Subalgebra \(A^{2}_1\) ↪ \(F^{1}_4\)
2 out of 59
Computations done by the calculator project.

Subalgebra type: \(\displaystyle A^{2}_1\) (click on type for detailed printout).
The subalgebra is regular (= the semisimple part of a root subalgebra).
Centralizer: \(\displaystyle A^{1}_3\) .
The semisimple part of the centralizer of the semisimple part of my centralizer: \(\displaystyle A^{2}_1\)
Basis of Cartan of centralizer: 3 vectors: (1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0)
Contained up to conjugation as a direct summand of: \(\displaystyle A^{2}_1+A^{1}_1\) , \(\displaystyle 2A^{2}_1\) , \(\displaystyle A^{4}_1+A^{2}_1\) , \(\displaystyle A^{10}_1+A^{2}_1\) , \(\displaystyle A^{2}_1+2A^{1}_1\) , \(\displaystyle 3A^{2}_1\) , \(\displaystyle A^{1}_2+A^{2}_1\) , \(\displaystyle B^{1}_2+A^{2}_1\) , \(\displaystyle A^{1}_3+A^{2}_1\) .

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

Semisimple subalgebra: W_{25}
Centralizer extension: 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}

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.
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Made total 177381398 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_{-16}+x_{2} g_{-18}+x_{3} g_{-20}+x_{4} g_{-21}+x_{5} g_{-22}+x_{6} g_{-23}+x_{7} g_{-24}, x_{14} g_{24}+x_{13} g_{23}+x_{12} g_{22}+x_{11} g_{21}+x_{10} g_{20}+x_{9} g_{18}+x_{8} g_{16})

Unknown splitting cartan of centralizer.
x_{18} h_{4}+x_{17} h_{3}+x_{16} h_{2}+x_{15} h_{1}, x_{22} h_{4}+x_{21} h_{3}+x_{20} h_{2}+x_{19} h_{1}, x_{26} h_{4}+x_{25} h_{3}+x_{24} h_{2}+x_{23} h_{1}
h: (2, 4, 6, 4), e = combination of g_{16} g_{18} g_{20} g_{21} g_{22} g_{23} g_{24} , f= combination of g_{-16} g_{-18} g_{-20} g_{-21} g_{-22} g_{-23} g_{-24} Positive weight subsystem: 1 vectors: (1)
Symmetric Cartan default scale: \begin{pmatrix}
2\\
\end{pmatrix}Character ambient Lie algebra: 7V_{2\omega_{1}}+8V_{\omega_{1}}+22V_{0}+8V_{-\omega_{1}}+7V_{-2\omega_{1}}
A necessary system to realize the candidate subalgebra.
1/2x_{16}^{2}x_{21}^{2}x_{26}^{2}x_{27} -3/2x_{15} x_{16} x_{21}^{2}x_{26}^{2}x_{27} +3/2x_{15}^{2}x_{21}^{2}x_{26}^{2}x_{27}
-x_{16} x_{17} x_{20} x_{21} x_{26}^{2}x_{27} +3/2x_{15} x_{17} x_{20} x_{21} x_{26}^{2}x_{27} +2x_{15} x_{16} x_{20} x_{21} x_{26}^{2}x_{27}
-4x_{15}^{2}x_{20} x_{21} x_{26}^{2}x_{27} +3/2x_{16} x_{17} x_{19} x_{21} x_{26}^{2}x_{27} -3x_{15} x_{17} x_{19} x_{21} x_{26}^{2}x_{27}
-2x_{16}^{2}x_{19} x_{21} x_{26}^{2}x_{27} +4x_{15} x_{16} x_{19} x_{21} x_{26}^{2}x_{27} +1/2x_{17}^{2}x_{20}^{2}x_{26}^{2}x_{27}
-2x_{15} x_{17} x_{20}^{2}x_{26}^{2}x_{27} +3x_{15}^{2}x_{20}^{2}x_{26}^{2}x_{27} -3/2x_{17}^{2}x_{19} x_{20} x_{26}^{2}x_{27}
