\verb|seed|\phantom{x}\verb|for|\phantom{x}\verb|a|\phantom{x}\verb|cluster|\phantom{x}\verb|algebra|\phantom{x}\verb|of|\phantom{x}\verb|rank|\phantom{x}\verb|9|\phantom{x}\verb|of|\phantom{x}\verb|type|\phantom{x}\verb|['E',|\phantom{x}\verb|7,|\phantom{x}\verb|[1,|\phantom{x}\verb|1]]|
}}}
{{{id=139|
Gr2.is_mutation_finite()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\mathrm{True}
}}}
{{{id=140|
Tr = ClusterSeed(['TR',5,3]); Tr; Tr.show()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\verb|A|\phantom{x}\verb|seed|\phantom{x}\verb|for|\phantom{x}\verb|a|\phantom{x}\verb|cluster|\phantom{x}\verb|algebra|\phantom{x}\verb|of|\phantom{x}\verb|rank|\phantom{x}\verb|15|\phantom{x}\verb|of|\phantom{x}\verb|type|\phantom{x}\verb|['TR',|\phantom{x}\verb|5,|\phantom{x}\verb|3]|
}}}
{{{id=138|
NSL = ClusterSeed(['F',4,1]); NSL; NSL.show()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\verb|A|\phantom{x}\verb|seed|\phantom{x}\verb|for|\phantom{x}\verb|a|\phantom{x}\verb|cluster|\phantom{x}\verb|algebra|\phantom{x}\verb|of|\phantom{x}\verb|rank|\phantom{x}\verb|5|\phantom{x}\verb|of|\phantom{x}\verb|type|\phantom{x}\verb|['F',|\phantom{x}\verb|4,|\phantom{x}\verb|1]|
}}}
{{{id=141|
NSL2 = ClusterSeed(['F',4,-1]); NSL2; NSL2.show()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\verb|A|\phantom{x}\verb|seed|\phantom{x}\verb|for|\phantom{x}\verb|a|\phantom{x}\verb|cluster|\phantom{x}\verb|algebra|\phantom{x}\verb|of|\phantom{x}\verb|rank|\phantom{x}\verb|5|\phantom{x}\verb|of|\phantom{x}\verb|type|\phantom{x}\verb|['F',|\phantom{x}\verb|4,|\phantom{x}\verb|-1]|
}}}
{{{id=142|
BB = NSL.b_matrix_class(); len(BB);
///
\newcommand{\Bold}[1]{\mathbf{#1}}60
}}}
{{{id=144|
BB
///
WARNING: Output truncated!
full_output.txt
\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left(\begin{array}{rrrrr}
0 & 0 & 0 & 0 & 1 \\
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 & 1 \\
0 & -1 & -2 & 0 & 0 \\
-1 & 0 & -1 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & 0 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 & 1 \\
0 & -2 & 0 & 1 & 0 \\
0 & 0 & -1 & 0 & 0 \\
-1 & -1 & 0 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & 0 & 0 & 0 & 1 \\
0 & 0 & 2 & 1 & 0 \\
0 & -1 & 0 & 0 & 1 \\
0 & -1 & 0 & 0 & 0 \\
-1 & 0 & -1 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 0 & 1 \\
-1 & 0 & 0 & 2 & 0 \\
0 & 0 & -1 & 0 & -1 \\
0 & -1 & 0 & 1 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & 0 & 0 & 0 & 1 \\
0 & 0 & 1 & 1 & 0 \\
0 & -1 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 & 1 \\
-1 & 0 & 0 & -2 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 & 1 \\
0 & 0 & 0 & 0 & -1 \\
-1 & -2 & 0 & 0 & 0 \\
0 & -1 & 1 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & 0 & 0 & 1 & -2 \\
0 & 0 & 1 & 0 & 1 \\
0 & -1 & 0 & 0 & 0 \\
-1 & 0 & 0 & 0 & 0 \\
1 & -1 & 0 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & 0 & 0 & 0 & 1 \\
0 & 0 & 1 & -1 & 1 \\
0 & -2 & 0 & 1 & 0 \\
0 & 2 & -1 & 0 & 0 \\
-1 & -1 & 0 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & 0 & 0 & 0 & 1 \\
0 & 0 & 1 & 2 & 0 \\
0 & -1 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 & -1 \\
-1 & 0 & 0 & 1 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & 1 & 0 & 0 & 1 \\
-2 & 0 & 1 & 0 & 0 \\
0 & -1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & -1 \\
...
