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Subalgebra B12F14
32 out of 59
Computations done by the calculator project.

Subalgebra type: B12 (click on type for detailed printout).
The subalgebra is regular (= the semisimple part of a root subalgebra).
Subalgebra is (parabolically) induced from A11 .
Centralizer: 2A11 .
The semisimple part of the centralizer of the semisimple part of my centralizer: B12
Basis of Cartan of centralizer: 2 vectors: (0, 1, 0, 0), (0, 0, 1, 0)
Contained up to conjugation as a direct summand of: B12+A11 , B12+A21 , B12+2A11 .

Elements Cartan subalgebra scaled to act by two by components: B12: (2, 3, 4, 2): 2, (-2, -2, -2, 0): 4
Dimension of subalgebra generated by predefined or computed generators: 10.
Negative simple generators: g24, g8
Positive simple generators: g24, g8
Cartan symmetric matrix: (2111)
Scalar products of elements of Cartan subalgebra scaled to act by 2 (co-symmetric Cartan matrix): (2224)
Decomposition of ambient Lie algebra: V2ω24Vω24Vω16V0
Primal decomposition of the ambient Lie algebra. This decomposition refines the above decomposition (please note the order is not the same as above). Vω1+2ψ1V2ψ2Vω2+ψ2V2ω2Vω2+2ψ1ψ2V4ψ12ψ2Vω12ψ1+2ψ2Vω1+2ψ12ψ2Vω22ψ1+ψ22V0Vω2ψ2Vω12ψ1V4ψ1+2ψ2V2ψ2
In the table below we indicate the highest weight vectors of the decomposition of the ambient Lie algebra as a module over the semisimple part. The second row indicates weights of the highest weight vectors relative to the Cartan of the semisimple subalgebra. As the centralizer is well-chosen and the centralizer of our subalgebra is non-trivial, we may in addition split highest weight vectors with the same weight over the semisimple part over the centralizer (recall that the centralizer preserves the weights over the subalgebra and in particular acts on the highest weight vectors). Therefore we have chosen our highest weight vectors to be, in addition, weight vectors over the Cartan of the centralizer of the starting subalgebra. Their weight over the sum of the Cartans of the semisimple subalgebra and its centralizer is indicated in the third row. The weights corresponding to the Cartan of the centralizer are again indicated with the letter \omega. As there is no preferred way of chosing a basis of the Cartan of the centralizer (unlike the starting semisimple Lie algebra: there we have a preferred basis induced by the fundamental weights), our centralizer weights are simply given by the constant by which the k^th basis element of the Cartan of the centralizer acts on the highest weight vector. Here, we use the choice for basis of the Cartan of the centralizer given at the start of the page.

Highest vectors of representations (total 15) ; the vectors are over the primal subalgebra.g9g2h3h2g2g9g18g20g22g23g4g7g10g13g16
weight000000ω1ω1ω1ω1ω2ω2ω2ω22ω2
weights rel. to Cartan of (centralizer+semisimple s.a.). 2ψ24ψ1+2ψ2004ψ12ψ22ψ2ω12ψ1ω1+2ψ12ψ2ω12ψ1+2ψ2ω1+2ψ1ω2ψ2ω22ψ1+ψ2ω2+2ψ1ψ2ω2+ψ22ω2
Isotypic module decomposition over primal subalgebra (total 14 isotypic components).
Isotypical components + highest weightV2ψ2 → (0, 0, 0, -2)V4ψ1+2ψ2 → (0, 0, -4, 2)V0 → (0, 0, 0, 0)V4ψ12ψ2 → (0, 0, 4, -2)V2ψ2 → (0, 0, 0, 2)Vω12ψ1 → (1, 0, -2, 0)Vω1+2ψ12ψ2 → (1, 0, 2, -2)Vω12ψ1+2ψ2 → (1, 0, -2, 2)Vω1+2ψ1 → (1, 0, 2, 0)Vω2ψ2 → (0, 1, 0, -1)Vω22ψ1+ψ2 → (0, 1, -2, 1)Vω2+2ψ1ψ2 → (0, 1, 2, -1)Vω2+ψ2 → (0, 1, 0, 1)V2ω2 → (0, 2, 0, 0)
Module label W1W2W3W4W5W6W7W8W9W10W11W12W13W14
Module elements (weight vectors). In blue - corresp. F element. In red -corresp. H element.