+2x_{16} x_{17} x_{19} x_{20} x_{26}^{2}x_{27} +4x_{15} x_{17} x_{19} x_{20} x_{26}^{2}x_{27} -6x_{15} x_{16} x_{19} x_{20} x_{26}^{2}x_{27}
+3/2x_{17}^{2}x_{19}^{2}x_{26}^{2}x_{27} -4x_{16} x_{17} x_{19}^{2}x_{26}^{2}x_{27} +3x_{16}^{2}x_{19}^{2}x_{26}^{2}x_{27}
-x_{16}^{2}x_{21} x_{22} x_{25} x_{26} x_{27} +3x_{15} x_{16} x_{21} x_{22} x_{25} x_{26} x_{27} -3x_{15}^{2}x_{21} x_{22} x_{25} x_{26} x_{27}
+x_{16} x_{17} x_{20} x_{22} x_{25} x_{26} x_{27} -3/2x_{15} x_{17} x_{20} x_{22} x_{25} x_{26} x_{27}
-2x_{15} x_{16} x_{20} x_{22} x_{25} x_{26} x_{27} +4x_{15}^{2}x_{20} x_{22} x_{25} x_{26} x_{27} -3/2x_{16} x_{17} x_{19} x_{22} x_{25} x_{26} x_{27}
+3x_{15} x_{17} x_{19} x_{22} x_{25} x_{26} x_{27} +2x_{16}^{2}x_{19} x_{22} x_{25} x_{26} x_{27} -4x_{15} x_{16} x_{19} x_{22} x_{25} x_{26} x_{27}
+x_{16} x_{18} x_{20} x_{21} x_{25} x_{26} x_{27} -3/2x_{15} x_{18} x_{20} x_{21} x_{25} x_{26} x_{27}
-x_{15} x_{16} x_{20} x_{21} x_{25} x_{26} x_{27} +2x_{15}^{2}x_{20} x_{21} x_{25} x_{26} x_{27} -3/2x_{16} x_{18} x_{19} x_{21} x_{25} x_{26} x_{27}
+3x_{15} x_{18} x_{19} x_{21} x_{25} x_{26} x_{27} +x_{16}^{2}x_{19} x_{21} x_{25} x_{26} x_{27} -2x_{15} x_{16} x_{19} x_{21} x_{25} x_{26} x_{27}
-x_{17} x_{18} x_{20}^{2}x_{25} x_{26} x_{27} +2x_{15} x_{18} x_{20}^{2}x_{25} x_{26} x_{27} +x_{15} x_{17} x_{20}^{2}x_{25} x_{26} x_{27}
-3x_{15}^{2}x_{20}^{2}x_{25} x_{26} x_{27} +3x_{17} x_{18} x_{19} x_{20} x_{25} x_{26} x_{27} -2x_{16} x_{18} x_{19} x_{20} x_{25} x_{26} x_{27}
-4x_{15} x_{18} x_{19} x_{20} x_{25} x_{26} x_{27} -x_{16} x_{17} x_{19} x_{20} x_{25} x_{26} x_{27}
-2x_{15} x_{17} x_{19} x_{20} x_{25} x_{26} x_{27} +6x_{15} x_{16} x_{19} x_{20} x_{25} x_{26} x_{27}
-3x_{17} x_{18} x_{19}^{2}x_{25} x_{26} x_{27} +4x_{16} x_{18} x_{19}^{2}x_{25} x_{26} x_{27} +2x_{16} x_{17} x_{19}^{2}x_{25} x_{26} x_{27}
-3x_{16}^{2}x_{19}^{2}x_{25} x_{26} x_{27} +x_{16} x_{17} x_{21} x_{22} x_{24} x_{26} x_{27} -3/2x_{15} x_{17} x_{21} x_{22} x_{24} x_{26} x_{27}
-2x_{15} x_{16} x_{21} x_{22} x_{24} x_{26} x_{27} +4x_{15}^{2}x_{21} x_{22} x_{24} x_{26} x_{27} -x_{17}^{2}x_{20} x_{22} x_{24} x_{26} x_{27}
+4x_{15} x_{17} x_{20} x_{22} x_{24} x_{26} x_{27} -6x_{15}^{2}x_{20} x_{22} x_{24} x_{26} x_{27} +3/2x_{17}^{2}x_{19} x_{22} x_{24} x_{26} x_{27}
-2x_{16} x_{17} x_{19} x_{22} x_{24} x_{26} x_{27} -4x_{15} x_{17} x_{19} x_{22} x_{24} x_{26} x_{27}
+6x_{15} x_{16} x_{19} x_{22} x_{24} x_{26} x_{27} -x_{16} x_{18} x_{21}^{2}x_{24} x_{26} x_{27} +3/2x_{15} x_{18} x_{21}^{2}x_{24} x_{26} x_{27}
+x_{15} x_{16} x_{21}^{2}x_{24} x_{26} x_{27} -2x_{15}^{2}x_{21}^{2}x_{24} x_{26} x_{27} +x_{17} x_{18} x_{20} x_{21} x_{24} x_{26} x_{27}