0 & 0 & -2 & 1 & 0 \\
0 & 0 & 0 & -1 & 1 \\
1 & 0 & 0 & -1 & 1 \\
-1 & 2 & 2 & 0 & -2 \\
0 & -1 & -1 & 1 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & 0 & -1 & 0 & 1 \\
0 & 0 & 1 & -2 & 0 \\
2 & -1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & -1 \\
-1 & 0 & 0 & 1 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & 2 & 1 & -2 & -2 \\
-1 & 0 & 0 & 1 & 1 \\
-1 & 0 & 0 & 0 & 2 \\
1 & -1 & 0 & 0 & 0 \\
1 & -1 & -1 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & 1 & 0 & 2 & -2 \\
-1 & 0 & 0 & 0 & 2 \\
0 & 0 & 0 & 1 & -1 \\
-1 & 0 & -1 & 0 & 1 \\
1 & -1 & 1 & -1 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & 1 & 0 & -1 & 1 \\
-2 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 & -1 \\
2 & -1 & -2 & 0 & 0 \\
-1 & 0 & 1 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & -1 & 0 & 0 & 1 \\
2 & 0 & 1 & -2 & 0 \\
0 & -1 & 0 & 2 & 0 \\
0 & 1 & -1 & 0 & -1 \\
-1 & 0 & 0 & 1 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 1 & -1 & 1 \\
0 & -1 & 0 & 0 & 1 \\
-1 & 2 & 0 & 0 & -2 \\
0 & -1 & -1 & 1 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & -1 & 0 & 1 & 1 \\
2 & 0 & 1 & 0 & -2 \\
0 & -1 & 0 & 0 & 0 \\
-1 & 0 & 0 & 0 & 1 \\
-1 & 1 & 0 & -1 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & 0 & 0 & 1 & 0 \\
0 & 0 & -2 & 1 & 1 \\
0 & 2 & 0 & -1 & -1 \\
-1 & -2 & 2 & 0 & 0 \\
0 & -1 & 1 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrrr}
0 & 1 & 0 & -2 & 1 \\
-2 & 0 & 1 & 2 & 0 \\
0 & -1 & 0 & 0 & 0 \\
2 & -1 & 0 & 0 & -1 \\
-1 & 0 & 0 & 1 & 0
\end{array}\right)\right]
}}}
{{{id=143|
BB2 = NSL2.b_matrix_class(); len(BB2)
///
\newcommand{\Bold}[1]{\mathbf{#1}}60
}}}
{{{id=145|
BB2 = NSL2.b_matrix_class(up_to_equivalence=False); len(BB2)
///
\newcommand{\Bold}[1]{\mathbf{#1}}720
}}}
{{{id=146|
for Mat in BB:
if Mat in BB2:
print("Found Matrix")
print("Done")
///
Done
}}}
{{{id=49|
NSL.interact()
///
}}}
{{{id=50|
EE7 = ClusterSeed(['E',7]); EE7.show()
///
}}}
{{{id=99|
VC = EE7.variable_class(); len(VC)
///
\newcommand{\Bold}[1]{\mathbf{#1}}70
}}}
{{{id=54|
VC[35]
///
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{x_{0} x_{2}^{2} x_{4}^{2} + x_{1} x_{3}^{2} x_{5} x_{6} + x_{0} x_{2}^{2} x_{4} + x_{0} x_{2} x_{3} x_{5} + x_{1} x_{3} x_{4} x_{6} + x_{0} x_{2} x_{4} + x_{2} x_{4}^{2} + x_{1} x_{3} x_{6} + x_{0} x_{2} + x_{2} x_{4} + x_{3} x_{5} + x_{4} + 1}{x_{1} x_{2} x_{3} x_{4} x_{5}}
}}}
{{{id=60|
for i in range(len(VC)):
if max(VC[i].denominator().exponents()[0]) > 1:
print(i)
///
34
38
41
43
44
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
}}}
{{{id=61|
VC[34]
///