g9
g2
Cartan of centralizer component.
h3
h2
g2
g9
g18
g14
g6
2g1
2g23
g20
g11
g3
2g5
2g22
g22
g5
g3
2g11
2g20
g23
g1
g6
2g14
2g18
g4
g12
g19
g13
g7
g15
g17
g10
g10
g17
g15
g7
g13
g19
g12
g4
Semisimple subalgebra component.
g16
g21
g8
2g24
2h3+2h2+2h1
4h4+8h3+6h2+4h1
2g24
2g8
2g21
4g16
Weights of elements in fundamental coords w.r.t. Cartan of subalgebra in same order as above00000ω1
ω1+2ω2
0
ω12ω2
ω1
ω1
ω1+2ω2
0
ω12ω2
ω1
ω1
ω1+2ω2
0
ω12ω2
ω1
ω1
ω1+2ω2
0
ω12ω2
ω1
ω2
ω1ω2
ω1+ω2
ω2
ω2
ω1ω2
ω1+ω2
ω2
ω2
ω1ω2
ω1+ω2
ω2
ω2
ω1ω2
ω1+ω2
ω2
2ω2
ω1
ω1+2ω2
2ω12ω2
0
0
2ω1+2ω2
ω12ω2
ω1
2ω2
Weights of elements in (fundamental coords w.r.t. Cartan of subalgebra) + Cartan centralizer2ψ24ψ1+2ψ204ψ12ψ22ψ2ω12ψ1
ω1+2ω22ψ1
2ψ1
ω12ω22ψ1
ω12ψ1
ω1+2ψ12ψ2
ω1+2ω2+2ψ12ψ2
2ψ12ψ2
ω12ω2+2ψ12ψ2
ω1+2ψ12ψ2
ω12ψ1+2ψ2
ω1+2ω22ψ1+2ψ2
2ψ1+2ψ2
ω12ω22ψ1+2ψ2
ω12ψ1+2ψ2
ω1+2ψ1
ω1+2ω2+2ψ1
2ψ1
ω12ω2+2ψ1
ω1+2ψ1
ω2ψ2
ω1ω2ψ2
ω1+ω2ψ2
ω2ψ2
ω22ψ1+ψ2
ω1ω22ψ1+ψ2
ω1+ω22ψ1+ψ2
ω22ψ1+ψ2
ω2+2ψ1ψ2
ω1ω2+2ψ1ψ2
ω1+ω2+2ψ1ψ2
ω2+2ψ1ψ2
ω2+ψ2
ω1ω2+ψ2
ω1+ω2+ψ2
ω2+ψ2
2ω2
ω1
ω1+2ω2
2ω12ω2
0
0
2ω1+2ω2
ω12ω2
ω1
2ω2
Single module character over Cartan of s.a.+ Cartan of centralizer of s.a.M2ψ2M4ψ1+2ψ2M0M4ψ12ψ2M2ψ2Mω1+2ω22ψ1Mω12ψ1M2ψ1Mω12ψ1Mω12ω22ψ1Mω1+2ω2+2ψ12ψ2Mω1+2ψ12ψ2M2ψ12ψ2Mω1+2ψ12ψ2Mω12ω2+2ψ12ψ2Mω1+2ω22ψ1+2ψ2Mω12ψ1+2ψ2M2ψ1+2ψ2Mω12ψ1+2ψ2Mω12ω22ψ1+2ψ2Mω1+2ω2+2ψ1Mω1+2ψ1M2ψ1Mω1+2ψ1Mω12ω2+2ψ1Mω2ψ2Mω1+ω2ψ2Mω1ω2ψ2Mω2ψ2Mω22ψ1+ψ2Mω1+ω22ψ1+ψ2Mω1ω22ψ1+ψ2Mω22ψ1+ψ2Mω2+2ψ1ψ2Mω1+ω2+2ψ1ψ2Mω1ω2+2ψ1ψ2Mω2+2ψ1ψ2Mω2+ψ2Mω1+ω2+ψ2Mω1ω2+ψ2Mω2+ψ2M2ω2Mω1+2ω2Mω1M2ω1+2ω22M0M2ω12ω2Mω1Mω12ω2M2ω2