-2x_{15} x_{18} x_{20} x_{21} x_{24} x_{26} x_{27} -x_{15} x_{17} x_{20} x_{21} x_{24} x_{26} x_{27}
+3x_{15}^{2}x_{20} x_{21} x_{24} x_{26} x_{27} -3/2x_{17} x_{18} x_{19} x_{21} x_{24} x_{26} x_{27} +4x_{16} x_{18} x_{19} x_{21} x_{24} x_{26} x_{27}
-4x_{15} x_{18} x_{19} x_{21} x_{24} x_{26} x_{27} -x_{16} x_{17} x_{19} x_{21} x_{24} x_{26} x_{27}
+4x_{15} x_{17} x_{19} x_{21} x_{24} x_{26} x_{27} -3x_{15} x_{16} x_{19} x_{21} x_{24} x_{26} x_{27}
-2x_{17} x_{18} x_{19} x_{20} x_{24} x_{26} x_{27} +6x_{15} x_{18} x_{19} x_{20} x_{24} x_{26} x_{27}
+x_{17}^{2}x_{19} x_{20} x_{24} x_{26} x_{27} -3x_{15} x_{17} x_{19} x_{20} x_{24} x_{26} x_{27} +4x_{17} x_{18} x_{19}^{2}x_{24} x_{26} x_{27}
-6x_{16} x_{18} x_{19}^{2}x_{24} x_{26} x_{27} -2x_{17}^{2}x_{19}^{2}x_{24} x_{26} x_{27} +3x_{16} x_{17} x_{19}^{2}x_{24} x_{26} x_{27}
-3/2x_{16} x_{17} x_{21} x_{22} x_{23} x_{26} x_{27} +3x_{15} x_{17} x_{21} x_{22} x_{23} x_{26} x_{27}
+2x_{16}^{2}x_{21} x_{22} x_{23} x_{26} x_{27} -4x_{15} x_{16} x_{21} x_{22} x_{23} x_{26} x_{27} +3/2x_{17}^{2}x_{20} x_{22} x_{23} x_{26} x_{27}
-2x_{16} x_{17} x_{20} x_{22} x_{23} x_{26} x_{27} -4x_{15} x_{17} x_{20} x_{22} x_{23} x_{26} x_{27}
+6x_{15} x_{16} x_{20} x_{22} x_{23} x_{26} x_{27} -3x_{17}^{2}x_{19} x_{22} x_{23} x_{26} x_{27} +8x_{16} x_{17} x_{19} x_{22} x_{23} x_{26} x_{27}
-6x_{16}^{2}x_{19} x_{22} x_{23} x_{26} x_{27} +3/2x_{16} x_{18} x_{21}^{2}x_{23} x_{26} x_{27} -3x_{15} x_{18} x_{21}^{2}x_{23} x_{26} x_{27}
-x_{16}^{2}x_{21}^{2}x_{23} x_{26} x_{27} +2x_{15} x_{16} x_{21}^{2}x_{23} x_{26} x_{27} -3/2x_{17} x_{18} x_{20} x_{21} x_{23} x_{26} x_{27}
-2x_{16} x_{18} x_{20} x_{21} x_{23} x_{26} x_{27} +8x_{15} x_{18} x_{20} x_{21} x_{23} x_{26} x_{27}
+2x_{16} x_{17} x_{20} x_{21} x_{23} x_{26} x_{27} -2x_{15} x_{17} x_{20} x_{21} x_{23} x_{26} x_{27}
-3x_{15} x_{16} x_{20} x_{21} x_{23} x_{26} x_{27} +3x_{17} x_{18} x_{19} x_{21} x_{23} x_{26} x_{27}
-4x_{16} x_{18} x_{19} x_{21} x_{23} x_{26} x_{27} -2x_{16} x_{17} x_{19} x_{21} x_{23} x_{26} x_{27}
+3x_{16}^{2}x_{19} x_{21} x_{23} x_{26} x_{27} +2x_{17} x_{18} x_{20}^{2}x_{23} x_{26} x_{27} -6x_{15} x_{18} x_{20}^{2}x_{23} x_{26} x_{27}
-x_{17}^{2}x_{20}^{2}x_{23} x_{26} x_{27} +3x_{15} x_{17} x_{20}^{2}x_{23} x_{26} x_{27} -4x_{17} x_{18} x_{19} x_{20} x_{23} x_{26} x_{27}
+6x_{16} x_{18} x_{19} x_{20} x_{23} x_{26} x_{27} +2x_{17}^{2}x_{19} x_{20} x_{23} x_{26} x_{27} -3x_{16} x_{17} x_{19} x_{20} x_{23} x_{26} x_{27}
+1/2x_{16}^{2}x_{22}^{2}x_{25}^{2}x_{27} -3/2x_{15} x_{16} x_{22}^{2}x_{25}^{2}x_{27} +3/2x_{15}^{2}x_{22}^{2}x_{25}^{2}x_{27}
