Subalgebra \(A^{12}_1\) ↪ \(E^{1}_6\)
11 out of 119
Computations done by the calculator project.

Subalgebra type: \(\displaystyle A^{12}_1\) (click on type for detailed printout).
Centralizer: \(\displaystyle T_{2}\) (toral part, subscript = dimension).
The semisimple part of the centralizer of the semisimple part of my centralizer: \(\displaystyle E^{1}_6\)
Basis of Cartan of centralizer: 2 vectors: (0, 0, 1, 0, -1, 0), (1, 0, 0, 0, 0, -1)

Elements Cartan subalgebra scaled to act by two by components: \(\displaystyle A^{12}_1\): (4, 6, 8, 12, 8, 4): 24
Dimension of subalgebra generated by predefined or computed generators: 3.
Negative simple generators: \(\displaystyle g_{-4}-2g_{-15}+g_{-19}+g_{-27}\)
Positive simple generators: \(\displaystyle 4g_{27}+g_{24}+2g_{19}-g_{15}+4g_{8}+4g_{4}\)
Cartan symmetric matrix: \(\displaystyle \begin{pmatrix}1/6\\ \end{pmatrix}\)
Scalar products of elements of Cartan subalgebra scaled to act by 2 (co-symmetric Cartan matrix): \(\displaystyle \begin{pmatrix}24\\ \end{pmatrix}\)
Decomposition of ambient Lie algebra: \(\displaystyle 2V_{6\omega_{1}}\oplus 7V_{4\omega_{1}}\oplus 9V_{2\omega_{1}}\oplus 2V_{0}\)
Primal decomposition of the ambient Lie algebra. This decomposition refines the above decomposition (please note the order is not the same as above). \(\displaystyle V_{4\omega_{1}+2\psi_{1}+2\psi_{2}}\oplus V_{4\omega_{1}-2\psi_{1}+4\psi_{2}}\oplus V_{2\omega_{1}+2\psi_{1}+2\psi_{2}}
\oplus 2V_{6\omega_{1}}\oplus V_{4\omega_{1}+4\psi_{1}-2\psi_{2}}\oplus V_{2\omega_{1}-2\psi_{1}+4\psi_{2}}\oplus V_{4\omega_{1}}
\oplus V_{2\omega_{1}+4\psi_{1}-2\psi_{2}}\oplus V_{4\omega_{1}-4\psi_{1}+2\psi_{2}}\oplus 3V_{2\omega_{1}}\oplus V_{4\omega_{1}+2\psi_{1}-4\psi_{2}}
\oplus V_{2\omega_{1}-4\psi_{1}+2\psi_{2}}\oplus 2V_{0}\oplus V_{4\omega_{1}-2\psi_{1}-2\psi_{2}}\oplus V_{2\omega_{1}+2\psi_{1}-4\psi_{2}}
\oplus V_{2\omega_{1}-2\psi_{1}-2\psi_{2}}\)
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 20) ; the vectors are over the primal subalgebra.\(-h_{5}+h_{3}\)\(-h_{6}+h_{1}\)\(-g_{20}+1/2g_{16}\)\(g_{25}+g_{21}\)\(g_{14}+1/4g_{10}\)\(g_{27}-1/4g_{15}-2/3g_{8}+5/6g_{4}\)\(g_{19}+1/4g_{15}+2g_{8}+1/2g_{4}\)\(-g_{24}+1/2g_{15}-8/3g_{8}+1/3g_{4}\)\(g_{13}+1/4g_{9}\)\(g_{22}+g_{18}\)\(-g_{17}+1/2g_{12}\)\(g_{31}\)\(g_{28}\)\(g_{33}\)\(g_{34}-2g_{30}+2g_{23}\)\(g_{32}\)\(g_{26}\)\(g_{29}\)\(g_{35}\)\(g_{36}\)
weight\(0\)\(0\)\(2\omega_{1}\)\(2\omega_{1}\)\(2\omega_{1}\)\(2\omega_{1}\)\(2\omega_{1}\)\(2\omega_{1}\)\(2\omega_{1}\)\(2\omega_{1}\)\(2\omega_{1}\)\(4\omega_{1}\)\(4\omega_{1}\)\(4\omega_{1}\)\(4\omega_{1}\)\(4\omega_{1}\)\(4\omega_{1}\)\(4\omega_{1}\)\(6\omega_{1}\)\(6\omega_{1}\)
weights rel. to Cartan of (centralizer+semisimple s.a.). \(0\)\(0\)\(2\omega_{1}-2\psi_{1}-2\psi_{2}\)\(2\omega_{1}+2\psi_{1}-4\psi_{2}\)\(2\omega_{1}-4\psi_{1}+2\psi_{2}\)\(2\omega_{1}\)\(2\omega_{1}\)\(2\omega_{1}\)\(2\omega_{1}+4\psi_{1}-2\psi_{2}\)\(2\omega_{1}-2\psi_{1}+4\psi_{2}\)\(2\omega_{1}+2\psi_{1}+2\psi_{2}\)\(4\omega_{1}-2\psi_{1}-2\psi_{2}\)\(4\omega_{1}+2\psi_{1}-4\psi_{2}\)\(4\omega_{1}-4\psi_{1}+2\psi_{2}\)\(4\omega_{1}\)\(4\omega_{1}+4\psi_{1}-2\psi_{2}\)\(4\omega_{1}-2\psi_{1}+4\psi_{2}\)\(4\omega_{1}+2\psi_{1}+2\psi_{2}\)\(6\omega_{1}\)\(6\omega_{1}\)
Isotypic module decomposition over primal subalgebra (total 17 isotypic components).
Isotypical components + highest weight\(\displaystyle V_{0} \) → (0, 0, 0)\(\displaystyle V_{2\omega_{1}-2\psi_{1}-2\psi_{2}} \) → (2, -2, -2)\(\displaystyle V_{2\omega_{1}+2\psi_{1}-4\psi_{2}} \) → (2, 2, -4)\(\displaystyle V_{2\omega_{1}-4\psi_{1}+2\psi_{2}} \) → (2, -4, 2)\(\displaystyle V_{2\omega_{1}} \) → (2, 0, 0)\(\displaystyle V_{2\omega_{1}+4\psi_{1}-2\psi_{2}} \) → (2, 4, -2)\(\displaystyle V_{2\omega_{1}-2\psi_{1}+4\psi_{2}} \) → (2, -2, 4)\(\displaystyle V_{2\omega_{1}+2\psi_{1}+2\psi_{2}} \) → (2, 2, 2)\(\displaystyle V_{4\omega_{1}-2\psi_{1}-2\psi_{2}} \) → (4, -2, -2)\(\displaystyle V_{4\omega_{1}+2\psi_{1}-4\psi_{2}} \) → (4, 2, -4)\(\displaystyle V_{4\omega_{1}-4\psi_{1}+2\psi_{2}} \) → (4, -4, 2)\(\displaystyle V_{4\omega_{1}} \) → (4, 0, 0)\(\displaystyle V_{4\omega_{1}+4\psi_{1}-2\psi_{2}} \) → (4, 4, -2)\(\displaystyle V_{4\omega_{1}-2\psi_{1}+4\psi_{2}} \) → (4, -2, 4)\(\displaystyle V_{4\omega_{1}+2\psi_{1}+2\psi_{2}} \) → (4, 2, 2)\(\displaystyle V_{6\omega_{1}} \) → (6, 0, 0)
Module label \(W_{1}\)\(W_{2}\)\(W_{3}\)\(W_{4}\)\(W_{5}\)\(W_{6}\)\(W_{7}\)\(W_{8}\)\(W_{9}\)\(W_{10}\)\(W_{11}\)\(W_{12}\)\(W_{13}\)\(W_{14}\)\(W_{15}\)\(W_{16}\)\(W_{17}\)
Module elements (weight vectors). In blue - corresp. F element. In red -corresp. H element. Cartan of centralizer component.
\(-h_{5}+h_{3}\)
\(-h_{6}+h_{1}\)
\(-g_{20}+1/2g_{16}\)
\(1/2g_{11}+g_{-7}\)
\(g_{-12}-1/2g_{-17}\)
\(g_{25}+g_{21}\)
\(-g_{6}-g_{-1}\)
\(2g_{-18}\)
\(g_{14}+1/4g_{10}\)
\(1/4g_{5}-1/2g_{-3}\)
\(-1/4g_{-13}\)
Semisimple subalgebra component.
\(-g_{27}-1/4g_{24}-1/2g_{19}+1/4g_{15}-g_{8}-g_{4}\)
\(h_{6}+2h_{5}+3h_{4}+2h_{3}+3/2h_{2}+h_{1}\)
\(1/2g_{-4}-g_{-15}+1/2g_{-19}+1/2g_{-27}\)
\(g_{19}+1/4g_{15}+2g_{8}+1/2g_{4}\)
\(-1/2h_{5}-h_{4}-1/2h_{3}-h_{2}-1/4g_{-2}\)
\(-1/4g_{-8}-1/2g_{-19}\)
\(g_{27}-1/4g_{15}-2/3g_{8}+5/6g_{4}\)
\(2/3g_{2}-h_{6}-3/2h_{5}-7/3h_{4}-3/2h_{3}-h_{2}-h_{1}+1/4g_{-2}\)
\(-2/3g_{-4}+1/4g_{-8}+2/3g_{-15}-1/6g_{-19}+2/3g_{-24}-2/3g_{-27}\)
\(g_{13}+1/4g_{9}\)
\(-1/4g_{3}+1/2g_{-5}\)
\(-1/4g_{-14}\)
\(g_{22}+g_{18}\)
\(g_{1}+g_{-6}\)
\(2g_{-21}\)
\(-g_{17}+1/2g_{12}\)
\(-1/2g_{7}-g_{-11}\)
\(g_{-16}-1/2g_{-20}\)
\(g_{31}\)
\(-2g_{20}-g_{16}\)
\(-g_{11}+2g_{-7}\)
\(2g_{-12}+g_{-17}\)
\(-4g_{-29}\)
\(g_{28}\)
\(g_{25}\)
\(g_{6}-g_{-1}\)
\(2g_{-18}-2g_{-22}\)
\(2g_{-26}\)
\(g_{33}\)
\(g_{10}\)
\(g_{5}+2g_{-3}\)
\(4g_{-9}-g_{-13}\)
\(4g_{-32}\)
\(g_{34}-2g_{30}+2g_{23}\)
\(g_{24}+2g_{19}+g_{15}-4g_{8}\)
\(8g_{2}-2h_{2}-2g_{-2}\)
\(2g_{-4}-2g_{-8}+4g_{-15}+2g_{-19}+8g_{-24}-2g_{-27}\)
\(-4g_{-23}+4g_{-30}-8g_{-34}\)
\(g_{32}\)
\(-g_{9}\)
\(g_{3}+2g_{-5}\)
\(-4g_{-10}+g_{-14}\)
\(4g_{-33}\)
\(g_{26}\)
\(g_{22}\)
\(-g_{1}+g_{-6}\)
\(2g_{-21}-2g_{-25}\)
\(2g_{-28}\)
\(g_{29}\)
\(2g_{17}+g_{12}\)
\(-g_{7}+2g_{-11}\)
\(-2g_{-16}-g_{-20}\)
\(-4g_{-31}\)
\(g_{35}\)
\(g_{34}+2g_{30}\)
\(4g_{27}+g_{24}+g_{15}-2g_{4}\)
\(-4h_{6}-2h_{5}-2h_{3}-4h_{2}-4h_{1}-2g_{-2}\)
\(8g_{-4}-2g_{-8}-16g_{-15}+4g_{-19}-12g_{-27}\)
\(20g_{-30}+40g_{-34}\)
\(-80g_{-35}+20g_{-36}\)
\(g_{36}\)
\(-g_{30}-g_{23}\)
\(-g_{27}-g_{19}+2g_{8}+2g_{4}\)
\(-4g_{2}+h_{6}+2h_{5}+2h_{3}+2h_{2}+h_{1}\)
\(-6g_{-4}-4g_{-15}+4g_{-19}-4g_{-24}+4g_{-27}\)
\(-10g_{-23}-10g_{-30}\)
\(20g_{-35}-20g_{-36}\)
Weights of elements in fundamental coords w.r.t. Cartan of subalgebra in same order as above\(0\)\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)		\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)		\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)		\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)		\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)		\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)		\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)		\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)		\(4\omega_{1}\)
\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)
\(-4\omega_{1}\)		\(4\omega_{1}\)
\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)
\(-4\omega_{1}\)		\(4\omega_{1}\)
\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)
\(-4\omega_{1}\)		\(4\omega_{1}\)
\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)
\(-4\omega_{1}\)		\(4\omega_{1}\)
\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)
\(-4\omega_{1}\)		\(4\omega_{1}\)