Isotypic characterM2ψ2M4ψ1+2ψ22M0M4ψ12ψ2M2ψ2Mω1+2ω22ψ1Mω12ψ1M2ψ1Mω12ψ1Mω12ω22ψ1Mω1+2ω2+2ψ12ψ2Mω1+2ψ12ψ2M2ψ12ψ2Mω1+2ψ12ψ2Mω12ω2+2ψ12ψ2Mω1+2ω22ψ1+2ψ2Mω12ψ1+2ψ2M2ψ1+2ψ2Mω12ψ1+2ψ2Mω12ω22ψ1+2ψ2Mω1+2ω2+2ψ1Mω1+2ψ1M2ψ1Mω1+2ψ1Mω12ω2+2ψ1Mω2ψ2Mω1+ω2ψ2Mω1ω2ψ2Mω2ψ2Mω22ψ1+ψ2Mω1+ω22ψ1+ψ2Mω1ω22ψ1+ψ2Mω22ψ1+ψ2Mω2+2ψ1ψ2Mω1+ω2+2ψ1ψ2Mω1ω2+2ψ1ψ2Mω2+2ψ1ψ2Mω2+ψ2Mω1+ω2+ψ2Mω1ω2+ψ2Mω2+ψ2M2ω2Mω1+2ω2Mω1M2ω1+2ω22M0M2ω12ω2Mω1Mω12ω2M2ω2

Semisimple subalgebra: W_{14}
Centralizer extension: W_{1}+W_{2}+W_{3}+W_{4}+W_{5}

Weight diagram. The coordinates corresponding to the simple roots of the subalgerba are fundamental.
The bilinear form is therefore given relative to the fundamental coordinates.
Canvas not supported




Mouse position: (0.00, 0.00)
Selected index: -1
Coordinate center in screen coordinates:
(200.00, 300.00)
The projection plane (drawn on the screen) is spanned by the following two vectors.
(1.00, 0.00, 0.00, 0.00)
(0.00, 1.00, 0.00, 0.00)
0: (1.00, 0.00, 0.00, 0.00): (300.00, 350.00)
1: (0.00, 1.00, 0.00, 0.00): (250.00, 350.00)
2: (0.00, 0.00, 1.00, 0.00): (200.00, 300.00)
3: (0.00, 0.00, 0.00, 1.00): (200.00, 300.00)



Made total 11689686 arithmetic operations while solving the Serre relations polynomial system.
The total number of arithmetic operations I needed to solve the Serre relations polynomial system was larger than 1 000 000. I am printing out the Serre relations system for you: maybe that can help improve the polynomial system algorithms.
Subalgebra realized.
2*2 (unknown) gens:
(
g_{-24}, g_{24},
x_{2} g_{14}+x_{3} g_{11}+x_{4} g_{8}+x_{5} g_{5}+x_{6} g_{1}, x_{12} g_{-1}+x_{11} g_{-5}+x_{10} g_{-8}+x_{9} g_{-11}+x_{8} g_{-14})

Unknown splitting cartan of centralizer.