-x_{16} x_{18} x_{20} x_{22} x_{25}^{2}x_{27} +3/2x_{15} x_{18} x_{20} x_{22} x_{25}^{2}x_{27} +x_{15} x_{16} x_{20} x_{22} x_{25}^{2}x_{27}
-2x_{15}^{2}x_{20} x_{22} x_{25}^{2}x_{27} +3/2x_{16} x_{18} x_{19} x_{22} x_{25}^{2}x_{27} -3x_{15} x_{18} x_{19} x_{22} x_{25}^{2}x_{27}
-x_{16}^{2}x_{19} x_{22} x_{25}^{2}x_{27} +2x_{15} x_{16} x_{19} x_{22} x_{25}^{2}x_{27} +1/2x_{18}^{2}x_{20}^{2}x_{25}^{2}x_{27}
-x_{15} x_{18} x_{20}^{2}x_{25}^{2}x_{27} +x_{15}^{2}x_{20}^{2}x_{25}^{2}x_{27} -3/2x_{18}^{2}x_{19} x_{20} x_{25}^{2}x_{27}
+x_{16} x_{18} x_{19} x_{20} x_{25}^{2}x_{27} +2x_{15} x_{18} x_{19} x_{20} x_{25}^{2}x_{27} -2x_{15} x_{16} x_{19} x_{20} x_{25}^{2}x_{27}
+3/2x_{18}^{2}x_{19}^{2}x_{25}^{2}x_{27} -2x_{16} x_{18} x_{19}^{2}x_{25}^{2}x_{27} +x_{16}^{2}x_{19}^{2}x_{25}^{2}x_{27}
-x_{16} x_{17} x_{22}^{2}x_{24} x_{25} x_{27} +3/2x_{15} x_{17} x_{22}^{2}x_{24} x_{25} x_{27} +2x_{15} x_{16} x_{22}^{2}x_{24} x_{25} x_{27}
-4x_{15}^{2}x_{22}^{2}x_{24} x_{25} x_{27} +x_{16} x_{18} x_{21} x_{22} x_{24} x_{25} x_{27} -3/2x_{15} x_{18} x_{21} x_{22} x_{24} x_{25} x_{27}
-x_{15} x_{16} x_{21} x_{22} x_{24} x_{25} x_{27} +2x_{15}^{2}x_{21} x_{22} x_{24} x_{25} x_{27} +x_{17} x_{18} x_{20} x_{22} x_{24} x_{25} x_{27}
-2x_{15} x_{18} x_{20} x_{22} x_{24} x_{25} x_{27} -x_{15} x_{17} x_{20} x_{22} x_{24} x_{25} x_{27}
+3x_{15}^{2}x_{20} x_{22} x_{24} x_{25} x_{27} -3/2x_{17} x_{18} x_{19} x_{22} x_{24} x_{25} x_{27} -2x_{16} x_{18} x_{19} x_{22} x_{24} x_{25} x_{27}
+8x_{15} x_{18} x_{19} x_{22} x_{24} x_{25} x_{27} +2x_{16} x_{17} x_{19} x_{22} x_{24} x_{25} x_{27}
-2x_{15} x_{17} x_{19} x_{22} x_{24} x_{25} x_{27} -3x_{15} x_{16} x_{19} x_{22} x_{24} x_{25} x_{27}
-x_{18}^{2}x_{20} x_{21} x_{24} x_{25} x_{27} +2x_{15} x_{18} x_{20} x_{21} x_{24} x_{25} x_{27} -2x_{15}^{2}x_{20} x_{21} x_{24} x_{25} x_{27}
+3/2x_{18}^{2}x_{19} x_{21} x_{24} x_{25} x_{27} -x_{16} x_{18} x_{19} x_{21} x_{24} x_{25} x_{27} -2x_{15} x_{18} x_{19} x_{21} x_{24} x_{25} x_{27}
+2x_{15} x_{16} x_{19} x_{21} x_{24} x_{25} x_{27} +2x_{18}^{2}x_{19} x_{20} x_{24} x_{25} x_{27} -x_{17} x_{18} x_{19} x_{20} x_{24} x_{25} x_{27}
-3x_{15} x_{18} x_{19} x_{20} x_{24} x_{25} x_{27} +2x_{15} x_{17} x_{19} x_{20} x_{24} x_{25} x_{27}
-4x_{18}^{2}x_{19}^{2}x_{24} x_{25} x_{27} +2x_{17} x_{18} x_{19}^{2}x_{24} x_{25} x_{27} +3x_{16} x_{18} x_{19}^{2}x_{24} x_{25} x_{27}
-2x_{16} x_{17} x_{19}^{2}x_{24} x_{25} x_{27} +3/2x_{16} x_{17} x_{22}^{2}x_{23} x_{25} x_{27} -3x_{15} x_{17} x_{22}^{2}x_{23} x_{25} x_{27}
-2x_{16}^{2}x_{22}^{2}x_{23} x_{25} x_{27} +4x_{15} x_{16} x_{22}^{2}x_{23} x_{25} x_{27} -3/2x_{16} x_{18} x_{21} x_{22} x_{23} x_{25} x_{27}