\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)
\(-4\omega_{1}\)		\(4\omega_{1}\)
\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)
\(-4\omega_{1}\)		\(6\omega_{1}\)
\(4\omega_{1}\)
\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)
\(-4\omega_{1}\)
\(-6\omega_{1}\)
Weights of elements in (fundamental coords w.r.t. Cartan of subalgebra) + Cartan centralizer\(0\)\(2\omega_{1}-2\psi_{1}-2\psi_{2}\)
\(-2\psi_{1}-2\psi_{2}\)
\(-2\omega_{1}-2\psi_{1}-2\psi_{2}\)		\(2\omega_{1}+2\psi_{1}-4\psi_{2}\)
\(2\psi_{1}-4\psi_{2}\)
\(-2\omega_{1}+2\psi_{1}-4\psi_{2}\)		\(2\omega_{1}-4\psi_{1}+2\psi_{2}\)
\(-4\psi_{1}+2\psi_{2}\)
\(-2\omega_{1}-4\psi_{1}+2\psi_{2}\)		\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)		\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)		\(2\omega_{1}+4\psi_{1}-2\psi_{2}\)
\(4\psi_{1}-2\psi_{2}\)
\(-2\omega_{1}+4\psi_{1}-2\psi_{2}\)		\(2\omega_{1}-2\psi_{1}+4\psi_{2}\)
\(-2\psi_{1}+4\psi_{2}\)
\(-2\omega_{1}-2\psi_{1}+4\psi_{2}\)		\(2\omega_{1}+2\psi_{1}+2\psi_{2}\)
\(2\psi_{1}+2\psi_{2}\)
\(-2\omega_{1}+2\psi_{1}+2\psi_{2}\)		\(4\omega_{1}-2\psi_{1}-2\psi_{2}\)
\(2\omega_{1}-2\psi_{1}-2\psi_{2}\)
\(-2\psi_{1}-2\psi_{2}\)
\(-2\omega_{1}-2\psi_{1}-2\psi_{2}\)
\(-4\omega_{1}-2\psi_{1}-2\psi_{2}\)		\(4\omega_{1}+2\psi_{1}-4\psi_{2}\)
\(2\omega_{1}+2\psi_{1}-4\psi_{2}\)
\(2\psi_{1}-4\psi_{2}\)
\(-2\omega_{1}+2\psi_{1}-4\psi_{2}\)
\(-4\omega_{1}+2\psi_{1}-4\psi_{2}\)		\(4\omega_{1}-4\psi_{1}+2\psi_{2}\)
\(2\omega_{1}-4\psi_{1}+2\psi_{2}\)
\(-4\psi_{1}+2\psi_{2}\)
\(-2\omega_{1}-4\psi_{1}+2\psi_{2}\)
\(-4\omega_{1}-4\psi_{1}+2\psi_{2}\)		\(4\omega_{1}\)
\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)
\(-4\omega_{1}\)		\(4\omega_{1}+4\psi_{1}-2\psi_{2}\)
\(2\omega_{1}+4\psi_{1}-2\psi_{2}\)
\(4\psi_{1}-2\psi_{2}\)
\(-2\omega_{1}+4\psi_{1}-2\psi_{2}\)
\(-4\omega_{1}+4\psi_{1}-2\psi_{2}\)		\(4\omega_{1}-2\psi_{1}+4\psi_{2}\)
\(2\omega_{1}-2\psi_{1}+4\psi_{2}\)
\(-2\psi_{1}+4\psi_{2}\)
\(-2\omega_{1}-2\psi_{1}+4\psi_{2}\)
\(-4\omega_{1}-2\psi_{1}+4\psi_{2}\)		\(4\omega_{1}+2\psi_{1}+2\psi_{2}\)
\(2\omega_{1}+2\psi_{1}+2\psi_{2}\)
\(2\psi_{1}+2\psi_{2}\)
\(-2\omega_{1}+2\psi_{1}+2\psi_{2}\)
\(-4\omega_{1}+2\psi_{1}+2\psi_{2}\)		\(6\omega_{1}\)
\(4\omega_{1}\)
\(2\omega_{1}\)
\(0\)
\(-2\omega_{1}\)
\(-4\omega_{1}\)
\(-6\omega_{1}\)
Single module character over Cartan of s.a.+ Cartan of centralizer of s.a.\(\displaystyle M_{0}\)\(\displaystyle M_{2\omega_{1}-2\psi_{1}-2\psi_{2}}\oplus M_{-2\psi_{1}-2\psi_{2}}\oplus M_{-2\omega_{1}-2\psi_{1}-2\psi_{2}}\)\(\displaystyle M_{2\omega_{1}+2\psi_{1}-4\psi_{2}}\oplus M_{2\psi_{1}-4\psi_{2}}\oplus M_{-2\omega_{1}+2\psi_{1}-4\psi_{2}}\)\(\displaystyle M_{2\omega_{1}-4\psi_{1}+2\psi_{2}}\oplus M_{-4\psi_{1}+2\psi_{2}}\oplus M_{-2\omega_{1}-4\psi_{1}+2\psi_{2}}\)\(\displaystyle M_{2\omega_{1}}\oplus M_{0}\oplus M_{-2\omega_{1}}\)\(\displaystyle M_{2\omega_{1}}\oplus M_{0}\oplus M_{-2\omega_{1}}\)\(\displaystyle M_{2\omega_{1}+4\psi_{1}-2\psi_{2}}\oplus M_{4\psi_{1}-2\psi_{2}}\oplus M_{-2\omega_{1}+4\psi_{1}-2\psi_{2}}\)\(\displaystyle M_{2\omega_{1}-2\psi_{1}+4\psi_{2}}\oplus M_{-2\psi_{1}+4\psi_{2}}\oplus M_{-2\omega_{1}-2\psi_{1}+4\psi_{2}}\)\(\displaystyle M_{2\omega_{1}+2\psi_{1}+2\psi_{2}}\oplus M_{2\psi_{1}+2\psi_{2}}\oplus M_{-2\omega_{1}+2\psi_{1}+2\psi_{2}}\)\(\displaystyle M_{4\omega_{1}-2\psi_{1}-2\psi_{2}}\oplus M_{2\omega_{1}-2\psi_{1}-2\psi_{2}}\oplus M_{-2\psi_{1}-2\psi_{2}}\oplus M_{-2\omega_{1}-2\psi_{1}-2\psi_{2}}
\oplus M_{-4\omega_{1}-2\psi_{1}-2\psi_{2}}\)		\(\displaystyle M_{4\omega_{1}+2\psi_{1}-4\psi_{2}}\oplus M_{2\omega_{1}+2\psi_{1}-4\psi_{2}}\oplus M_{2\psi_{1}-4\psi_{2}}\oplus M_{-2\omega_{1}+2\psi_{1}-4\psi_{2}}
\oplus M_{-4\omega_{1}+2\psi_{1}-4\psi_{2}}\)		\(\displaystyle M_{4\omega_{1}-4\psi_{1}+2\psi_{2}}\oplus M_{2\omega_{1}-4\psi_{1}+2\psi_{2}}\oplus M_{-4\psi_{1}+2\psi_{2}}\oplus M_{-2\omega_{1}-4\psi_{1}+2\psi_{2}}
\oplus M_{-4\omega_{1}-4\psi_{1}+2\psi_{2}}\)		\(\displaystyle M_{4\omega_{1}}\oplus M_{2\omega_{1}}\oplus M_{0}\oplus M_{-2\omega_{1}}\oplus M_{-4\omega_{1}}\)\(\displaystyle M_{4\omega_{1}+4\psi_{1}-2\psi_{2}}\oplus M_{2\omega_{1}+4\psi_{1}-2\psi_{2}}\oplus M_{4\psi_{1}-2\psi_{2}}\oplus M_{-2\omega_{1}+4\psi_{1}-2\psi_{2}}
\oplus M_{-4\omega_{1}+4\psi_{1}-2\psi_{2}}\)		\(\displaystyle M_{4\omega_{1}-2\psi_{1}+4\psi_{2}}\oplus M_{2\omega_{1}-2\psi_{1}+4\psi_{2}}\oplus M_{-2\psi_{1}+4\psi_{2}}\oplus M_{-2\omega_{1}-2\psi_{1}+4\psi_{2}}
\oplus M_{-4\omega_{1}-2\psi_{1}+4\psi_{2}}\)		\(\displaystyle M_{4\omega_{1}+2\psi_{1}+2\psi_{2}}\oplus M_{2\omega_{1}+2\psi_{1}+2\psi_{2}}\oplus M_{2\psi_{1}+2\psi_{2}}\oplus M_{-2\omega_{1}+2\psi_{1}+2\psi_{2}}
\oplus M_{-4\omega_{1}+2\psi_{1}+2\psi_{2}}\)		\(\displaystyle M_{6\omega_{1}}\oplus M_{4\omega_{1}}\oplus M_{2\omega_{1}}\oplus M_{0}\oplus M_{-2\omega_{1}}\oplus M_{-4\omega_{1}}\oplus M_{-6\omega_{1}}\)
Isotypic character\(\displaystyle 2M_{0}\)\(\displaystyle M_{2\omega_{1}-2\psi_{1}-2\psi_{2}}\oplus M_{-2\psi_{1}-2\psi_{2}}\oplus M_{-2\omega_{1}-2\psi_{1}-2\psi_{2}}\)\(\displaystyle M_{2\omega_{1}+2\psi_{1}-4\psi_{2}}\oplus M_{2\psi_{1}-4\psi_{2}}\oplus M_{-2\omega_{1}+2\psi_{1}-4\psi_{2}}\)\(\displaystyle M_{2\omega_{1}-4\psi_{1}+2\psi_{2}}\oplus M_{-4\psi_{1}+2\psi_{2}}\oplus M_{-2\omega_{1}-4\psi_{1}+2\psi_{2}}\)\(\displaystyle M_{2\omega_{1}}\oplus M_{0}\oplus M_{-2\omega_{1}}\)\(\displaystyle 2M_{2\omega_{1}}\oplus 2M_{0}\oplus 2M_{-2\omega_{1}}\)\(\displaystyle M_{2\omega_{1}+4\psi_{1}-2\psi_{2}}\oplus M_{4\psi_{1}-2\psi_{2}}\oplus M_{-2\omega_{1}+4\psi_{1}-2\psi_{2}}\)\(\displaystyle M_{2\omega_{1}-2\psi_{1}+4\psi_{2}}\oplus M_{-2\psi_{1}+4\psi_{2}}\oplus M_{-2\omega_{1}-2\psi_{1}+4\psi_{2}}\)\(\displaystyle M_{2\omega_{1}+2\psi_{1}+2\psi_{2}}\oplus M_{2\psi_{1}+2\psi_{2}}\oplus M_{-2\omega_{1}+2\psi_{1}+2\psi_{2}}\)\(\displaystyle M_{4\omega_{1}-2\psi_{1}-2\psi_{2}}\oplus M_{2\omega_{1}-2\psi_{1}-2\psi_{2}}\oplus M_{-2\psi_{1}-2\psi_{2}}\oplus M_{-2\omega_{1}-2\psi_{1}-2\psi_{2}}
\oplus M_{-4\omega_{1}-2\psi_{1}-2\psi_{2}}\)		\(\displaystyle M_{4\omega_{1}+2\psi_{1}-4\psi_{2}}\oplus M_{2\omega_{1}+2\psi_{1}-4\psi_{2}}\oplus M_{2\psi_{1}-4\psi_{2}}\oplus M_{-2\omega_{1}+2\psi_{1}-4\psi_{2}}
\oplus M_{-4\omega_{1}+2\psi_{1}-4\psi_{2}}\)		\(\displaystyle M_{4\omega_{1}-4\psi_{1}+2\psi_{2}}\oplus M_{2\omega_{1}-4\psi_{1}+2\psi_{2}}\oplus M_{-4\psi_{1}+2\psi_{2}}\oplus M_{-2\omega_{1}-4\psi_{1}+2\psi_{2}}
\oplus M_{-4\omega_{1}-4\psi_{1}+2\psi_{2}}\)		\(\displaystyle M_{4\omega_{1}}\oplus M_{2\omega_{1}}\oplus M_{0}\oplus M_{-2\omega_{1}}\oplus M_{-4\omega_{1}}\)\(\displaystyle M_{4\omega_{1}+4\psi_{1}-2\psi_{2}}\oplus M_{2\omega_{1}+4\psi_{1}-2\psi_{2}}\oplus M_{4\psi_{1}-2\psi_{2}}\oplus M_{-2\omega_{1}+4\psi_{1}-2\psi_{2}}
\oplus M_{-4\omega_{1}+4\psi_{1}-2\psi_{2}}\)		\(\displaystyle M_{4\omega_{1}-2\psi_{1}+4\psi_{2}}\oplus M_{2\omega_{1}-2\psi_{1}+4\psi_{2}}\oplus M_{-2\psi_{1}+4\psi_{2}}\oplus M_{-2\omega_{1}-2\psi_{1}+4\psi_{2}}
\oplus M_{-4\omega_{1}-2\psi_{1}+4\psi_{2}}\)		\(\displaystyle M_{4\omega_{1}+2\psi_{1}+2\psi_{2}}\oplus M_{2\omega_{1}+2\psi_{1}+2\psi_{2}}\oplus M_{2\psi_{1}+2\psi_{2}}\oplus M_{-2\omega_{1}+2\psi_{1}+2\psi_{2}}
\oplus M_{-4\omega_{1}+2\psi_{1}+2\psi_{2}}\)		\(\displaystyle 2M_{6\omega_{1}}\oplus 2M_{4\omega_{1}}\oplus 2M_{2\omega_{1}}\oplus 2M_{0}\oplus 2M_{-2\omega_{1}}\oplus 2M_{-4\omega_{1}}\oplus 2M_{-6\omega_{1}}\)

Semisimple subalgebra: W_{5}
Centralizer extension: W_{1}

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



Made total 583010629 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.