x_{16} h_{4}+x_{15} h_{3}+x_{14} h_{2}+x_{13} h_{1}, x_{20} h_{4}+x_{19} h_{3}+x_{18} h_{2}+x_{17} h_{1}
h: (2, 3, 4, 2), e = combination of g_{24} , f= combination of g_{-24} h: (-1, -1, -1, 0), e = combination of g_{-14} g_{-11} g_{-8} g_{-5} g_{-1} , f= combination of g_{14} g_{11} g_{8} g_{5} g_{1} Positive weight subsystem: 4 vectors: (1, 0), (0, 1), (1, 1), (1, 2)
Symmetric Cartan default scale: \begin{pmatrix}
2 & -1\\
-1 & 1\\
\end{pmatrix}Character ambient Lie algebra: V_{2\omega_{2}}+5V_{-\omega_{1}+2\omega_{2}}+4V_{\omega_{2}}+5V_{\omega_{1}}+V_{-2\omega_{1}+2\omega_{2}}+4V_{-\omega_{1}+\omega_{2}}+12V_{0}+4V_{\omega_{1}-\omega_{2}}+V_{2\omega_{1}-2\omega_{2}}+5V_{-\omega_{1}}+4V_{-\omega_{2}}+5V_{\omega_{1}-2\omega_{2}}+V_{-2\omega_{2}}
A necessary system to realize the candidate subalgebra.
3/4x_{15}^{2}x_{20}^{2}x_{21} -2x_{14} x_{15} x_{20}^{2}x_{21} +2x_{14}^{2}x_{20}^{2}x_{21} -2x_{13} x_{14} x_{20}^{2}x_{21}
+2x_{13}^{2}x_{20}^{2}x_{21} -3/2x_{15} x_{16} x_{19} x_{20} x_{21} +2x_{14} x_{16} x_{19} x_{20} x_{21}
+x_{14} x_{15} x_{19} x_{20} x_{21} -2x_{14}^{2}x_{19} x_{20} x_{21} +2x_{13} x_{14} x_{19} x_{20} x_{21}
-2x_{13}^{2}x_{19} x_{20} x_{21} +2x_{15} x_{16} x_{18} x_{20} x_{21} -4x_{14} x_{16} x_{18} x_{20} x_{21}
+2x_{13} x_{16} x_{18} x_{20} x_{21} -x_{15}^{2}x_{18} x_{20} x_{21} +2x_{14} x_{15} x_{18} x_{20} x_{21}
-x_{13} x_{15} x_{18} x_{20} x_{21} +2x_{14} x_{16} x_{17} x_{20} x_{21} -4x_{13} x_{16} x_{17} x_{20} x_{21}
-x_{14} x_{15} x_{17} x_{20} x_{21} +2x_{13} x_{15} x_{17} x_{20} x_{21} +3/4x_{16}^{2}x_{19}^{2}x_{21}
-x_{14} x_{16} x_{19}^{2}x_{21} +x_{14}^{2}x_{19}^{2}x_{21} -2x_{13} x_{14} x_{19}^{2}x_{21} +2x_{13}^{2}x_{19}^{2}x_{21}
-2x_{16}^{2}x_{18} x_{19} x_{21} +x_{15} x_{16} x_{18} x_{19} x_{21} +2x_{14} x_{16} x_{18} x_{19} x_{21}
-x_{13} x_{16} x_{18} x_{19} x_{21} -2x_{14} x_{15} x_{18} x_{19} x_{21} +2x_{13} x_{15} x_{18} x_{19} x_{21}
+2x_{13} x_{14} x_{18} x_{19} x_{21} -4x_{13}^{2}x_{18} x_{19} x_{21} -x_{14} x_{16} x_{17} x_{19} x_{21}