+3x_{15} x_{18} x_{21} x_{22} x_{23} x_{25} x_{27} +x_{16}^{2}x_{21} x_{22} x_{23} x_{25} x_{27} -2x_{15} x_{16} x_{21} x_{22} x_{23} x_{25} x_{27}
-3/2x_{17} x_{18} x_{20} x_{22} x_{23} x_{25} x_{27} +4x_{16} x_{18} x_{20} x_{22} x_{23} x_{25} x_{27}
-4x_{15} x_{18} x_{20} x_{22} x_{23} x_{25} x_{27} -x_{16} x_{17} x_{20} x_{22} x_{23} x_{25} x_{27}
+4x_{15} x_{17} x_{20} x_{22} x_{23} x_{25} x_{27} -3x_{15} x_{16} x_{20} x_{22} x_{23} x_{25} x_{27}
+3x_{17} x_{18} x_{19} x_{22} x_{23} x_{25} x_{27} -4x_{16} x_{18} x_{19} x_{22} x_{23} x_{25} x_{27}
-2x_{16} x_{17} x_{19} x_{22} x_{23} x_{25} x_{27} +3x_{16}^{2}x_{19} x_{22} x_{23} x_{25} x_{27} +3/2x_{18}^{2}x_{20} x_{21} x_{23} x_{25} x_{27}
-x_{16} x_{18} x_{20} x_{21} x_{23} x_{25} x_{27} -2x_{15} x_{18} x_{20} x_{21} x_{23} x_{25} x_{27}
+2x_{15} x_{16} x_{20} x_{21} x_{23} x_{25} x_{27} -3x_{18}^{2}x_{19} x_{21} x_{23} x_{25} x_{27} +4x_{16} x_{18} x_{19} x_{21} x_{23} x_{25} x_{27}
-2x_{16}^{2}x_{19} x_{21} x_{23} x_{25} x_{27} -2x_{18}^{2}x_{20}^{2}x_{23} x_{25} x_{27} +x_{17} x_{18} x_{20}^{2}x_{23} x_{25} x_{27}
+3x_{15} x_{18} x_{20}^{2}x_{23} x_{25} x_{27} -2x_{15} x_{17} x_{20}^{2}x_{23} x_{25} x_{27} +4x_{18}^{2}x_{19} x_{20} x_{23} x_{25} x_{27}
-2x_{17} x_{18} x_{19} x_{20} x_{23} x_{25} x_{27} -3x_{16} x_{18} x_{19} x_{20} x_{23} x_{25} x_{27}
+2x_{16} x_{17} x_{19} x_{20} x_{23} x_{25} x_{27} +1/2x_{17}^{2}x_{22}^{2}x_{24}^{2}x_{27} -2x_{15} x_{17} x_{22}^{2}x_{24}^{2}x_{27}
+3x_{15}^{2}x_{22}^{2}x_{24}^{2}x_{27} -x_{17} x_{18} x_{21} x_{22} x_{24}^{2}x_{27} +2x_{15} x_{18} x_{21} x_{22} x_{24}^{2}x_{27}
+x_{15} x_{17} x_{21} x_{22} x_{24}^{2}x_{27} -3x_{15}^{2}x_{21} x_{22} x_{24}^{2}x_{27} +2x_{17} x_{18} x_{19} x_{22} x_{24}^{2}x_{27}
-6x_{15} x_{18} x_{19} x_{22} x_{24}^{2}x_{27} -x_{17}^{2}x_{19} x_{22} x_{24}^{2}x_{27} +3x_{15} x_{17} x_{19} x_{22} x_{24}^{2}x_{27}
+1/2x_{18}^{2}x_{21}^{2}x_{24}^{2}x_{27} -x_{15} x_{18} x_{21}^{2}x_{24}^{2}x_{27} +x_{15}^{2}x_{21}^{2}x_{24}^{2}x_{27}
-2x_{18}^{2}x_{19} x_{21} x_{24}^{2}x_{27} +x_{17} x_{18} x_{19} x_{21} x_{24}^{2}x_{27} +3x_{15} x_{18} x_{19} x_{21} x_{24}^{2}x_{27}
-2x_{15} x_{17} x_{19} x_{21} x_{24}^{2}x_{27} +3x_{18}^{2}x_{19}^{2}x_{24}^{2}x_{27} -3x_{17} x_{18} x_{19}^{2}x_{24}^{2}x_{27}
+x_{17}^{2}x_{19}^{2}x_{24}^{2}x_{27} -3/2x_{17}^{2}x_{22}^{2}x_{23} x_{24} x_{27} +2x_{16} x_{17} x_{22}^{2}x_{23} x_{24} x_{27}
+4x_{15} x_{17} x_{22}^{2}x_{23} x_{24} x_{27} -6x_{15} x_{16} x_{22}^{2}x_{23} x_{24} x_{27} +3x_{17} x_{18} x_{21} x_{22} x_{23} x_{24} x_{27}
-2x_{16} x_{18} x_{21} x_{22} x_{23} x_{24} x_{27} -4x_{15} x_{18} x_{21} x_{22} x_{23} x_{24} x_{27}
-x_{16} x_{17} x_{21} x_{22} x_{23} x_{24} x_{27} -2x_{15} x_{17} x_{21} x_{22} x_{23} x_{24} x_{27}