1*2 (unknown) gens:
(
x_{1} g_{-4}+x_{2} g_{-8}+x_{3} g_{-9}+x_{4} g_{-10}+x_{5} g_{-12}+x_{6} g_{-13}+x_{7} g_{-14}+x_{8} g_{-15} \\ +x_{9} g_{-16}+x_{10} g_{-17}+x_{11} g_{-18}+x_{12} g_{-19}+x_{13} g_{-20}+x_{14} g_{-21}+x_{15} g_{-22} \\ +x_{16} g_{-24}+x_{17} g_{-25}+x_{18} g_{-27}, x_{36} g_{27}+x_{35} g_{25}+x_{34} g_{24}+x_{33} g_{22}+x_{32} g_{21}+x_{31} g_{20}+x_{30} g_{19}+x_{29} g_{18} \\ +x_{28} g_{17}+x_{27} g_{16}+x_{26} g_{15}+x_{25} g_{14}+x_{24} g_{13}+x_{23} g_{12}+x_{22} g_{10}+x_{21} g_{9} \\ +x_{20} g_{8}+x_{19} g_{4})

Unknown splitting cartan of centralizer.
x_{42} h_{6}+x_{41} h_{5}+x_{40} h_{4}+x_{39} h_{3}+x_{38} h_{2}+x_{37} h_{1}, x_{48} h_{6}+x_{47} h_{5}+x_{46} h_{4}+x_{45} h_{3}+x_{44} h_{2}+x_{43} h_{1}
h: (4, 6, 8, 12, 8, 4), e = combination of g_{4} g_{8} g_{9} g_{10} g_{12} g_{13} g_{14} g_{15} g_{16} g_{17} g_{18} g_{19} g_{20} g_{21} g_{22} g_{24} g_{25} g_{27} , f= combination of g_{-4} g_{-8} g_{-9} g_{-10} g_{-12} g_{-13} g_{-14} g_{-15} g_{-16} g_{-17} g_{-18} g_{-19} g_{-20} g_{-21} g_{-22} g_{-24} g_{-25} g_{-27} Positive weight subsystem: 1 vectors: (1)
Symmetric Cartan default scale: \begin{pmatrix}
2\\
\end{pmatrix}Character ambient Lie algebra: 2V_{6\omega_{1}}+9V_{4\omega_{1}}+18V_{2\omega_{1}}+20V_{0}+18V_{-2\omega_{1}}+9V_{-4\omega_{1}}+2V_{-6\omega_{1}}
A necessary system to realize the candidate subalgebra.
3x_{41}^{2}x_{48}^{2}x_{49} -4x_{40} x_{41} x_{48}^{2}x_{49} +4x_{40}^{2}x_{48}^{2}x_{49} -4x_{39} x_{40} x_{48}^{2}x_{49}
-4x_{38} x_{40} x_{48}^{2}x_{49} +4x_{39}^{2}x_{48}^{2}x_{49} -4x_{37} x_{39} x_{48}^{2}x_{49} +4x_{38}^{2}x_{48}^{2}x_{49}
+4x_{37}^{2}x_{48}^{2}x_{49} -6x_{41} x_{42} x_{47} x_{48} x_{49} +4x_{40} x_{42} x_{47} x_{48} x_{49}
+2x_{40} x_{41} x_{47} x_{48} x_{49} -4x_{40}^{2}x_{47} x_{48} x_{49} +4x_{39} x_{40} x_{47} x_{48} x_{49}
+4x_{38} x_{40} x_{47} x_{48} x_{49} -4x_{39}^{2}x_{47} x_{48} x_{49} +4x_{37} x_{39} x_{47} x_{48} x_{49}
-4x_{38}^{2}x_{47} x_{48} x_{49} -4x_{37}^{2}x_{47} x_{48} x_{49} +4x_{41} x_{42} x_{46} x_{48} x_{49}
-8x_{40} x_{42} x_{46} x_{48} x_{49} +4x_{39} x_{42} x_{46} x_{48} x_{49} +4x_{38} x_{42} x_{46} x_{48} x_{49}
-2x_{41}^{2}x_{46} x_{48} x_{49} +4x_{40} x_{41} x_{46} x_{48} x_{49} -2x_{39} x_{41} x_{46} x_{48} x_{49}
-2x_{38} x_{41} x_{46} x_{48} x_{49} +4x_{40} x_{42} x_{45} x_{48} x_{49} -8x_{39} x_{42} x_{45} x_{48} x_{49}
+4x_{37} x_{42} x_{45} x_{48} x_{49} -2x_{40} x_{41} x_{45} x_{48} x_{49} +4x_{39} x_{41} x_{45} x_{48} x_{49}
-2x_{37} x_{41} x_{45} x_{48} x_{49} +4x_{40} x_{42} x_{44} x_{48} x_{49} -8x_{38} x_{42} x_{44} x_{48} x_{49}
-2x_{40} x_{41} x_{44} x_{48} x_{49} +4x_{38} x_{41} x_{44} x_{48} x_{49} +4x_{39} x_{42} x_{43} x_{48} x_{49}
-8x_{37} x_{42} x_{43} x_{48} x_{49} -2x_{39} x_{41} x_{43} x_{48} x_{49} +4x_{37} x_{41} x_{43} x_{48} x_{49}
+3x_{42}^{2}x_{47}^{2}x_{49} -2x_{40} x_{42} x_{47}^{2}x_{49} +3x_{40}^{2}x_{47}^{2}x_{49} -4x_{39} x_{40} x_{47}^{2}x_{49}
-4x_{38} x_{40} x_{47}^{2}x_{49} +4x_{39}^{2}x_{47}^{2}x_{49} -4x_{37} x_{39} x_{47}^{2}x_{49} +4x_{38}^{2}x_{47}^{2}x_{49}
+4x_{37}^{2}x_{47}^{2}x_{49} -4x_{42}^{2}x_{46} x_{47} x_{49} +2x_{41} x_{42} x_{46} x_{47} x_{49} +4x_{40} x_{42} x_{46} x_{47} x_{49}
-2x_{39} x_{42} x_{46} x_{47} x_{49} -2x_{38} x_{42} x_{46} x_{47} x_{49} -6x_{40} x_{41} x_{46} x_{47} x_{49}
+4x_{39} x_{41} x_{46} x_{47} x_{49} +4x_{38} x_{41} x_{46} x_{47} x_{49} +2x_{39} x_{40} x_{46} x_{47} x_{49}
+2x_{38} x_{40} x_{46} x_{47} x_{49} -4x_{39}^{2}x_{46} x_{47} x_{49} +4x_{37} x_{39} x_{46} x_{47} x_{49}
-4x_{38}^{2}x_{46} x_{47} x_{49} -4x_{37}^{2}x_{46} x_{47} x_{49} -2x_{40} x_{42} x_{45} x_{47} x_{49}
+4x_{39} x_{42} x_{45} x_{47} x_{49} -2x_{37} x_{42} x_{45} x_{47} x_{49} +4x_{40} x_{41} x_{45} x_{47} x_{49}
-8x_{39} x_{41} x_{45} x_{47} x_{49} +4x_{37} x_{41} x_{45} x_{47} x_{49} -2x_{40}^{2}x_{45} x_{47} x_{49}
+4x_{39} x_{40} x_{45} x_{47} x_{49} -2x_{37} x_{40} x_{45} x_{47} x_{49} -2x_{40} x_{42} x_{44} x_{47} x_{49}
+4x_{38} x_{42} x_{44} x_{47} x_{49} +4x_{40} x_{41} x_{44} x_{47} x_{49} -8x_{38} x_{41} x_{44} x_{47} x_{49}
-2x_{40}^{2}x_{44} x_{47} x_{49} +4x_{38} x_{40} x_{44} x_{47} x_{49} -2x_{39} x_{42} x_{43} x_{47} x_{49}
+4x_{37} x_{42} x_{43} x_{47} x_{49} +4x_{39} x_{41} x_{43} x_{47} x_{49} -8x_{37} x_{41} x_{43} x_{47} x_{49}
-2x_{39} x_{40} x_{43} x_{47} x_{49} +4x_{37} x_{40} x_{43} x_{47} x_{49} +4x_{42}^{2}x_{46}^{2}x_{49}
-4x_{41} x_{42} x_{46}^{2}x_{49} +3x_{41}^{2}x_{46}^{2}x_{49} -2x_{39} x_{41} x_{46}^{2}x_{49} -2x_{38} x_{41} x_{46}^{2}x_{49}
+3x_{39}^{2}x_{46}^{2}x_{49} -2x_{38} x_{39} x_{46}^{2}x_{49} -4x_{37} x_{39} x_{46}^{2}x_{49} +3x_{38}^{2}x_{46}^{2}x_{49}
+4x_{37}^{2}x_{46}^{2}x_{49} -4x_{42}^{2}x_{45} x_{46} x_{49} +4x_{41} x_{42} x_{45} x_{46} x_{49} -4x_{41}^{2}x_{45} x_{46} x_{49}
+2x_{40} x_{41} x_{45} x_{46} x_{49} +4x_{39} x_{41} x_{45} x_{46} x_{49} -2x_{37} x_{41} x_{45} x_{46} x_{49}
-6x_{39} x_{40} x_{45} x_{46} x_{49} +2x_{38} x_{40} x_{45} x_{46} x_{49} +4x_{37} x_{40} x_{45} x_{46} x_{49}
+4x_{38} x_{39} x_{45} x_{46} x_{49} +2x_{37} x_{39} x_{45} x_{46} x_{49} -4x_{38}^{2}x_{45} x_{46} x_{49}
-2x_{37} x_{38} x_{45} x_{46} x_{49} -4x_{37}^{2}x_{45} x_{46} x_{49} -4x_{42}^{2}x_{44} x_{46} x_{49}
+4x_{41} x_{42} x_{44} x_{46} x_{49} -4x_{41}^{2}x_{44} x_{46} x_{49} +2x_{40} x_{41} x_{44} x_{46} x_{49}
+4x_{38} x_{41} x_{44} x_{46} x_{49} +2x_{39} x_{40} x_{44} x_{46} x_{49} -6x_{38} x_{40} x_{44} x_{46} x_{49}
-4x_{39}^{2}x_{44} x_{46} x_{49} +4x_{38} x_{39} x_{44} x_{46} x_{49} +4x_{37} x_{39} x_{44} x_{46} x_{49}
-4x_{37}^{2}x_{44} x_{46} x_{49} -2x_{39} x_{41} x_{43} x_{46} x_{49} +4x_{37} x_{41} x_{43} x_{46} x_{49}
+4x_{39} x_{40} x_{43} x_{46} x_{49} -8x_{37} x_{40} x_{43} x_{46} x_{49} -2x_{39}^{2}x_{43} x_{46} x_{49}
-2x_{38} x_{39} x_{43} x_{46} x_{49} +4x_{37} x_{39} x_{43} x_{46} x_{49} +4x_{37} x_{38} x_{43} x_{46} x_{49}
+4x_{42}^{2}x_{45}^{2}x_{49} -4x_{41} x_{42} x_{45}^{2}x_{49} +4x_{41}^{2}x_{45}^{2}x_{49} -4x_{40} x_{41} x_{45}^{2}x_{49}
+3x_{40}^{2}x_{45}^{2}x_{49} -4x_{38} x_{40} x_{45}^{2}x_{49} -2x_{37} x_{40} x_{45}^{2}x_{49} +4x_{38}^{2}x_{45}^{2}x_{49}
+3x_{37}^{2}x_{45}^{2}x_{49} -2x_{40}^{2}x_{44} x_{45} x_{49} +4x_{39} x_{40} x_{44} x_{45} x_{49} +4x_{38} x_{40} x_{44} x_{45} x_{49}
-2x_{37} x_{40} x_{44} x_{45} x_{49} -8x_{38} x_{39} x_{44} x_{45} x_{49} +4x_{37} x_{38} x_{44} x_{45} x_{49}
-4x_{42}^{2}x_{43} x_{45} x_{49} +4x_{41} x_{42} x_{43} x_{45} x_{49} -4x_{41}^{2}x_{43} x_{45} x_{49}
+4x_{40} x_{41} x_{43} x_{45} x_{49} -4x_{40}^{2}x_{43} x_{45} x_{49} +2x_{39} x_{40} x_{43} x_{45} x_{49}
+4x_{38} x_{40} x_{43} x_{45} x_{49} +4x_{37} x_{40} x_{43} x_{45} x_{49} -6x_{37} x_{39} x_{43} x_{45} x_{49}
-4x_{38}^{2}x_{43} x_{45} x_{49} +4x_{42}^{2}x_{44}^{2}x_{49} -4x_{41} x_{42} x_{44}^{2}x_{49} +4x_{41}^{2}x_{44}^{2}x_{49}
-4x_{40} x_{41} x_{44}^{2}x_{49} +3x_{40}^{2}x_{44}^{2}x_{49} -4x_{39} x_{40} x_{44}^{2}x_{49} +4x_{39}^{2}x_{44}^{2}x_{49}
-4x_{37} x_{39} x_{44}^{2}x_{49} +4x_{37}^{2}x_{44}^{2}x_{49} -2x_{39} x_{40} x_{43} x_{44} x_{49} +4x_{37} x_{40} x_{43} x_{44} x_{49}
+4x_{38} x_{39} x_{43} x_{44} x_{49} -8x_{37} x_{38} x_{43} x_{44} x_{49} +4x_{42}^{2}x_{43}^{2}x_{49}
-4x_{41} x_{42} x_{43}^{2}x_{49} +4x_{41}^{2}x_{43}^{2}x_{49} -4x_{40} x_{41} x_{43}^{2}x_{49} +4x_{40}^{2}x_{43}^{2}x_{49}