+2x_{13} x_{16} x_{17} x_{19} x_{21} +2x_{14} x_{15} x_{17} x_{19} x_{21} -4x_{13} x_{15} x_{17} x_{19} x_{21}
-2x_{14}^{2}x_{17} x_{19} x_{21} +4x_{13} x_{14} x_{17} x_{19} x_{21} +2x_{16}^{2}x_{18}^{2}x_{21} -2x_{15} x_{16} x_{18}^{2}x_{21}
+x_{15}^{2}x_{18}^{2}x_{21} -2x_{13} x_{15} x_{18}^{2}x_{21} +3x_{13}^{2}x_{18}^{2}x_{21} -2x_{16}^{2}x_{17} x_{18} x_{21}
+2x_{15} x_{16} x_{17} x_{18} x_{21} -2x_{15}^{2}x_{17} x_{18} x_{21} +2x_{14} x_{15} x_{17} x_{18} x_{21}
+4x_{13} x_{15} x_{17} x_{18} x_{21} -6x_{13} x_{14} x_{17} x_{18} x_{21} +2x_{16}^{2}x_{17}^{2}x_{21}
-2x_{15} x_{16} x_{17}^{2}x_{21} +2x_{15}^{2}x_{17}^{2}x_{21} -4x_{14} x_{15} x_{17}^{2}x_{21} +3x_{14}^{2}x_{17}^{2}x_{21}
-1= 0
x_{13} = 0
x_{17} = 0
x_{6} x_{12} +x_{5} x_{11} +2x_{4} x_{10} +x_{3} x_{9} +x_{2} x_{8} -2= 0
x_{5} x_{11} +2x_{4} x_{10} +x_{3} x_{9} +2x_{2} x_{8} -2= 0
x_{4} x_{10} +x_{3} x_{9} +x_{2} x_{8} -1= 0
x_{6} x_{11} -x_{3} x_{8} = 0
x_{6} x_{10} -x_{4} x_{8} = 0
x_{6} x_{9} -x_{5} x_{8} = 0
x_{5} x_{12} -x_{2} x_{9} = 0
x_{5} x_{10} -x_{4} x_{9} = 0
x_{4} x_{12} -x_{2} x_{10} = 0
x_{4} x_{11} -x_{3} x_{10} = 0
x_{3} x_{12} -x_{2} x_{11} = 0
x_{2} x_{16} -x_{2} x_{14} = 0
x_{3} x_{16} -x_{3} x_{15} +x_{3} x_{14} -x_{3} x_{13} = 0
x_{4} x_{16} -2x_{4} x_{13} = 0
x_{5} x_{15} -x_{5} x_{14} -x_{5} x_{13} = 0
x_{6} x_{14} -2x_{6} x_{13} = 0
x_{8} x_{16} -x_{8} x_{14} = 0
x_{9} x_{16} -x_{9} x_{15} +x_{9} x_{14} -x_{9} x_{13} = 0
x_{10} x_{16} -2x_{10} x_{13} = 0
x_{11} x_{15} -x_{11} x_{14} -x_{11} x_{13} = 0
x_{12} x_{14} -2x_{12} x_{13} = 0
x_{2} x_{20} -x_{2} x_{18} = 0
x_{3} x_{20} -x_{3} x_{19} +x_{3} x_{18} -x_{3} x_{17} = 0
x_{4} x_{20} -2x_{4} x_{17} = 0
x_{5} x_{19} -x_{5} x_{18} -x_{5} x_{17} = 0
x_{6} x_{18} -2x_{6} x_{17} = 0
x_{8} x_{20} -x_{8} x_{18} = 0
x_{9} x_{20} -x_{9} x_{19} +x_{9} x_{18} -x_{9} x_{17} = 0
x_{10} x_{20} -2x_{10} x_{17} = 0
x_{11} x_{19} -x_{11} x_{18} -x_{11} x_{17} = 0
x_{12} x_{18} -2x_{12} x_{17} = 0
The above system after transformation.