+6x_{15} x_{16} x_{21} x_{22} x_{23} x_{24} x_{27} -2x_{17} x_{18} x_{20} x_{22} x_{23} x_{24} x_{27}
+6x_{15} x_{18} x_{20} x_{22} x_{23} x_{24} x_{27} +x_{17}^{2}x_{20} x_{22} x_{23} x_{24} x_{27} -3x_{15} x_{17} x_{20} x_{22} x_{23} x_{24} x_{27}
-4x_{17} x_{18} x_{19} x_{22} x_{23} x_{24} x_{27} +6x_{16} x_{18} x_{19} x_{22} x_{23} x_{24} x_{27}
+2x_{17}^{2}x_{19} x_{22} x_{23} x_{24} x_{27} -3x_{16} x_{17} x_{19} x_{22} x_{23} x_{24} x_{27} -3/2x_{18}^{2}x_{21}^{2}x_{23} x_{24} x_{27}
+x_{16} x_{18} x_{21}^{2}x_{23} x_{24} x_{27} +2x_{15} x_{18} x_{21}^{2}x_{23} x_{24} x_{27} -2x_{15} x_{16} x_{21}^{2}x_{23} x_{24} x_{27}
+2x_{18}^{2}x_{20} x_{21} x_{23} x_{24} x_{27} -x_{17} x_{18} x_{20} x_{21} x_{23} x_{24} x_{27} -3x_{15} x_{18} x_{20} x_{21} x_{23} x_{24} x_{27}
+2x_{15} x_{17} x_{20} x_{21} x_{23} x_{24} x_{27} +4x_{18}^{2}x_{19} x_{21} x_{23} x_{24} x_{27} -2x_{17} x_{18} x_{19} x_{21} x_{23} x_{24} x_{27}
-3x_{16} x_{18} x_{19} x_{21} x_{23} x_{24} x_{27} +2x_{16} x_{17} x_{19} x_{21} x_{23} x_{24} x_{27}
-6x_{18}^{2}x_{19} x_{20} x_{23} x_{24} x_{27} +6x_{17} x_{18} x_{19} x_{20} x_{23} x_{24} x_{27} -2x_{17}^{2}x_{19} x_{20} x_{23} x_{24} x_{27}
+3/2x_{17}^{2}x_{22}^{2}x_{23}^{2}x_{27} -4x_{16} x_{17} x_{22}^{2}x_{23}^{2}x_{27} +3x_{16}^{2}x_{22}^{2}x_{23}^{2}x_{27}
-3x_{17} x_{18} x_{21} x_{22} x_{23}^{2}x_{27} +4x_{16} x_{18} x_{21} x_{22} x_{23}^{2}x_{27} +2x_{16} x_{17} x_{21} x_{22} x_{23}^{2}x_{27}
-3x_{16}^{2}x_{21} x_{22} x_{23}^{2}x_{27} +4x_{17} x_{18} x_{20} x_{22} x_{23}^{2}x_{27} -6x_{16} x_{18} x_{20} x_{22} x_{23}^{2}x_{27}
-2x_{17}^{2}x_{20} x_{22} x_{23}^{2}x_{27} +3x_{16} x_{17} x_{20} x_{22} x_{23}^{2}x_{27} +3/2x_{18}^{2}x_{21}^{2}x_{23}^{2}x_{27}
-2x_{16} x_{18} x_{21}^{2}x_{23}^{2}x_{27} +x_{16}^{2}x_{21}^{2}x_{23}^{2}x_{27} -4x_{18}^{2}x_{20} x_{21} x_{23}^{2}x_{27}
+2x_{17} x_{18} x_{20} x_{21} x_{23}^{2}x_{27} +3x_{16} x_{18} x_{20} x_{21} x_{23}^{2}x_{27} -2x_{16} x_{17} x_{20} x_{21} x_{23}^{2}x_{27}
+3x_{18}^{2}x_{20}^{2}x_{23}^{2}x_{27} -3x_{17} x_{18} x_{20}^{2}x_{23}^{2}x_{27} +x_{17}^{2}x_{20}^{2}x_{23}^{2}x_{27}
-1= 0
3x_{7} x_{14} +3x_{6} x_{13} +2x_{5} x_{12} +4x_{4} x_{11} +2x_{3} x_{10} +x_{2} x_{9} +x_{1} x_{8} -4= 0
2x_{7} x_{14} +2x_{6} x_{13} +2x_{5} x_{12} +3x_{4} x_{11} +x_{3} x_{10} +x_{2} x_{9} +x_{1} x_{8} -3= 0
x_{7} x_{14} +x_{6} x_{13} +x_{5} x_{12} +2x_{4} x_{11} +x_{3} x_{10} +x_{2} x_{9} +x_{1} x_{8} -2= 0
x_{7} x_{13} +x_{2} x_{8} = 0
x_{7} x_{12} -x_{3} x_{8} = 0
x_{7} x_{11} +x_{4} x_{8} = 0
x_{7} x_{10} -x_{5} x_{8} = 0
x_{7} x_{9} +x_{6} x_{8} = 0
x_{6} x_{14} +x_{1} x_{9} = 0
2x_{7} x_{14} +x_{6} x_{13} +x_{5} x_{12} +2x_{4} x_{11} +x_{3} x_{10} +x_{2} x_{9} -2= 0