-4x_{39} x_{40} x_{43}^{2}x_{49} -4x_{38} x_{40} x_{43}^{2}x_{49} +3x_{39}^{2}x_{43}^{2}x_{49} +4x_{38}^{2}x_{43}^{2}x_{49}
-1= 0
x_{18} x_{36} +x_{17} x_{35} +x_{16} x_{34} +x_{15} x_{33} +x_{14} x_{32} +x_{13} x_{31} +x_{12} x_{30}
+x_{11} x_{29} +x_{10} x_{28} +x_{9} x_{27} +x_{8} x_{26} +x_{7} x_{25} +x_{6} x_{24} +x_{5} x_{23} +x_{4} x_{22}
+x_{3} x_{21} +x_{2} x_{20} +x_{1} x_{19} -12= 0
x_{18} x_{34} +x_{17} x_{32} +x_{15} x_{29} +x_{13} x_{27} +x_{12} x_{26} +x_{10} x_{23} +x_{7} x_{22}
+x_{6} x_{21} +x_{2} x_{19} = 0
x_{17} x_{31} +x_{14} x_{27} +x_{12} x_{25} +x_{8} x_{22} +x_{6} x_{20} +x_{3} x_{19} = 0
x_{15} x_{28} +x_{12} x_{24} +x_{11} x_{23} +x_{8} x_{21} +x_{7} x_{20} +x_{4} x_{19} = 0
x_{18} x_{31} +x_{16} x_{27} +x_{15} x_{25} +x_{11} x_{22} +x_{10} x_{20} +x_{5} x_{19} = 0
x_{18} x_{28} +x_{17} x_{24} +x_{16} x_{23} +x_{14} x_{21} +x_{13} x_{20} +x_{9} x_{19} = 0
x_{16} x_{36} +x_{14} x_{35} +x_{11} x_{33} +x_{9} x_{31} +x_{8} x_{30} +x_{5} x_{28} +x_{4} x_{25} +x_{3} x_{24}
+x_{1} x_{20} = 0
x_{18} x_{36} +x_{17} x_{35} +x_{15} x_{33} +x_{13} x_{31} +x_{12} x_{30} +x_{10} x_{28} +x_{7} x_{25}
+x_{6} x_{24} +x_{2} x_{20} -6= 0
x_{13} x_{35} +x_{9} x_{32} +x_{7} x_{30} +x_{4} x_{26} +x_{2} x_{24} +x_{1} x_{21} = 0
x_{18} x_{36} +x_{17} x_{35} +x_{16} x_{34} +x_{15} x_{33} +x_{14} x_{32} +x_{12} x_{30} +x_{11} x_{29}
+x_{10} x_{28} +x_{8} x_{26} +x_{6} x_{24} +x_{5} x_{23} +x_{3} x_{21} -8= 0
x_{18} x_{35} +x_{16} x_{32} +x_{15} x_{30} +x_{11} x_{26} +x_{10} x_{24} +x_{5} x_{21} = 0
x_{10} x_{33} +x_{6} x_{30} +x_{5} x_{29} +x_{3} x_{26} +x_{2} x_{25} +x_{1} x_{22} = 0
x_{18} x_{36} +x_{17} x_{35} +x_{16} x_{34} +x_{15} x_{33} +x_{14} x_{32} +x_{13} x_{31} +x_{12} x_{30}
+x_{11} x_{29} +x_{9} x_{27} +x_{8} x_{26} +x_{7} x_{25} +x_{4} x_{22} -8= 0
x_{18} x_{33} +x_{17} x_{30} +x_{16} x_{29} +x_{14} x_{26} +x_{13} x_{25} +x_{9} x_{22} = 0
x_{13} x_{36} +x_{9} x_{34} +x_{7} x_{33} +x_{4} x_{29} +x_{2} x_{28} +x_{1} x_{23} = 0
x_{17} x_{36} +x_{14} x_{34} +x_{12} x_{33} +x_{8} x_{29} +x_{6} x_{28} +x_{3} x_{23} = 0
x_{18} x_{36} +x_{16} x_{34} +x_{15} x_{33} +x_{11} x_{29} +x_{10} x_{28} +x_{5} x_{23} -4= 0
x_{10} x_{36} +x_{6} x_{35} +x_{5} x_{34} +x_{3} x_{32} +x_{2} x_{31} +x_{1} x_{27} = 0
x_{15} x_{36} +x_{12} x_{35} +x_{11} x_{34} +x_{8} x_{32} +x_{7} x_{31} +x_{4} x_{27} = 0
x_{18} x_{36} +x_{17} x_{35} +x_{16} x_{34} +x_{14} x_{32} +x_{13} x_{31} +x_{9} x_{27} -4= 0
x_{1} x_{41} -2x_{1} x_{40} +x_{1} x_{39} +x_{1} x_{38} = 0
x_{2} x_{41} -x_{2} x_{40} +x_{2} x_{39} -x_{2} x_{38} = 0
x_{3} x_{41} -x_{3} x_{40} -x_{3} x_{39} +x_{3} x_{38} +x_{3} x_{37} = 0
x_{4} x_{42} -x_{4} x_{41} -x_{4} x_{40} +x_{4} x_{39} +x_{4} x_{38} = 0
x_{5} x_{41} -x_{5} x_{40} +x_{5} x_{38} -x_{5} x_{37} = 0
x_{6} x_{41} -x_{6} x_{39} -x_{6} x_{38} +x_{6} x_{37} = 0
x_{7} x_{42} -x_{7} x_{41} +x_{7} x_{39} -x_{7} x_{38} = 0
x_{8} x_{42} -x_{8} x_{41} -x_{8} x_{39} +x_{8} x_{38} +x_{8} x_{37} = 0
x_{9} x_{42} +x_{9} x_{40} -x_{9} x_{39} -x_{9} x_{38} = 0
x_{10} x_{41} -x_{10} x_{38} -x_{10} x_{37} = 0
x_{11} x_{42} -x_{11} x_{41} +x_{11} x_{38} -x_{11} x_{37} = 0
x_{12} x_{42} -x_{12} x_{41} +x_{12} x_{40} -x_{12} x_{39} -x_{12} x_{38} +x_{12} x_{37} = 0
x_{13} x_{42} -x_{13} x_{39} +x_{13} x_{38} = 0
x_{14} x_{42} +x_{14} x_{39} -x_{14} x_{38} -x_{14} x_{37} = 0
x_{15} x_{42} -x_{15} x_{41} +x_{15} x_{40} -x_{15} x_{38} -x_{15} x_{37} = 0
x_{16} x_{42} -x_{16} x_{38} +x_{16} x_{37} = 0
x_{17} x_{42} -x_{17} x_{40} +x_{17} x_{39} +x_{17} x_{38} -x_{17} x_{37} = 0
x_{18} x_{42} -x_{18} x_{40} +x_{18} x_{38} +x_{18} x_{37} = 0
x_{19} x_{41} -2x_{19} x_{40} +x_{19} x_{39} +x_{19} x_{38} = 0
x_{20} x_{41} -x_{20} x_{40} +x_{20} x_{39} -x_{20} x_{38} = 0
x_{21} x_{41} -x_{21} x_{40} -x_{21} x_{39} +x_{21} x_{38} +x_{21} x_{37} = 0
x_{22} x_{42} -x_{22} x_{41} -x_{22} x_{40} +x_{22} x_{39} +x_{22} x_{38} = 0
x_{23} x_{41} -x_{23} x_{40} +x_{23} x_{38} -x_{23} x_{37} = 0
x_{24} x_{41} -x_{24} x_{39} -x_{24} x_{38} +x_{24} x_{37} = 0
x_{25} x_{42} -x_{25} x_{41} +x_{25} x_{39} -x_{25} x_{38} = 0
x_{26} x_{42} -x_{26} x_{41} -x_{26} x_{39} +x_{26} x_{38} +x_{26} x_{37} = 0
x_{27} x_{42} +x_{27} x_{40} -x_{27} x_{39} -x_{27} x_{38} = 0
x_{28} x_{41} -x_{28} x_{38} -x_{28} x_{37} = 0
x_{29} x_{42} -x_{29} x_{41} +x_{29} x_{38} -x_{29} x_{37} = 0
x_{30} x_{42} -x_{30} x_{41} +x_{30} x_{40} -x_{30} x_{39} -x_{30} x_{38} +x_{30} x_{37} = 0
x_{31} x_{42} -x_{31} x_{39} +x_{31} x_{38} = 0
x_{32} x_{42} +x_{32} x_{39} -x_{32} x_{38} -x_{32} x_{37} = 0
x_{33} x_{42} -x_{33} x_{41} +x_{33} x_{40} -x_{33} x_{38} -x_{33} x_{37} = 0
x_{34} x_{42} -x_{34} x_{38} +x_{34} x_{37} = 0
x_{35} x_{42} -x_{35} x_{40} +x_{35} x_{39} +x_{35} x_{38} -x_{35} x_{37} = 0
x_{36} x_{42} -x_{36} x_{40} +x_{36} x_{38} +x_{36} x_{37} = 0
x_{1} x_{47} -2x_{1} x_{46} +x_{1} x_{45} +x_{1} x_{44} = 0
x_{2} x_{47} -x_{2} x_{46} +x_{2} x_{45} -x_{2} x_{44} = 0
x_{3} x_{47} -x_{3} x_{46} -x_{3} x_{45} +x_{3} x_{44} +x_{3} x_{43} = 0
x_{4} x_{48} -x_{4} x_{47} -x_{4} x_{46} +x_{4} x_{45} +x_{4} x_{44} = 0
x_{5} x_{47} -x_{5} x_{46} +x_{5} x_{44} -x_{5} x_{43} = 0
x_{6} x_{47} -x_{6} x_{45} -x_{6} x_{44} +x_{6} x_{43} = 0
x_{7} x_{48} -x_{7} x_{47} +x_{7} x_{45} -x_{7} x_{44} = 0
x_{8} x_{48} -x_{8} x_{47} -x_{8} x_{45} +x_{8} x_{44} +x_{8} x_{43} = 0
x_{9} x_{48} +x_{9} x_{46} -x_{9} x_{45} -x_{9} x_{44} = 0
x_{10} x_{47} -x_{10} x_{44} -x_{10} x_{43} = 0
x_{11} x_{48} -x_{11} x_{47} +x_{11} x_{44} -x_{11} x_{43} = 0
x_{12} x_{48} -x_{12} x_{47} +x_{12} x_{46} -x_{12} x_{45} -x_{12} x_{44} +x_{12} x_{43} = 0
x_{13} x_{48} -x_{13} x_{45} +x_{13} x_{44} = 0
x_{14} x_{48} +x_{14} x_{45} -x_{14} x_{44} -x_{14} x_{43} = 0
x_{15} x_{48} -x_{15} x_{47} +x_{15} x_{46} -x_{15} x_{44} -x_{15} x_{43} = 0
x_{16} x_{48} -x_{16} x_{44} +x_{16} x_{43} = 0
x_{17} x_{48} -x_{17} x_{46} +x_{17} x_{45} +x_{17} x_{44} -x_{17} x_{43} = 0
x_{18} x_{48} -x_{18} x_{46} +x_{18} x_{44} +x_{18} x_{43} = 0
x_{19} x_{47} -2x_{19} x_{46} +x_{19} x_{45} +x_{19} x_{44} = 0
x_{20} x_{47} -x_{20} x_{46} +x_{20} x_{45} -x_{20} x_{44} = 0
x_{21} x_{47} -x_{21} x_{46} -x_{21} x_{45} +x_{21} x_{44} +x_{21} x_{43} = 0
x_{22} x_{48} -x_{22} x_{47} -x_{22} x_{46} +x_{22} x_{45} +x_{22} x_{44} = 0
x_{23} x_{47} -x_{23} x_{46} +x_{23} x_{44} -x_{23} x_{43} = 0
x_{24} x_{47} -x_{24} x_{45} -x_{24} x_{44} +x_{24} x_{43} = 0
x_{25} x_{48} -x_{25} x_{47} +x_{25} x_{45} -x_{25} x_{44} = 0
x_{26} x_{48} -x_{26} x_{47} -x_{26} x_{45} +x_{26} x_{44} +x_{26} x_{43} = 0
x_{27} x_{48} +x_{27} x_{46} -x_{27} x_{45} -x_{27} x_{44} = 0
x_{28} x_{47} -x_{28} x_{44} -x_{28} x_{43} = 0
x_{29} x_{48} -x_{29} x_{47} +x_{29} x_{44} -x_{29} x_{43} = 0
x_{30} x_{48} -x_{30} x_{47} +x_{30} x_{46} -x_{30} x_{45} -x_{30} x_{44} +x_{30} x_{43} = 0
x_{31} x_{48} -x_{31} x_{45} +x_{31} x_{44} = 0
x_{32} x_{48} +x_{32} x_{45} -x_{32} x_{44} -x_{32} x_{43} = 0
x_{33} x_{48} -x_{33} x_{47} +x_{33} x_{46} -x_{33} x_{44} -x_{33} x_{43} = 0
x_{34} x_{48} -x_{34} x_{44} +x_{34} x_{43} = 0
x_{35} x_{48} -x_{35} x_{46} +x_{35} x_{45} +x_{35} x_{44} -x_{35} x_{43} = 0
x_{36} x_{48} -x_{36} x_{46} +x_{36} x_{44} +x_{36} x_{43} = 0
The above system after transformation.