3/4x_{15}^{2}x_{20}^{2}x_{21} -2x_{14} x_{15} x_{20}^{2}x_{21} +2x_{14}^{2}x_{20}^{2}x_{21} -2x_{13} x_{14} x_{20}^{2}x_{21}
+2x_{13}^{2}x_{20}^{2}x_{21} -3/2x_{15} x_{16} x_{19} x_{20} x_{21} +2x_{14} x_{16} x_{19} x_{20} x_{21}
+x_{14} x_{15} x_{19} x_{20} x_{21} -2x_{14}^{2}x_{19} x_{20} x_{21} +2x_{13} x_{14} x_{19} x_{20} x_{21}
-2x_{13}^{2}x_{19} x_{20} x_{21} +2x_{15} x_{16} x_{18} x_{20} x_{21} -4x_{14} x_{16} x_{18} x_{20} x_{21}
+2x_{13} x_{16} x_{18} x_{20} x_{21} -x_{15}^{2}x_{18} x_{20} x_{21} +2x_{14} x_{15} x_{18} x_{20} x_{21}
-x_{13} x_{15} x_{18} x_{20} x_{21} +2x_{14} x_{16} x_{17} x_{20} x_{21} -4x_{13} x_{16} x_{17} x_{20} x_{21}
-x_{14} x_{15} x_{17} x_{20} x_{21} +2x_{13} x_{15} x_{17} x_{20} x_{21} +3/4x_{16}^{2}x_{19}^{2}x_{21}
-x_{14} x_{16} x_{19}^{2}x_{21} +x_{14}^{2}x_{19}^{2}x_{21} -2x_{13} x_{14} x_{19}^{2}x_{21} +2x_{13}^{2}x_{19}^{2}x_{21}
-2x_{16}^{2}x_{18} x_{19} x_{21} +x_{15} x_{16} x_{18} x_{19} x_{21} +2x_{14} x_{16} x_{18} x_{19} x_{21}
-x_{13} x_{16} x_{18} x_{19} x_{21} -2x_{14} x_{15} x_{18} x_{19} x_{21} +2x_{13} x_{15} x_{18} x_{19} x_{21}
+2x_{13} x_{14} x_{18} x_{19} x_{21} -4x_{13}^{2}x_{18} x_{19} x_{21} -x_{14} x_{16} x_{17} x_{19} x_{21}
+2x_{13} x_{16} x_{17} x_{19} x_{21} +2x_{14} x_{15} x_{17} x_{19} x_{21} -4x_{13} x_{15} x_{17} x_{19} x_{21}
-2x_{14}^{2}x_{17} x_{19} x_{21} +4x_{13} x_{14} x_{17} x_{19} x_{21} +2x_{16}^{2}x_{18}^{2}x_{21} -2x_{15} x_{16} x_{18}^{2}x_{21}
+x_{15}^{2}x_{18}^{2}x_{21} -2x_{13} x_{15} x_{18}^{2}x_{21} +3x_{13}^{2}x_{18}^{2}x_{21} -2x_{16}^{2}x_{17} x_{18} x_{21}
+2x_{15} x_{16} x_{17} x_{18} x_{21} -2x_{15}^{2}x_{17} x_{18} x_{21} +2x_{14} x_{15} x_{17} x_{18} x_{21}
+4x_{13} x_{15} x_{17} x_{18} x_{21} -6x_{13} x_{14} x_{17} x_{18} x_{21} +2x_{16}^{2}x_{17}^{2}x_{21}
-2x_{15} x_{16} x_{17}^{2}x_{21} +2x_{15}^{2}x_{17}^{2}x_{21} -4x_{14} x_{15} x_{17}^{2}x_{21} +3x_{14}^{2}x_{17}^{2}x_{21}
-1= 0
x_{13} = 0
x_{17} = 0
x_{6} x_{12} +x_{5} x_{11} +2x_{4} x_{10} +x_{3} x_{9} +x_{2} x_{8} -2= 0
x_{5} x_{11} +2x_{4} x_{10} +x_{3} x_{9} +2x_{2} x_{8} -2= 0
x_{4} x_{10} +x_{3} x_{9} +x_{2} x_{8} -1= 0
x_{6} x_{11} -x_{3} x_{8} = 0
x_{6} x_{10} -x_{4} x_{8} = 0