x_{6} x_{12} +x_{3} x_{9} = 0
x_{6} x_{11} -x_{4} x_{9} = 0
x_{6} x_{10} +x_{5} x_{9} = 0
x_{5} x_{14} -x_{1} x_{10} = 0
x_{5} x_{13} +x_{2} x_{10} = 0
x_{5} x_{11} +x_{4} x_{10} = 0
x_{4} x_{14} +x_{1} x_{11} = 0
x_{4} x_{13} -x_{2} x_{11} = 0
x_{4} x_{12} +x_{3} x_{11} = 0
x_{3} x_{14} -x_{1} x_{12} = 0
x_{3} x_{13} +x_{2} x_{12} = 0
x_{2} x_{14} +x_{1} x_{13} = 0
x_{1} x_{18} -x_{1} x_{15} = 0
x_{2} x_{18} -x_{2} x_{16} +x_{2} x_{15} = 0
x_{3} x_{18} -x_{3} x_{17} +x_{3} x_{16} = 0
x_{4} x_{18} = 0
x_{5} x_{17} -x_{5} x_{16} = 0
x_{6} x_{16} -x_{6} x_{15} = 0
x_{7} x_{15} = 0
x_{8} x_{18} -x_{8} x_{15} = 0
x_{9} x_{18} -x_{9} x_{16} +x_{9} x_{15} = 0
x_{10} x_{18} -x_{10} x_{17} +x_{10} x_{16} = 0
x_{11} x_{18} = 0
x_{12} x_{17} -x_{12} x_{16} = 0
x_{13} x_{16} -x_{13} x_{15} = 0
x_{14} x_{15} = 0
x_{1} x_{22} -x_{1} x_{19} = 0
x_{2} x_{22} -x_{2} x_{20} +x_{2} x_{19} = 0
x_{3} x_{22} -x_{3} x_{21} +x_{3} x_{20} = 0
x_{4} x_{22} = 0
x_{5} x_{21} -x_{5} x_{20} = 0
x_{6} x_{20} -x_{6} x_{19} = 0
x_{7} x_{19} = 0
x_{8} x_{22} -x_{8} x_{19} = 0
x_{9} x_{22} -x_{9} x_{20} +x_{9} x_{19} = 0
x_{10} x_{22} -x_{10} x_{21} +x_{10} x_{20} = 0
x_{11} x_{22} = 0
x_{12} x_{21} -x_{12} x_{20} = 0
x_{13} x_{20} -x_{13} x_{19} = 0
x_{14} x_{19} = 0
x_{1} x_{26} -x_{1} x_{23} = 0
x_{2} x_{26} -x_{2} x_{24} +x_{2} x_{23} = 0
x_{3} x_{26} -x_{3} x_{25} +x_{3} x_{24} = 0
x_{4} x_{26} = 0
x_{5} x_{25} -x_{5} x_{24} = 0
x_{6} x_{24} -x_{6} x_{23} = 0
x_{7} x_{23} = 0
x_{8} x_{26} -x_{8} x_{23} = 0
x_{9} x_{26} -x_{9} x_{24} +x_{9} x_{23} = 0
x_{10} x_{26} -x_{10} x_{25} +x_{10} x_{24} = 0
x_{11} x_{26} = 0
x_{12} x_{25} -x_{12} x_{24} = 0
x_{13} x_{24} -x_{13} x_{23} = 0
x_{14} x_{23} = 0
The above system after transformation.
1/2x_{16}^{2}x_{21}^{2}x_{26}^{2}x_{27} -3/2x_{15} x_{16} x_{21}^{2}x_{26}^{2}x_{27} +3/2x_{15}^{2}x_{21}^{2}x_{26}^{2}x_{27}
-x_{16} x_{17} x_{20} x_{21} x_{26}^{2}x_{27} +3/2x_{15} x_{17} x_{20} x_{21} x_{26}^{2}x_{27} +2x_{15} x_{16} x_{20} x_{21} x_{26}^{2}x_{27}
-4x_{15}^{2}x_{20} x_{21} x_{26}^{2}x_{27} +3/2x_{16} x_{17} x_{19} x_{21} x_{26}^{2}x_{27} -3x_{15} x_{17} x_{19} x_{21} x_{26}^{2}x_{27}
-2x_{16}^{2}x_{19} x_{21} x_{26}^{2}x_{27} +4x_{15} x_{16} x_{19} x_{21} x_{26}^{2}x_{27} +1/2x_{17}^{2}x_{20}^{2}x_{26}^{2}x_{27}
-2x_{15} x_{17} x_{20}^{2}x_{26}^{2}x_{27} +3x_{15}^{2}x_{20}^{2}x_{26}^{2}x_{27} -3/2x_{17}^{2}x_{19} x_{20} x_{26}^{2}x_{27}
+2x_{16} x_{17} x_{19} x_{20} x_{26}^{2}x_{27} +4x_{15} x_{17} x_{19} x_{20} x_{26}^{2}x_{27} -6x_{15} x_{16} x_{19} x_{20} x_{26}^{2}x_{27}
+3/2x_{17}^{2}x_{19}^{2}x_{26}^{2}x_{27} -4x_{16} x_{17} x_{19}^{2}x_{26}^{2}x_{27} +3x_{16}^{2}x_{19}^{2}x_{26}^{2}x_{27}