3x_{41}^{2}x_{48}^{2}x_{49} -4x_{40} x_{41} x_{48}^{2}x_{49} +4x_{40}^{2}x_{48}^{2}x_{49} -4x_{39} x_{40} x_{48}^{2}x_{49}
-4x_{38} x_{40} x_{48}^{2}x_{49} +4x_{39}^{2}x_{48}^{2}x_{49} -4x_{37} x_{39} x_{48}^{2}x_{49} +4x_{38}^{2}x_{48}^{2}x_{49}
+4x_{37}^{2}x_{48}^{2}x_{49} -6x_{41} x_{42} x_{47} x_{48} x_{49} +4x_{40} x_{42} x_{47} x_{48} x_{49}
+2x_{40} x_{41} x_{47} x_{48} x_{49} -4x_{40}^{2}x_{47} x_{48} x_{49} +4x_{39} x_{40} x_{47} x_{48} x_{49}
+4x_{38} x_{40} x_{47} x_{48} x_{49} -4x_{39}^{2}x_{47} x_{48} x_{49} +4x_{37} x_{39} x_{47} x_{48} x_{49}
-4x_{38}^{2}x_{47} x_{48} x_{49} -4x_{37}^{2}x_{47} x_{48} x_{49} +4x_{41} x_{42} x_{46} x_{48} x_{49}
-8x_{40} x_{42} x_{46} x_{48} x_{49} +4x_{39} x_{42} x_{46} x_{48} x_{49} +4x_{38} x_{42} x_{46} x_{48} x_{49}
-2x_{41}^{2}x_{46} x_{48} x_{49} +4x_{40} x_{41} x_{46} x_{48} x_{49} -2x_{39} x_{41} x_{46} x_{48} x_{49}
-2x_{38} x_{41} x_{46} x_{48} x_{49} +4x_{40} x_{42} x_{45} x_{48} x_{49} -8x_{39} x_{42} x_{45} x_{48} x_{49}
+4x_{37} x_{42} x_{45} x_{48} x_{49} -2x_{40} x_{41} x_{45} x_{48} x_{49} +4x_{39} x_{41} x_{45} x_{48} x_{49}
-2x_{37} x_{41} x_{45} x_{48} x_{49} +4x_{40} x_{42} x_{44} x_{48} x_{49} -8x_{38} x_{42} x_{44} x_{48} x_{49}
-2x_{40} x_{41} x_{44} x_{48} x_{49} +4x_{38} x_{41} x_{44} x_{48} x_{49} +4x_{39} x_{42} x_{43} x_{48} x_{49}
-8x_{37} x_{42} x_{43} x_{48} x_{49} -2x_{39} x_{41} x_{43} x_{48} x_{49} +4x_{37} x_{41} x_{43} x_{48} x_{49}
+3x_{42}^{2}x_{47}^{2}x_{49} -2x_{40} x_{42} x_{47}^{2}x_{49} +3x_{40}^{2}x_{47}^{2}x_{49} -4x_{39} x_{40} x_{47}^{2}x_{49}
-4x_{38} x_{40} x_{47}^{2}x_{49} +4x_{39}^{2}x_{47}^{2}x_{49} -4x_{37} x_{39} x_{47}^{2}x_{49} +4x_{38}^{2}x_{47}^{2}x_{49}
+4x_{37}^{2}x_{47}^{2}x_{49} -4x_{42}^{2}x_{46} x_{47} x_{49} +2x_{41} x_{42} x_{46} x_{47} x_{49} +4x_{40} x_{42} x_{46} x_{47} x_{49}
-2x_{39} x_{42} x_{46} x_{47} x_{49} -2x_{38} x_{42} x_{46} x_{47} x_{49} -6x_{40} x_{41} x_{46} x_{47} x_{49}
+4x_{39} x_{41} x_{46} x_{47} x_{49} +4x_{38} x_{41} x_{46} x_{47} x_{49} +2x_{39} x_{40} x_{46} x_{47} x_{49}
+2x_{38} x_{40} x_{46} x_{47} x_{49} -4x_{39}^{2}x_{46} x_{47} x_{49} +4x_{37} x_{39} x_{46} x_{47} x_{49}
-4x_{38}^{2}x_{46} x_{47} x_{49} -4x_{37}^{2}x_{46} x_{47} x_{49} -2x_{40} x_{42} x_{45} x_{47} x_{49}
+4x_{39} x_{42} x_{45} x_{47} x_{49} -2x_{37} x_{42} x_{45} x_{47} x_{49} +4x_{40} x_{41} x_{45} x_{47} x_{49}
-8x_{39} x_{41} x_{45} x_{47} x_{49} +4x_{37} x_{41} x_{45} x_{47} x_{49} -2x_{40}^{2}x_{45} x_{47} x_{49}
+4x_{39} x_{40} x_{45} x_{47} x_{49} -2x_{37} x_{40} x_{45} x_{47} x_{49} -2x_{40} x_{42} x_{44} x_{47} x_{49}
+4x_{38} x_{42} x_{44} x_{47} x_{49} +4x_{40} x_{41} x_{44} x_{47} x_{49} -8x_{38} x_{41} x_{44} x_{47} x_{49}
-2x_{40}^{2}x_{44} x_{47} x_{49} +4x_{38} x_{40} x_{44} x_{47} x_{49} -2x_{39} x_{42} x_{43} x_{47} x_{49}
+4x_{37} x_{42} x_{43} x_{47} x_{49} +4x_{39} x_{41} x_{43} x_{47} x_{49} -8x_{37} x_{41} x_{43} x_{47} x_{49}
-2x_{39} x_{40} x_{43} x_{47} x_{49} +4x_{37} x_{40} x_{43} x_{47} x_{49} +4x_{42}^{2}x_{46}^{2}x_{49}
-4x_{41} x_{42} x_{46}^{2}x_{49} +3x_{41}^{2}x_{46}^{2}x_{49} -2x_{39} x_{41} x_{46}^{2}x_{49} -2x_{38} x_{41} x_{46}^{2}x_{49}
+3x_{39}^{2}x_{46}^{2}x_{49} -2x_{38} x_{39} x_{46}^{2}x_{49} -4x_{37} x_{39} x_{46}^{2}x_{49} +3x_{38}^{2}x_{46}^{2}x_{49}
+4x_{37}^{2}x_{46}^{2}x_{49} -4x_{42}^{2}x_{45} x_{46} x_{49} +4x_{41} x_{42} x_{45} x_{46} x_{49} -4x_{41}^{2}x_{45} x_{46} x_{49}
+2x_{40} x_{41} x_{45} x_{46} x_{49} +4x_{39} x_{41} x_{45} x_{46} x_{49} -2x_{37} x_{41} x_{45} x_{46} x_{49}
-6x_{39} x_{40} x_{45} x_{46} x_{49} +2x_{38} x_{40} x_{45} x_{46} x_{49} +4x_{37} x_{40} x_{45} x_{46} x_{49}
+4x_{38} x_{39} x_{45} x_{46} x_{49} +2x_{37} x_{39} x_{45} x_{46} x_{49} -4x_{38}^{2}x_{45} x_{46} x_{49}
-2x_{37} x_{38} x_{45} x_{46} x_{49} -4x_{37}^{2}x_{45} x_{46} x_{49} -4x_{42}^{2}x_{44} x_{46} x_{49}
+4x_{41} x_{42} x_{44} x_{46} x_{49} -4x_{41}^{2}x_{44} x_{46} x_{49} +2x_{40} x_{41} x_{44} x_{46} x_{49}
+4x_{38} x_{41} x_{44} x_{46} x_{49} +2x_{39} x_{40} x_{44} x_{46} x_{49} -6x_{38} x_{40} x_{44} x_{46} x_{49}
-4x_{39}^{2}x_{44} x_{46} x_{49} +4x_{38} x_{39} x_{44} x_{46} x_{49} +4x_{37} x_{39} x_{44} x_{46} x_{49}
-4x_{37}^{2}x_{44} x_{46} x_{49} -2x_{39} x_{41} x_{43} x_{46} x_{49} +4x_{37} x_{41} x_{43} x_{46} x_{49}
+4x_{39} x_{40} x_{43} x_{46} x_{49} -8x_{37} x_{40} x_{43} x_{46} x_{49} -2x_{39}^{2}x_{43} x_{46} x_{49}
-2x_{38} x_{39} x_{43} x_{46} x_{49} +4x_{37} x_{39} x_{43} x_{46} x_{49} +4x_{37} x_{38} x_{43} x_{46} x_{49}
+4x_{42}^{2}x_{45}^{2}x_{49} -4x_{41} x_{42} x_{45}^{2}x_{49} +4x_{41}^{2}x_{45}^{2}x_{49} -4x_{40} x_{41} x_{45}^{2}x_{49}
+3x_{40}^{2}x_{45}^{2}x_{49} -4x_{38} x_{40} x_{45}^{2}x_{49} -2x_{37} x_{40} x_{45}^{2}x_{49} +4x_{38}^{2}x_{45}^{2}x_{49}
+3x_{37}^{2}x_{45}^{2}x_{49} -2x_{40}^{2}x_{44} x_{45} x_{49} +4x_{39} x_{40} x_{44} x_{45} x_{49} +4x_{38} x_{40} x_{44} x_{45} x_{49}
-2x_{37} x_{40} x_{44} x_{45} x_{49} -8x_{38} x_{39} x_{44} x_{45} x_{49} +4x_{37} x_{38} x_{44} x_{45} x_{49}
-4x_{42}^{2}x_{43} x_{45} x_{49} +4x_{41} x_{42} x_{43} x_{45} x_{49} -4x_{41}^{2}x_{43} x_{45} x_{49}
+4x_{40} x_{41} x_{43} x_{45} x_{49} -4x_{40}^{2}x_{43} x_{45} x_{49} +2x_{39} x_{40} x_{43} x_{45} x_{49}
+4x_{38} x_{40} x_{43} x_{45} x_{49} +4x_{37} x_{40} x_{43} x_{45} x_{49} -6x_{37} x_{39} x_{43} x_{45} x_{49}
-4x_{38}^{2}x_{43} x_{45} x_{49} +4x_{42}^{2}x_{44}^{2}x_{49} -4x_{41} x_{42} x_{44}^{2}x_{49} +4x_{41}^{2}x_{44}^{2}x_{49}
-4x_{40} x_{41} x_{44}^{2}x_{49} +3x_{40}^{2}x_{44}^{2}x_{49} -4x_{39} x_{40} x_{44}^{2}x_{49} +4x_{39}^{2}x_{44}^{2}x_{49}
-4x_{37} x_{39} x_{44}^{2}x_{49} +4x_{37}^{2}x_{44}^{2}x_{49} -2x_{39} x_{40} x_{43} x_{44} x_{49} +4x_{37} x_{40} x_{43} x_{44} x_{49}
+4x_{38} x_{39} x_{43} x_{44} x_{49} -8x_{37} x_{38} x_{43} x_{44} x_{49} +4x_{42}^{2}x_{43}^{2}x_{49}
-4x_{41} x_{42} x_{43}^{2}x_{49} +4x_{41}^{2}x_{43}^{2}x_{49} -4x_{40} x_{41} x_{43}^{2}x_{49} +4x_{40}^{2}x_{43}^{2}x_{49}
-4x_{39} x_{40} x_{43}^{2}x_{49} -4x_{38} x_{40} x_{43}^{2}x_{49} +3x_{39}^{2}x_{43}^{2}x_{49} +4x_{38}^{2}x_{43}^{2}x_{49}
-1= 0
x_{18} x_{36} +x_{17} x_{35} +x_{16} x_{34} +x_{15} x_{33} +x_{14} x_{32} +x_{13} x_{31} +x_{12} x_{30}
+x_{11} x_{29} +x_{10} x_{28} +x_{9} x_{27} +x_{8} x_{26} +x_{7} x_{25} +x_{6} x_{24} +x_{5} x_{23} +x_{4} x_{22}
+x_{3} x_{21} +x_{2} x_{20} +x_{1} x_{19} -12= 0
x_{18} x_{34} +x_{17} x_{32} +x_{15} x_{29} +x_{13} x_{27} +x_{12} x_{26} +x_{10} x_{23} +x_{7} x_{22}
+x_{6} x_{21} +x_{2} x_{19} = 0
x_{17} x_{31} +x_{14} x_{27} +x_{12} x_{25} +x_{8} x_{22} +x_{6} x_{20} +x_{3} x_{19} = 0
x_{15} x_{28} +x_{12} x_{24} +x_{11} x_{23} +x_{8} x_{21} +x_{7} x_{20} +x_{4} x_{19} = 0