x_{6} x_{9} -x_{5} x_{8} = 0
x_{5} x_{12} -x_{2} x_{9} = 0
x_{5} x_{10} -x_{4} x_{9} = 0
x_{4} x_{12} -x_{2} x_{10} = 0
x_{4} x_{11} -x_{3} x_{10} = 0
x_{3} x_{12} -x_{2} x_{11} = 0
x_{2} x_{16} -x_{2} x_{14} = 0
x_{3} x_{16} -x_{3} x_{15} +x_{3} x_{14} -x_{3} x_{13} = 0
x_{4} x_{16} -2x_{4} x_{13} = 0
x_{5} x_{15} -x_{5} x_{14} -x_{5} x_{13} = 0
x_{6} x_{14} -2x_{6} x_{13} = 0
x_{8} x_{16} -x_{8} x_{14} = 0
x_{9} x_{16} -x_{9} x_{15} +x_{9} x_{14} -x_{9} x_{13} = 0
x_{10} x_{16} -2x_{10} x_{13} = 0
x_{11} x_{15} -x_{11} x_{14} -x_{11} x_{13} = 0
x_{12} x_{14} -2x_{12} x_{13} = 0
x_{2} x_{20} -x_{2} x_{18} = 0
x_{3} x_{20} -x_{3} x_{19} +x_{3} x_{18} -x_{3} x_{17} = 0
x_{4} x_{20} -2x_{4} x_{17} = 0
x_{5} x_{19} -x_{5} x_{18} -x_{5} x_{17} = 0
x_{6} x_{18} -2x_{6} x_{17} = 0
x_{8} x_{20} -x_{8} x_{18} = 0
x_{9} x_{20} -x_{9} x_{19} +x_{9} x_{18} -x_{9} x_{17} = 0
x_{10} x_{20} -2x_{10} x_{17} = 0
x_{11} x_{19} -x_{11} x_{18} -x_{11} x_{17} = 0
x_{12} x_{18} -2x_{12} x_{17} = 0
For the calculator:
(DynkinType =B^{1}_2; ElementsCartan =((2, 3, 4, 2), (-1, -1, -1, 0)); generators =(g_{-24}, g_{24}, x_{2} g_{14}+x_{3} g_{11}+x_{4} g_{8}+x_{5} g_{5}+x_{6} g_{1}, x_{12} g_{-1}+x_{11} g_{-5}+x_{10} g_{-8}+x_{9} g_{-11}+x_{8} g_{-14}) );
FindOneSolutionSerreLikePolynomialSystem{}( 3/4x_{15}^{2}x_{20}^{2}x_{21} -2x_{14} x_{15} x_{20}^{2}x_{21} +2x_{14}^{2}x_{20}^{2}x_{21} -2x_{13} x_{14} x_{20}^{2}x_{21} +2x_{13}^{2}x_{20}^{2}x_{21} -3/2x_{15} x_{16} x_{19} x_{20} x_{21} +2x_{14} x_{16} x_{19} x_{20} x_{21} +x_{14} x_{15} x_{19} x_{20} x_{21} -2x_{14}^{2}x_{19} x_{20} x_{21} +2x_{13} x_{14} x_{19} x_{20} x_{21} -2x_{13}^{2}x_{19} x_{20} x_{21} +2x_{15} x_{16} x_{18} x_{20} x_{21} -4x_{14} x_{16} x_{18} x_{20} x_{21} +2x_{13} x_{16} x_{18} x_{20} x_{21} -x_{15}^{2}x_{18} x_{20} x_{21} +2x_{14} x_{15} x_{18} x_{20} x_{21} -x_{13} x_{15} x_{18} x_{20} x_{21} +2x_{14} x_{16} x_{17} x_{20} x_{21} -4x_{13} x_{16} x_{17} x_{20} x_{21} -x_{14} x_{15} x_{17} x_{20} x_{21} +2x_{13} x_{15} x_{17} x_{20} x_{21} +3/4x_{16}^{2}x_{19}^{2}x_{21} -x_{14} x_{16} x_{19}^{2}x_{21} +x_{14}^{2}x_{19}^{2}x_{21} -2x_{13} x_{14} x_{19}^{2}x_{21} +2x_{13}^{2}x_{19}^{2}x_{21} -2x_{16}^{2}x_{18} x_{19