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{x_{1}^{2} x_{3}^{2} x_{6}^{2} + x_{0} x_{2}^{3} x_{4} + x_{0} x_{1} x_{2} x_{3} x_{6} + x_{1} x_{2} x_{3} x_{4} x_{6} + x_{0} x_{2}^{2} x_{4} + x_{1} x_{2} x_{3} x_{6} + x_{0} x_{2}^{2} + x_{2}^{2} x_{4} + 2 x_{1} x_{3} x_{6} + x_{0} x_{2} + x_{2} x_{4} + x_{2} + 1}{x_{1} x_{2}^{2} x_{3} x_{6}}
}}}
{{{id=67|
X = ClusterSeed(['X',6,2]); X; X.show()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\verb|A|\phantom{x}\verb|seed|\phantom{x}\verb|for|\phantom{x}\verb|a|\phantom{x}\verb|cluster|\phantom{x}\verb|algebra|\phantom{x}\verb|of|\phantom{x}\verb|rank|\phantom{x}\verb|6|\phantom{x}\verb|of|\phantom{x}\verb|type|\phantom{x}\verb|['X',|\phantom{x}\verb|6,|\phantom{x}\verb|2]|
}}}
{{{id=68|
S = ClusterSeed(['X',7,2]); S; S.show()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\verb|A|\phantom{x}\verb|seed|\phantom{x}\verb|for|\phantom{x}\verb|a|\phantom{x}\verb|cluster|\phantom{x}\verb|algebra|\phantom{x}\verb|of|\phantom{x}\verb|rank|\phantom{x}\verb|7|\phantom{x}\verb|of|\phantom{x}\verb|type|\phantom{x}\verb|['X',|\phantom{x}\verb|7,|\phantom{x}\verb|2]|
}}}
{{{id=71|
X.is_finite()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\mathrm{False}
}}}
{{{id=69|
X.is_mutation_finite()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\mathrm{True}
}}}
{{{id=70|
V = ClusterSeed(['V',4,2]); V; V.show()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\verb|A|\phantom{x}\verb|seed|\phantom{x}\verb|for|\phantom{x}\verb|a|\phantom{x}\verb|cluster|\phantom{x}\verb|algebra|\phantom{x}\verb|of|\phantom{x}\verb|rank|\phantom{x}\verb|4|\phantom{x}\verb|of|\phantom{x}\verb|type|\phantom{x}\verb|['V',|\phantom{x}\verb|4,|\phantom{x}\verb|2]|
}}}
{{{id=72|
VMC = V.b_matrix_class(); len(VMC); VMC
///
\newcommand{\Bold}[1]{\mathbf{#1}}7
\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left(\begin{array}{rrrr}
0 & 0 & -1 & 1 \\
0 & 0 & 1 & -3 \\
3 & -1 & 0 & 0 \\
-1 & 1 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrr}
0 & -3 & 0 & 1 \\
1 & 0 & 1 & -1 \\
0 & -1 & 0 & 1 \\
-1 & 3 & -3 & 0
\end{array}\right), \left(\begin{array}{rrrr}
0 & -1 & 0 & 1 \\
3 & 0 & 1 & -3 \\
0 & -1 & 0 & 3 \\
-1 & 1 & -1 & 0
\end{array}\right), \left(\begin{array}{rrrr}
0 & 2 & -1 & 0 \\
-2 & 0 & 1 & 0 \\
3 & -3 & 0 & 1 \\
0 & 0 & -1 & 0
\end{array}\right), \left(\begin{array}{rrrr}
0 & 0 & 0 & 1 \\
0 & 0 & -2 & 3 \\
0 & 2 & 0 & -3 \\
-1 & -1 & 1 & 0
\end{array}\right), \left(\begin{array}{rrrr}
0 & 3 & -2 & 0 \\
-1 & 0 & 1 & 1 \\
2 & -3 & 0 & 0 \\
0 & -1 & 0 & 0
\end{array}\right), \left(\begin{array}{rrrr}