x_{18} x_{31} +x_{16} x_{27} +x_{15} x_{25} +x_{11} x_{22} +x_{10} x_{20} +x_{5} x_{19} = 0
x_{18} x_{28} +x_{17} x_{24} +x_{16} x_{23} +x_{14} x_{21} +x_{13} x_{20} +x_{9} x_{19} = 0
x_{16} x_{36} +x_{14} x_{35} +x_{11} x_{33} +x_{9} x_{31} +x_{8} x_{30} +x_{5} x_{28} +x_{4} x_{25} +x_{3} x_{24}
+x_{1} x_{20} = 0
x_{18} x_{36} +x_{17} x_{35} +x_{15} x_{33} +x_{13} x_{31} +x_{12} x_{30} +x_{10} x_{28} +x_{7} x_{25}
+x_{6} x_{24} +x_{2} x_{20} -6= 0
x_{13} x_{35} +x_{9} x_{32} +x_{7} x_{30} +x_{4} x_{26} +x_{2} x_{24} +x_{1} x_{21} = 0
x_{18} x_{36} +x_{17} x_{35} +x_{16} x_{34} +x_{15} x_{33} +x_{14} x_{32} +x_{12} x_{30} +x_{11} x_{29}
+x_{10} x_{28} +x_{8} x_{26} +x_{6} x_{24} +x_{5} x_{23} +x_{3} x_{21} -8= 0
x_{18} x_{35} +x_{16} x_{32} +x_{15} x_{30} +x_{11} x_{26} +x_{10} x_{24} +x_{5} x_{21} = 0
x_{10} x_{33} +x_{6} x_{30} +x_{5} x_{29} +x_{3} x_{26} +x_{2} x_{25} +x_{1} x_{22} = 0
x_{18} x_{36} +x_{17} x_{35} +x_{16} x_{34} +x_{15} x_{33} +x_{14} x_{32} +x_{13} x_{31} +x_{12} x_{30}
+x_{11} x_{29} +x_{9} x_{27} +x_{8} x_{26} +x_{7} x_{25} +x_{4} x_{22} -8= 0
x_{18} x_{33} +x_{17} x_{30} +x_{16} x_{29} +x_{14} x_{26} +x_{13} x_{25} +x_{9} x_{22} = 0
x_{13} x_{36} +x_{9} x_{34} +x_{7} x_{33} +x_{4} x_{29} +x_{2} x_{28} +x_{1} x_{23} = 0
x_{17} x_{36} +x_{14} x_{34} +x_{12} x_{33} +x_{8} x_{29} +x_{6} x_{28} +x_{3} x_{23} = 0
x_{18} x_{36} +x_{16} x_{34} +x_{15} x_{33} +x_{11} x_{29} +x_{10} x_{28} +x_{5} x_{23} -4= 0
x_{10} x_{36} +x_{6} x_{35} +x_{5} x_{34} +x_{3} x_{32} +x_{2} x_{31} +x_{1} x_{27} = 0
x_{15} x_{36} +x_{12} x_{35} +x_{11} x_{34} +x_{8} x_{32} +x_{7} x_{31} +x_{4} x_{27} = 0
x_{18} x_{36} +x_{17} x_{35} +x_{16} x_{34} +x_{14} x_{32} +x_{13} x_{31} +x_{9} x_{27} -4= 0
x_{1} x_{41} -2x_{1} x_{40} +x_{1} x_{39} +x_{1} x_{38} = 0
x_{2} x_{41} -x_{2} x_{40} +x_{2} x_{39} -x_{2} x_{38} = 0
x_{3} x_{41} -x_{3} x_{40} -x_{3} x_{39} +x_{3} x_{38} +x_{3} x_{37} = 0
x_{4} x_{42} -x_{4} x_{41} -x_{4} x_{40} +x_{4} x_{39} +x_{4} x_{38} = 0
x_{5} x_{41} -x_{5} x_{40} +x_{5} x_{38} -x_{5} x_{37} = 0
x_{6} x_{41} -x_{6} x_{39} -x_{6} x_{38} +x_{6} x_{37} = 0
x_{7} x_{42} -x_{7} x_{41} +x_{7} x_{39} -x_{7} x_{38} = 0
x_{8} x_{42} -x_{8} x_{41} -x_{8} x_{39} +x_{8} x_{38} +x_{8} x_{37} = 0
x_{9} x_{42} +x_{9} x_{40} -x_{9} x_{39} -x_{9} x_{38} = 0
x_{10} x_{41} -x_{10} x_{38} -x_{10} x_{37} = 0
x_{11} x_{42} -x_{11} x_{41} +x_{11} x_{38} -x_{11} x_{37} = 0
x_{12} x_{42} -x_{12} x_{41} +x_{12} x_{40} -x_{12} x_{39} -x_{12} x_{38} +x_{12} x_{37} = 0
x_{13} x_{42} -x_{13} x_{39} +x_{13} x_{38} = 0
x_{14} x_{42} +x_{14} x_{39} -x_{14} x_{38} -x_{14} x_{37} = 0
x_{15} x_{42} -x_{15} x_{41} +x_{15} x_{40} -x_{15} x_{38} -x_{15} x_{37} = 0
x_{16} x_{42} -x_{16} x_{38} +x_{16} x_{37} = 0
x_{17} x_{42} -x_{17} x_{40} +x_{17} x_{39} +x_{17} x_{38} -x_{17} x_{37} = 0
x_{18} x_{42} -x_{18} x_{40} +x_{18} x_{38} +x_{18} x_{37} = 0
x_{19} x_{41} -2x_{19} x_{40} +x_{19} x_{39} +x_{19} x_{38} = 0
x_{20} x_{41} -x_{20} x_{40} +x_{20} x_{39} -x_{20} x_{38} = 0
x_{21} x_{41} -x_{21} x_{40} -x_{21} x_{39} +x_{21} x_{38} +x_{21} x_{37} = 0
x_{22} x_{42} -x_{22} x_{41} -x_{22} x_{40} +x_{22} x_{39} +x_{22} x_{38} = 0
x_{23} x_{41} -x_{23} x_{40} +x_{23} x_{38} -x_{23} x_{37} = 0
x_{24} x_{41} -x_{24} x_{39} -x_{24} x_{38} +x_{24} x_{37} = 0
x_{25} x_{42} -x_{25} x_{41} +x_{25} x_{39} -x_{25} x_{38} = 0
x_{26} x_{42} -x_{26} x_{41} -x_{26} x_{39} +x_{26} x_{38} +x_{26} x_{37} = 0
x_{27} x_{42} +x_{27} x_{40} -x_{27} x_{39} -x_{27} x_{38} = 0
x_{28} x_{41} -x_{28} x_{38} -x_{28} x_{37} = 0
x_{29} x_{42} -x_{29} x_{41} +x_{29} x_{38} -x_{29} x_{37} = 0
x_{30} x_{42} -x_{30} x_{41} +x_{30} x_{40} -x_{30} x_{39} -x_{30} x_{38} +x_{30} x_{37} = 0
x_{31} x_{42} -x_{31} x_{39} +x_{31} x_{38} = 0
x_{32} x_{42} +x_{32} x_{39} -x_{32} x_{38} -x_{32} x_{37} = 0
x_{33} x_{42} -x_{33} x_{41} +x_{33} x_{40} -x_{33} x_{38} -x_{33} x_{37} = 0
x_{34} x_{42} -x_{34} x_{38} +x_{34} x_{37} = 0
x_{35} x_{42} -x_{35} x_{40} +x_{35} x_{39} +x_{35} x_{38} -x_{35} x_{37} = 0
x_{36} x_{42} -x_{36} x_{40} +x_{36} x_{38} +x_{36} x_{37} = 0
x_{1} x_{47} -2x_{1} x_{46} +x_{1} x_{45} +x_{1} x_{44} = 0
x_{2} x_{47} -x_{2} x_{46} +x_{2} x_{45} -x_{2} x_{44} = 0
x_{3} x_{47} -x_{3} x_{46} -x_{3} x_{45} +x_{3} x_{44} +x_{3} x_{43} = 0
x_{4} x_{48} -x_{4} x_{47} -x_{4} x_{46} +x_{4} x_{45} +x_{4} x_{44} = 0
x_{5} x_{47} -x_{5} x_{46} +x_{5} x_{44} -x_{5} x_{43} = 0
x_{6} x_{47} -x_{6} x_{45} -x_{6} x_{44} +x_{6} x_{43} = 0
x_{7} x_{48} -x_{7} x_{47} +x_{7} x_{45} -x_{7} x_{44} = 0
x_{8} x_{48} -x_{8} x_{47} -x_{8} x_{45} +x_{8} x_{44} +x_{8} x_{43} = 0
x_{9} x_{48} +x_{9} x_{46} -x_{9} x_{45} -x_{9} x_{44} = 0
x_{10} x_{47} -x_{10} x_{44} -x_{10} x_{43} = 0
x_{11} x_{48} -x_{11} x_{47} +x_{11} x_{44} -x_{11} x_{43} = 0
x_{12} x_{48} -x_{12} x_{47} +x_{12} x_{46} -x_{12} x_{45} -x_{12} x_{44} +x_{12} x_{43} = 0
x_{13} x_{48} -x_{13} x_{45} +x_{13} x_{44} = 0
x_{14} x_{48} +x_{14} x_{45} -x_{14} x_{44} -x_{14} x_{43} = 0
x_{15} x_{48} -x_{15} x_{47} +x_{15} x_{46} -x_{15} x_{44} -x_{15} x_{43} = 0
x_{16} x_{48} -x_{16} x_{44} +x_{16} x_{43} = 0
x_{17} x_{48} -x_{17} x_{46} +x_{17} x_{45} +x_{17} x_{44} -x_{17} x_{43} = 0
x_{18} x_{48} -x_{18} x_{46} +x_{18} x_{44} +x_{18} x_{43} = 0
x_{19} x_{47} -2x_{19} x_{46} +x_{19} x_{45} +x_{19} x_{44} = 0
x_{20} x_{47} -x_{20} x_{46} +x_{20} x_{45} -x_{20} x_{44} = 0
x_{21} x_{47} -x_{21} x_{46} -x_{21} x_{45} +x_{21} x_{44} +x_{21} x_{43} = 0
x_{22} x_{48} -x_{22} x_{47} -x_{22} x_{46} +x_{22} x_{45} +x_{22} x_{44} = 0
x_{23} x_{47} -x_{23} x_{46} +x_{23} x_{44} -x_{23} x_{43} = 0
x_{24} x_{47} -x_{24} x_{45} -x_{24} x_{44} +x_{24} x_{43} = 0
x_{25} x_{48} -x_{25} x_{47} +x_{25} x_{45} -x_{25} x_{44} = 0
x_{26} x_{48} -x_{26} x_{47} -x_{26} x_{45} +x_{26} x_{44} +x_{26} x_{43} = 0
x_{27} x_{48} +x_{27} x_{46} -x_{27} x_{45} -x_{27} x_{44} = 0
x_{28} x_{47} -x_{28} x_{44} -x_{28} x_{43} = 0
x_{29} x_{48} -x_{29} x_{47} +x_{29} x_{44} -x_{29} x_{43} = 0
x_{30} x_{48} -x_{30} x_{47} +x_{30} x_{46} -x_{30} x_{45} -x_{30} x_{44} +x_{30} x_{43} = 0
x_{31} x_{48} -x_{31} x_{45} +x_{31} x_{44} = 0
x_{32} x_{48} +x_{32} x_{45} -x_{32} x_{44} -x_{32} x_{43} = 0
x_{33} x_{48} -x_{33} x_{47} +x_{33} x_{46} -x_{33} x_{44} -x_{33} x_{43} = 0
x_{34} x_{48} -x_{34} x_{44} +x_{34} x_{43} = 0
x_{35} x_{48} -x_{35} x_{46} +x_{35} x_{45} +x_{35} x_{44} -x_{35} x_{43} = 0
x_{36} x_{48} -x_{36} x_{46} +x_{36} x_{44} +x_{36} x_{43} = 0
For the calculator:
(DynkinType =A^{12}_1; ElementsCartan =((4, 6, 8, 12, 8, 4)); generators =(x_{1} g_{-4}+x_{2} g_{-8}+x_{3} g_{-9}+x_{4} g_{-10}+x_{5} g_{-12}+x_{6} g_{-13}+x_{7} g_{-14}+x_{8} g_{-15}+x_{9} g_{-16}+x_{10} g_{-17}+x_{11} g_{-18}+x_{12} g_{-19}+x_{13} g_{-20}+x_{14} g_{-21}+x_{15} g_{-22}+x_{16} g_{-24}+x_{17} g_{-25}+x_{18} g_{-27}, x_{36} g_{27}+x_{35} g_{25}+x_{34} g_{24}+x_{33} g_{22}+x_{32} g_{21}+x_{31} g_{20}+x_{30} g_{19}+x_{29} g_{18}+x_{28} g_{17}+x_{27} g_{16}+x_{26} g_{15}+x_{25} g_{14}+x_{24} g_{13}+x_{23} g_{12}+x_{22} g_{10}+x_{21} g_{9}+x_{20} g_{8}+x_{19} g_{4}) );
FindOneSolutionSerreLikePolynomialSystem{}( 3x_{41}^{2}x_{48}^{2}x_{49} -4x_{40} x_{41} x_{48}^{2}x_{49} +4x_{40}^{2}x_{48}^{2}x_{49} -4x_{39} x_{40} x_{48}^{2}x_{49} -4x_{38} x_{40} x_{48}^{2}x_{49} +4x_{39}^{2}x_{48}^{2}x_{49} -4x_{37} x_{39} x_{48}^{2}x_{49} +4x_{38}^{2}x_{48}^{2}x_{49} +4x_{37}^{2}x_{48}^{2}x_{49} -6x_{41} x_{42} x_{47} x_{48} x_{49} +4x_{40} x_{42} x_{47} x_{48} x_{49} +2x_{40} x_{41} x_{47} x_{48} x_{49} -4x_{40}^{2}x_{47} x_{48} x_{49} +4x_{39} x_{40} x_{47} x_{48} x_{49} +4x_{38} x_{40} x_{47} x_{48} x_{49} -4x_{39}^{2}x_{47} x_{48} x_{49} +4x_{37} x_{39} x_{47} x_{48} x_{49} -4x_{38}^{2}x_{47} x_{48} x_{49} -4x_{37}^{2}x_{47} x_{48} x_{49} +4x_{41} x_{42} x_{46} x_{48} x_{49} -8x_{40} x_{42} x_{46} x_{48} x_{49} +4x_{39} x_{42} x_{46} x_{48} x_{49} +4x_{38} x_{42} x_{46} x_{48} x_{49} -2x_{41}^{2}x_{46} x_{48} x_{49} +4x_{40} x_{41} x_{46} x_{48} x_{49} -2x_{39} x_{41} x_{46} x_{48} x_{49} -2x_{38} x_{41} x_{46} x_{48} x_{49} +4x_{40} x_{42} x_{45} x_{48} x_{49} -8x_{39} x_{42} x_{45} x_{48} x_{49} +4x_{37} x_{42} x_{45} x_{48} x_{49} -2x_{40} x_{41} x_{45} x_{48} x_{49} +4x_{39} x_{41} x_{45} x_{48} x_{49} -2x_{37} x_{41} x_{45} x_{48} x_{49} +4x_{40} x_{42} x_{44} x_{48} x_{49} -8x_{38} x_{42} x_{44} x_{48} x_{49} -2x_{40} x_{41} x_{44} x_{48} x_{49} +4x_{38} x_{41} x_{44} x_{48} x_{49} +4x_{39} x_{42} x_{43} x_{48} x_{49} -8x_{37} x_{42} x_{43} x_{48} x_{49} -2x_{39} x_{41} x_{43} x_{48} x_{49} +4x_{37} x_{41} x_{43} x_{48} x_{49} +3x_{42}^{2}x_{47}^{2}x_{49} -2x_{40} x_{42} x_{47}^{2}x_{49} +3x_{40}^{2}x_{47}^{2}x_{49} -4x_{39} x_{40} x_{47}^{2}x_{49} -4x_{38} x_{40} x_{47}^{2}x_{49} +4x_{39}^{2}x_{47}^{2}x_{49} -4x_{37} x_{39} x_{47}^{2}x_{49} +4x_{38}^{2}x_{47}^{2}x_{49} +4x_{37}^{2}x_{47}^{2}x_{49} -4x_{42}^{2}x_{46} x_{47} x_{49} +2x_{41} x_{42} x_{46} x_{47} x_{49} +4x_{40} x_{42} x_{46} x_{47} x_{49} -2x_{39} x_{42} x_{46} x_{47} x_{49} -2x_{38} x_{42} x_{46} x_{47} x_{49} -6x_{40} x_{41} x_{46} x_{47} x_{49} +4x_{39} x_{41} x_{46} x_{47} x_{49} +4x_{38} x_{41} x_{46} x_{47} x_{49} +2x_{39} x_{40} x_{46} x_{47} x_{49} +2x_{38} x_{40} x_{46} x_{47} x_{49} -4x_{39}^{2}x_{46} x_{47} x_{49} +4x_{37} x_{39} x_{46} x_{47} x_{49} -4x_{38}^{2}x_{46} x_{47} x_{49} -4x_{37}^{2}x_{46} x_{47} x_{49} -2x_{40} x_{42} x_{45} x_{47} x_{49} +4x_{39} x_{42} x_{45} x_{47} x_{49} -2x_{37} x_{42} x_{45} x_{47} x_{49} +4x_{40} x_{41} x_{45} x_{47} x_{49} -8x_{39} x_{41} x_{45} x_{47} x_{49} +4x_{37} x_{41} x_{45} x_{47} x_{49} -2x_{40}^{2}x_{45} x_{47} x_{49} +4x_{39} x_{40} x_{45} x_{47} x_{49} -2x_{37} x_{40} x_{45} x_{47} x_{49} -2x_{40} x_{42} x_{44} x_{47} x_{49} +4x_{38} x_{42} x_{44} x_{47} x_{49} +4x_{40} x_{41} x_{44} x_{47} x_{49} -8x_{38} x_{41} x_{44} x_{47} x_{49} -2x_{40}^{2}x_{44} x_{47} x_{49} +4x_{38} x_{40} x_{44} x_{47} x_{49} -2x_{39} x_{42} x_{43} x_{47} x_{49} +4x_{37} x_{42} x_{43} x_{47} x_{49} +4x_{39} x_{41} x_{43} x_{47} x_{49} -8x_{37} x_{41} x_{43} x_{47} x_{49} -2x_{39} x_{40} x_{43} x_{47} x_{49} +4x_{37} x_{40} x_{43} x_{47} x_{49} +4x_{42}^{2}x_{46}^{2}x_{49} -4x_{41} x_{42} x_{46}^{2}x_{49} +3x_{41}^{2}x_{46}^{2}x_{49} -2x_{39} x_{41} x_{46}^{2}x_{49} -2x_{38} x_{41} x_{46}^{2}x_{49} +3x_{39}^{2}x_{46}^{2}x_{49} -2x_{38} x_{39} x_{46}^{2}x_{49} -4x_{37} x_{39} x_{46}^{2}x_{49} +3x_{38}^{2}x_{46}^{2}x_{49} +4x_{37}^{2}x_{46}^{2}x_{49} -4x_{42}^{2}x_{45} x_{46} x_{49} +4x_{41} x_{42} x_{45} x_{46} x_{49} -4x_{41}^{2}x_{45} x_{46} x_{49} +2x_{40} x_{41} x_{45} x_{46} x_{49} +4x_{39} x_{41} x_{45} x_{46} x_{49} -2x_{37} x_{41} x_{45} x_{46} x_{49} -6x_{39} x_{40} x_{45} x_{46} x_{49} +2x_{38} x_{40} x_{45} x_{46} x_{49} +4x_{37} x_{40} x_{45} x_{46} x_{49} +4x_{38} x_{39} x_{45} x_{46} x_{49} +2x_{37} x_{39} x_{45} x_{46} x_{49} -4x_{38}^{2}x_{45} x_{46} x_{49} -2x_{37} x_{38} x_{45} x_{46} x_{49} -4x_{37}^{2}x_{45} x_{46} x_{49} -4x_{42}^{2}x_{44} x_{46} x_{49} +4x_{41} x_{42} x_{44} x_{46} x_{49} -4x_{41}^{2}x_{44} x_{46} x_{49} +2x_{40} x_{41} x_{44} x_{46} x_{49} +4x_{38} x_{41} x_{44} x_{46} x_{49} +2x_{39} x_{40} x_{44} x_{46} x_{49} -6x_{38} x_{40} x_{44} x_{46} x_{49} -4x_{39}^{2}x_{44} x_{46} x_{49} +4x_{38} x_{39} x_{44} x_{46} x_{49} +4x_{37} x_{39} x_{44} x_{46} x_{49} -4x_{37}^{2}x_{44} x_{46} x_{49} -2x_{39} x_{41} x_{43} x_{46} x_{49} +4x_{37} x_{41} x_{43} x_{46} x_{49} +4x_{39} x_{40} x_{43} x_{46} x_{49} -8x_{37} x_{40} x_{43} x_{46} x_{49} -2x_{39}^{2}x_{43} x_{46} x_{49} -2x_{38} x_{39} x_{43} x_{46} x_{49} +4x_{37} x_{39} x_{43} x_{46} x_{49} +4x_{37} x_{38} x_{43} x_{46} x_{49} +4x_{42}^{2}x_{45}^{2}x_{49} -4x_{41} x_{42} x_{45}^{2}x_{49} +4x_{41}^{2}x_{45}^{2}x_{49} -4x_{40} x_{41} x_{45}^{2}x_{49} +3x_{40}^{2}x_{45}^{2}x_{49} -4x_{38} x_{40} x_{45}^{2}x_{49} -2x_{37} x_{40} x_{45}^{2}x_{49} +4x_{38}^{2}x_{45}^{2}x_{49} +3x_{37}^{2}x_{45}^{2}x_{49} -2x_{40}^{2}x_{44} x_{45} x_{49} +4x_{39} x_{40} x_{44} x_{45} x_{49} +4x_{38} x_{40} x_{44} x_{45} x_{49} -2x_{37} x_{40} x_{44} x_{45} x_{49} -8x_{38} x_{39} x_{44} x_{45} x_{49} +4x_{37} x_{38} x_{44} x_{45} x_{49} -4x_{42}^{2}x_{43} x_{45} x_{49} +4x_{41} x_{42} x_{43} x_{45} x_{49} -4x_{41}^{2}x_{43} x_{45} x_{49} +4x_{40} x_{41} x_{43} x_{45} x_{49} -4x_{40}^{2}x_{43} x_{45} x_{49} +2x_{39} x_{40} x_{43} x_{45} x_{49} +4x_{38} x_{40} x_{43} x_{45} x_{49} +4x_{37} x_{40} x_{43} x_{45} x_{49} -6x_{37} x_{39} x_{43} x_{45} x_{49} -4x_{38}^{2}x_{43} x_{45} x_{49} +4x_{42}^{2}x_{44}^{2}x_{49} -4x_{41} x_{42} x_{44}^{2}x_{49} +4x_{41}^{2}x_{44}^{2}x_{49} -4x_{40} x_{41} x_{44}^{2}x_{49} +3x_{40}^{2}x_{44}^{2}x_{49} -4x_{39} x_{40} x_{44}^{2}x_{49} +4x_{39}^{2}x_{44}^{2}x_{49} -4x_{37} x_{39} x_{44}^{2}x_{49} +4x_{37}^{2}x_{44}^{2}x_{49} -2x_{39} x_{40} x_{43} x_{44} x_{49} +4x_{37} x_{40} x_{43} x_{44} x_{49} +4x_{38} x_{39} x_{43} x_{44} x_{49} -8x_{37} x_{38} x_{43} x_{44} x_{49} +4x_{42}^{2}x_{43}^{2}x_{49} -4x_{41} x_{42} x_{43}^{2}x_{49} +4x_{41}^{2}x_{43}^{2}x_{49} -4x_{40} x_{41} x_{43}^{2}x_{49} +4x_{40}^{2}x_{43}^{2}x_{49} -4x_{39} x_{40} x_{43}^{2}x_{49} -4x_{38} x_{40} x_{43}^{2}x_{49} +3x_{39}^{2}x_{43}^{2}x_{49} +4x_{38}^{2}x_{43}^{2}x_{49} -1, x_{18} x_{36} +x_{17} x_{35} +x_{16} x_{34} +x_{15} x_{33} +x_{14} x_{32} +x_{13} x_{31} +x_{12} x_{30} +x_{11} x_{29} +x_{10} x_{28} +x_{9} x_{27} +x_{8} x_{26} +x_{7} x_{25} +x_{