} x_{21} +x_{15} x_{16} x_{18} x_{19} x_{21} +2x_{14} x_{16} x_{18} x_{19} x_{21} -x_{13} x_{16} x_{18} x_{19} x_{21} -2x_{14} x_{15} x_{18} x_{19} x_{21} +2x_{13} x_{15} x_{18} x_{19} x_{21} +2x_{13} x_{14} x_{18} x_{19} x_{21} -4x_{13}^{2}x_{18} x_{19} x_{21} -x_{14} x_{16} x_{17} x_{19} x_{21} +2x_{13} x_{16} x_{17} x_{19} x_{21} +2x_{14} x_{15} x_{17} x_{19} x_{21} -4x_{13} x_{15} x_{17} x_{19} x_{21} -2x_{14}^{2}x_{17} x_{19} x_{21} +4x_{13} x_{14} x_{17} x_{19} x_{21} +2x_{16}^{2}x_{18}^{2}x_{21} -2x_{15} x_{16} x_{18}^{2}x_{21} +x_{15}^{2}x_{18}^{2}x_{21} -2x_{13} x_{15} x_{18}^{2}x_{21} +3x_{13}^{2}x_{18}^{2}x_{21} -2x_{16}^{2}x_{17} x_{18} x_{21} +2x_{15} x_{16} x_{17} x_{18} x_{21} -2x_{15}^{2}x_{17} x_{18} x_{21} +2x_{14} x_{15} x_{17} x_{18} x_{21} +4x_{13} x_{15} x_{17} x_{18} x_{21} -6x_{13} x_{14} x_{17} x_{18} x_{21} +2x_{16}^{2}x_{17}^{2}x_{21} -2x_{15} x_{16} x_{17}^{2}x_{21} +2x_{15}^{2}x_{17}^{2}x_{21} -4x_{14} x_{15} x_{17}^{2}x_{21} +3x_{14}^{2}x_{17}^{2}x_{21} -1, x_{13} , x_{17} , x_{6} x_{12} +x_{5} x_{11} +2x_{4} x_{10} +x_{3} x_{9} +x_{2} x_{8} -2, x_{5} x_{11} +2x_{4} x_{10} +x_{3} x_{9} +2x_{2} x_{8} -2, x_{4} x_{10} +x_{3} x_{9} +x_{2} x_{8} -1, x_{6} x_{11} -x_{3} x_{8} , x_{6} x_{10} -x_{4} x_{8} , x_{6} x_{9} -x_{5} x_{8} , x_{5} x_{12} -x_{2} x_{9} , x_{5} x_{10} -x_{4} x_{9} , x_{4} x_{12} -x_{2} x_{10} , x_{4} x_{11} -x_{3} x_{10} , x_{3} x_{12} -x_{2} x_{11} , x_{2} x_{16} -x_{2} x_{14} , x_{3} x_{16} -x_{3} x_{15} +x_{3} x_{14} -x_{3} x_{13} , x_{4} x_{16} -2x_{4} x_{13} , x_{5} x_{15} -x_{5} x_{14} -x_{5} x_{13} , x_{6} x_{14} -2x_{6} x_{13} , x_{8} x_{16} -x_{8} x_{14} , x_{9} x_{16} -x_{9} x_{15} +x_{9} x_{14} -x_{9} x_{13} , x_{10} x_{16} -2x_{10} x_{13} , x_{11} x_{15} -x_{11} x_{14} -x_{11} x_{13} , x_{12} x_{14} -2x_{12} x_{13} , x_{2} x_{20} -x_{2} x_{18} , x_{3} x_{20} -x_{3} x_{19} +x_{3} x_{18} -x_{3} x_{17} , x_{4} x_{20} -2x_{4} x_{17} , x_{5} x_{19} -x_{5} x_{18} -x_{5} x_{17} , x_{6} x_{18} -2x_{6} x_{17} , x_{8} x_{20} -x_{8} x_{18} , x_{9} x_{20} -x_{9} x_{19} +x_{9} x_{18} -x_{9} x_{17} , x_{10} x_{20} -2x_{10} x_{17} , x_{11} x_{19} -x_{11} x_{18} -x_{11} x_{17} , x_{12} x_{18} -2x_{12} x_{17} )