0 & 0 & 0 & 1 \\
0 & 0 & 2 & -1 \\
0 & -2 & 0 & 1 \\
-1 & 3 & -3 & 0
\end{array}\right)\right]
}}}
{{{id=81|
WW = ClusterSeed(['W',4,2]); WW; WW.show()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\verb|A|\phantom{x}\verb|seed|\phantom{x}\verb|for|\phantom{x}\verb|a|\phantom{x}\verb|cluster|\phantom{x}\verb|algebra|\phantom{x}\verb|of|\phantom{x}\verb|rank|\phantom{x}\verb|4|\phantom{x}\verb|of|\phantom{x}\verb|type|\phantom{x}\verb|['W',|\phantom{x}\verb|4,|\phantom{x}\verb|2]|
}}}
{{{id=147|
WW2 = ClusterSeed(['W',4,-2]); WW2; WW2.show()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\verb|A|\phantom{x}\verb|seed|\phantom{x}\verb|for|\phantom{x}\verb|a|\phantom{x}\verb|cluster|\phantom{x}\verb|algebra|\phantom{x}\verb|of|\phantom{x}\verb|rank|\phantom{x}\verb|4|\phantom{x}\verb|of|\phantom{x}\verb|type|\phantom{x}\verb|['W',|\phantom{x}\verb|4,|\phantom{x}\verb|-2]|
}}}
{{{id=148|
WW.b_matrix_class()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left(\begin{array}{rrrr}
0 & 1 & 1 & -2 \\
-3 & 0 & 0 & 3 \\
-1 & 0 & 0 & 1 \\
2 & -1 & -1 & 0
\end{array}\right), \left(\begin{array}{rrrr}
0 & -1 & 1 & 1 \\
3 & 0 & 0 & -3 \\
-1 & 0 & 0 & 1 \\
-1 & 1 & -1 & 0
\end{array}\right)\right]
}}}
{{{id=149|
WW2.b_matrix_class()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left(\begin{array}{rrrr}
0 & 3 & 1 & -2 \\
-1 & 0 & 0 & 1 \\
-1 & 0 & 0 & 1 \\
2 & -3 & -1 & 0
\end{array}\right), \left(\begin{array}{rrrr}
0 & 1 & 0 & -1 \\
-3 & 0 & 1 & 1 \\
0 & -1 & 0 & 1 \\
3 & -1 & -1 & 0
\end{array}\right)\right]
}}}
{{{id=97|
So4 = Matrix([[0,-1,2,-1],[1,0,-3,2],[-2,3,0,-1],[1,-2,1,0]])
///
}}}
{{{id=150|
Somos4 = ClusterSeed(So4); Somos4
///
\newcommand{\Bold}[1]{\mathbf{#1}}\verb|A|\phantom{x}\verb|seed|\phantom{x}\verb|for|\phantom{x}\verb|a|\phantom{x}\verb|cluster|\phantom{x}\verb|algebra|\phantom{x}\verb|of|\phantom{x}\verb|rank|\phantom{x}\verb|4|
}}}
{{{id=95|
Somos4.set_cluster([1,1,1,1])
///
}}}
{{{id=77|
Somos4.show()
///
}}}
{{{id=151|
Somos4.mutate([0,1,2,3]); Somos4.show(); Somos4.cluster()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\left[2, 3, 7, 23\right]
}}}
{{{id=152|
Somos4.mutate([0,1,2,3]); Somos4.show(); Somos4.cluster()
///
\newcommand{\Bold}[1]{\mathbf{#1}}\left[59, 314, 1529, 8209\right]
}}}
{{{id=153|
Somos4.mutation_sequence([0,1,2,3,0,1,2,3],return_output='var')
///
\newcommand{\Bold}[1]{\mathbf{#1}}\left[83313, 620297, 7869898, 126742987, 1687054711, 47301104551, 1123424582771, 32606721084786\right]
}}}
{{{id=154|
///
}}}
{{{id=159|
///
}}}
{{{id=160|
///
}}}
{{{id=162|
///
}}}