6} x_{24} +x_{5} x_{23} +x_{4} x_{22} +x_{3} x_{21} +x_{2} x_{20} +x_{1} x_{19} -12, x_{18} x_{34} +x_{17} x_{32} +x_{15} x_{29} +x_{13} x_{27} +x_{12} x_{26} +x_{10} x_{23} +x_{7} x_{22} +x_{6} x_{21} +x_{2} x_{19} , x_{17} x_{31} +x_{14} x_{27} +x_{12} x_{25} +x_{8} x_{22} +x_{6} x_{20} +x_{3} x_{19} , x_{15} x_{28} +x_{12} x_{24} +x_{11} x_{23} +x_{8} x_{21} +x_{7} x_{20} +x_{4} x_{19} , x_{18} x_{31} +x_{16} x_{27} +x_{15} x_{25} +x_{11} x_{22} +x_{10} x_{20} +x_{5} x_{19} , x_{18} x_{28} +x_{17} x_{24} +x_{16} x_{23} +x_{14} x_{21} +x_{13} x_{20} +x_{9} x_{19} , x_{16} x_{36} +x_{14} x_{35} +x_{11} x_{33} +x_{9} x_{31} +x_{8} x_{30} +x_{5} x_{28} +x_{4} x_{25} +x_{3} x_{24} +x_{1} x_{20} , x_{18} x_{36} +x_{17} x_{35} +x_{15} x_{33} +x_{13} x_{31} +x_{12} x_{30} +x_{10} x_{28} +x_{7} x_{25} +x_{6} x_{24} +x_{2} x_{20} -6, x_{13} x_{35} +x_{9} x_{32} +x_{7} x_{30} +x_{4} x_{26} +x_{2} x_{24} +x_{1} x_{21} , x_{18} x_{36} +x_{17} x_{35} +x_{16} x_{34} +x_{15} x_{33} +x_{14} x_{32} +x_{12} x_{30} +x_{11} x_{29} +x_{10} x_{28} +x_{8} x_{26} +x_{6} x_{24} +x_{5} x_{23} +x_{3} x_{21} -8, x_{18} x_{35} +x_{16} x_{32} +x_{15} x_{30} +x_{11} x_{26} +x_{10} x_{24} +x_{5} x_{21} , x_{10} x_{33} +x_{6} x_{30} +x_{5} x_{29} +x_{3} x_{26} +x_{2} x_{25} +x_{1} x_{22} , x_{18} x_{36} +x_{17} x_{35} +x_{16} x_{34} +x_{15} x_{33} +x_{14} x_{32} +x_{13} x_{31} +x_{12} x_{30} +x_{11} x_{29} +x_{9} x_{27} +x_{8} x_{26} +x_{7} x_{25} +x_{4} x_{22} -8, x_{18} x_{33} +x_{17} x_{30} +x_{16} x_{29} +x_{14} x_{26} +x_{13} x_{25} +x_{9} x_{22} , x_{13} x_{36} +x_{9} x_{34} +x_{7} x_{33} +x_{4} x_{29} +x_{2} x_{28} +x_{1} x_{23} , x_{17} x_{36} +x_{14} x_{34} +x_{12} x_{33} +x_{8} x_{29} +x_{6} x_{28} +x_{3} x_{23} , x_{18} x_{36} +x_{16} x_{34} +x_{15} x_{33} +x_{11} x_{29} +x_{10} x_{28} +x_{5} x_{23} -4, x_{10} x_{36} +x_{6} x_{35} +x_{5} x_{34} +x_{3} x_{32} +x_{2} x_{31} +x_{1} x_{27} , x_{15} x_{36} +x_{12} x_{35} +x_{11} x_{34} +x_{8} x_{32} +x_{7} x_{31} +x_{4} x_{27} , x_{18} x_{36} +x_{17} x_{35} +x_{16} x_{34} +x_{14} x_{32} +x_{13} x_{31} +x_{9} x_{27} -4, x_{1} x_{41} -2x_{1} x_{40} +x_{1} x_{39} +x_{1} x_{38} , x_{2} x_{41} -x_{2} x_{40} +x_{2} x_{39} -x_{2} x_{38} , x_{3} x_{41} -x_{3} x_{40} -x_{3} x_{39} +x_{3} x_{38} +x_{3} x_{37} , x_{4} x_{42} -x_{4} x_{41} -x_{4} x_{40} +x_{4} x_{39} +x_{4} x_{38} , x_{5} x_{41} -x_{5} x_{40} +x_{5} x_{38} -x_{5} x_{37} , x_{6} x_{41} -x_{6} x_{39} -x_{6} x_{38} +x_{6} x_{37} , x_{7} x_{42} -x_{7} x_{41} +x_{7} x_{39} -x_{7} x_{38} , x_{8} x_{42} -x_{8} x_{41} -x_{8} x_{39} +x_{8} x_{38} +x_{8} x_{37} , x_{9} x_{42} +x_{9} x_{40} -x_{9} x_{39} -x_{9} x_{38} , x_{10} x_{41} -x_{10} x_{38} -x_{10} x_{37} , x_{11} x_{42} -x_{11} x_{41} +x_{11} x_{38} -x_{11} x_{37} , x_{12} x_{42} -x_{12} x_{41} +x_{12} x_{40} -x_{12} x_{39} -x_{12} x_{38} +x_{12} x_{37} , x_{13} x_{42} -x_{13} x_{39} +x_{13} x_{38} , x_{14} x_{42} +x_{14} x_{39} -x_{14} x_{38} -x_{14} x_{37} , x_{15} x_{42} -x_{15} x_{41} +x_{15} x_{40} -x_{15} x_{38} -x_{15} x_{37} , x_{16} x_{42} -x_{16} x_{38} +x_{16} x_{37} , x_{17} x_{42} -x_{17} x_{40} +x_{17} x_{39} +x_{17} x_{38} -x_{17} x_{37} , x_{18} x_{42} -x_{18} x_{40} +x_{18} x_{38} +x_{18} x_{37} , x_{19} x_{41} -2x_{19} x_{40} +x_{19} x_{39} +x_{19} x_{38} , x_{20} x_{41} -x_{20} x_{40} +x_{20} x_{39} -x_{20} x_{38} , x_{21} x_{41} -x_{21} x_{40} -x_{21} x_{39} +x_{21} x_{38} +x_{21} x_{37} , x_{22} x_{42} -x_{22} x_{41} -x_{22} x_{40} +x_{22} x_{39} +x_{22} x_{38} , x_{23} x_{41} -x_{23} x_{40} +x_{23} x_{38} -x_{23} x_{37} , x_{24} x_{41} -x_{24} x_{39} -x_{24} x_{38} +x_{24} x_{37} , x_{25} x_{42} -x_{25} x_{41} +x_{25} x_{39} -x_{25} x_{38} , x_{26} x_{42} -x_{26} x_{41} -x_{26} x_{39} +x_{26} x_{38} +x_{26} x_{37} , x_{27} x_{42} +x_{27} x_{40} -x_{27} x_{39} -x_{27} x_{38} , x_{28} x_{41} -x_{28} x_{38} -x_{28} x_{37} , x_{29} x_{42} -x_{29} x_{41} +x_{29} x_{38} -x_{29} x_{37} , x_{30} x_{42} -x_{30} x_{41} +x_{30} x_{40} -x_{30} x_{39} -x_{30} x_{38} +x_{30} x_{37} , x_{31} x_{42} -x_{31} x_{39} +x_{31} x_{38} , x_{32} x_{42} +x_{32} x_{39} -x_{32} x_{38} -x_{32} x_{37} , x_{33} x_{42} -x_{33} x_{41} +x_{33} x_{40} -x_{33} x_{38} -x_{33} x_{37} , x_{34} x_{42} -x_{34} x_{38} +x_{34} x_{37} , x_{35} x_{42} -x_{35} x_{40} +x_{35} x_{39} +x_{35} x_{38} -x_{35} x_{37} , x_{36} x_{42} -x_{36} x_{40} +x_{36} x_{38} +x_{36} x_{37} , x_{1} x_{47} -2x_{1} x_{46} +x_{1} x_{45} +x_{1} x_{44} , x_{2} x_{47} -x_{2} x_{46} +x_{2} x_{45} -x_{2} x_{44} , x_{3} x_{47} -x_{3} x_{46} -x_{3} x_{45} +x_{3} x_{44} +x_{3} x_{43} , x_{4} x_{48} -x_{4} x_{47} -x_{4} x_{46} +x_{4} x_{45} +x_{4} x_{44} , x_{5} x_{47} -x_{5} x_{46} +x_{5} x_{44} -x_{5} x_{43} , x_{6} x_{47} -x_{6} x_{45} -x_{6} x_{44} +x_{6} x_{43} , x_{7} x_{48} -x_{7} x_{47} +x_{7} x_{45} -x_{7} x_{44} , x_{8} x_{48} -x_{8} x_{47} -x_{8} x_{45} +x_{8} x_{44} +x_{8} x_{43} , x_{9} x_{48} +x_{9} x_{46} -x_{9} x_{45} -x_{9} x_{44} , x_{10} x_{47} -x_{10} x_{44} -x_{10} x_{43} , x_{11} x_{48} -x_{11} x_{47} +x_{11} x_{44} -x_{11} x_{43} , x_{12} x_{48} -x_{12} x_{47} +x_{12} x_{46} -x_{12} x_{45} -x_{12} x_{44} +x_{12} x_{43} , x_{13} x_{48} -x_{13} x_{45} +x_{13} x_{44} , x_{14} x_{48} +x_{14} x_{45} -x_{14} x_{44} -x_{14} x_{43} , x_{15} x_{48} -x_{15} x_{47} +x_{15} x_{46} -x_{15} x_{44} -x_{15} x_{43} , x_{16} x_{48} -x_{16} x_{44} +x_{16} x_{43} , x_{17} x_{48} -x_{17} x_{46} +x_{17} x_{45} +x_{17} x_{44} -x_{17} x_{43} , x_{18} x_{48} -x_{18} x_{46} +x_{18} x_{44} +x_{18} x_{43} , x_{19} x_{47} -2x_{19} x_{46} +x_{19} x_{45} +x_{19} x_{44} , x_{20} x_{47} -x_{20} x_{46} +x_{20} x_{45} -x_{20} x_{44} , x_{21} x_{47} -x_{21} x_{46} -x_{21} x_{45} +x_{21} x_{44} +x_{21} x_{43} , x_{22} x_{48} -x_{22} x_{47} -x_{22} x_{46} +x_{22} x_{45} +x_{22} x_{44} , x_{23} x_{47} -x_{23} x_{46} +x_{23} x_{44} -x_{23} x_{43} , x_{24} x_{47} -x_{24} x_{45} -x_{24} x_{44} +x_{24} x_{43} , x_{25} x_{48} -x_{25} x_{47} +x_{25} x_{45} -x_{25} x_{44} , x_{26} x_{48} -x_{26} x_{47} -x_{26} x_{45} +x_{26} x_{44} +x_{26} x_{43} , x_{27} x_{48} +x_{27} x_{46} -x_{27} x_{45} -x_{27} x_{44} , x_{28} x_{47} -x_{28} x_{44} -x_{28} x_{43} , x_{29} x_{48} -x_{29} x_{47} +x_{29} x_{44} -x_{29} x_{43} , x_{30} x_{48} -x_{30} x_{47} +x_{30} x_{46} -x_{30} x_{45} -x_{30} x_{44} +x_{30} x_{43} , x_{31} x_{48} -x_{31} x_{45} +x_{31} x_{44} , x_{32} x_{48} +x_{32} x_{45} -x_{32} x_{44} -x_{32} x_{43} , x_{33} x_{48} -x_{33} x_{47} +x_{33} x_{46} -x_{33} x_{44} -x_{33} x_{43} , x_{34} x_{48} -x_{34} x_{44} +x_{34} x_{43} , x_{35} x_{48} -x_{35} x_{46} +x_{35} x_{45} +x_{35} x_{44} -x_{35} x_{43} , x_{36} x_{48} -x_{36} x_{46} +x_{36} x_{44} +x_{36} x_{43} )