-x_{16}^{2}x_{21} x_{22} x_{25} x_{26} x_{27} +3x_{15} x_{16} x_{21} x_{22} x_{25} x_{26} x_{27} -3x_{15}^{2}x_{21} x_{22} x_{25} x_{26} x_{27}
+x_{16} x_{17} x_{20} x_{22} x_{25} x_{26} x_{27} -3/2x_{15} x_{17} x_{20} x_{22} x_{25} x_{26} x_{27}
-2x_{15} x_{16} x_{20} x_{22} x_{25} x_{26} x_{27} +4x_{15}^{2}x_{20} x_{22} x_{25} x_{26} x_{27} -3/2x_{16} x_{17} x_{19} x_{22} x_{25} x_{26} x_{27}
+3x_{15} x_{17} x_{19} x_{22} x_{25} x_{26} x_{27} +2x_{16}^{2}x_{19} x_{22} x_{25} x_{26} x_{27} -4x_{15} x_{16} x_{19} x_{22} x_{25} x_{26} x_{27}
+x_{16} x_{18} x_{20} x_{21} x_{25} x_{26} x_{27} -3/2x_{15} x_{18} x_{20} x_{21} x_{25} x_{26} x_{27}
-x_{15} x_{16} x_{20} x_{21} x_{25} x_{26} x_{27} +2x_{15}^{2}x_{20} x_{21} x_{25} x_{26} x_{27} -3/2x_{16} x_{18} x_{19} x_{21} x_{25} x_{26} x_{27}
+3x_{15} x_{18} x_{19} x_{21} x_{25} x_{26} x_{27} +x_{16}^{2}x_{19} x_{21} x_{25} x_{26} x_{27} -2x_{15} x_{16} x_{19} x_{21} x_{25} x_{26} x_{27}
-x_{17} x_{18} x_{20}^{2}x_{25} x_{26} x_{27} +2x_{15} x_{18} x_{20}^{2}x_{25} x_{26} x_{27} +x_{15} x_{17} x_{20}^{2}x_{25} x_{26} x_{27}
-3x_{15}^{2}x_{20}^{2}x_{25} x_{26} x_{27} +3x_{17} x_{18} x_{19} x_{20} x_{25} x_{26} x_{27} -2x_{16} x_{18} x_{19} x_{20} x_{25} x_{26} x_{27}
-4x_{15} x_{18} x_{19} x_{20} x_{25} x_{26} x_{27} -x_{16} x_{17} x_{19} x_{20} x_{25} x_{26} x_{27}
-2x_{15} x_{17} x_{19} x_{20} x_{25} x_{26} x_{27} +6x_{15} x_{16} x_{19} x_{20} x_{25} x_{26} x_{27}
-3x_{17} x_{18} x_{19}^{2}x_{25} x_{26} x_{27} +4x_{16} x_{18} x_{19}^{2}x_{25} x_{26} x_{27} +2x_{16} x_{17} x_{19}^{2}x_{25} x_{26} x_{27}
-3x_{16}^{2}x_{19}^{2}x_{25} x_{26} x_{27} +x_{16} x_{17} x_{21} x_{22} x_{24} x_{26} x_{27} -3/2x_{15} x_{17} x_{21} x_{22} x_{24} x_{26} x_{27}
-2x_{15} x_{16} x_{21} x_{22} x_{24} x_{26} x_{27} +4x_{15}^{2}x_{21} x_{22} x_{24} x_{26} x_{27} -x_{17}^{2}x_{20} x_{22} x_{24} x_{26} x_{27}
+4x_{15} x_{17} x_{20} x_{22} x_{24} x_{26} x_{27} -6x_{15}^{2}x_{20} x_{22} x_{24} x_{26} x_{27} +3/2x_{17}^{2}x_{19} x_{22} x_{24} x_{26} x_{27}
-2x_{16} x_{17} x_{19} x_{22} x_{24} x_{26} x_{27} -4x_{15} x_{17} x_{19} x_{22} x_{24} x_{26} x_{27}
+6x_{15} x_{16} x_{19} x_{22} x_{24} x_{26} x_{27} -x_{16} x_{18} x_{21}^{2}x_{24} x_{26} x_{27} +3/2x_{15} x_{18} x_{21}^{2}x_{24} x_{26} x_{27}
+x_{15} x_{16} x_{21}^{2}x_{24} x_{26} x_{27} -2x_{15}^{2}x_{21}^{2}x_{24} x_{26} x_{27} +x_{17} x_{18} x_{20} x_{21} x_{24} x_{26} x_{27}
-2x_{15} x_{18} x_{20} x_{21} x_{24} x_{26} x_{27} -x_{15} x_{17} x_{20} x_{21} x_{24} x_{26} x_{27}
+3x_{15}^{2}x_{20} x_{21} x_{24} x_{26} x_{27} -3/2x_{17} x_{18} x_{19} x_{21} x_{24} x_{26} x_{27} +4x_{16} x_{18} x_{19} x_{21} x_{24} x_{26} x_{27}
-4x_{15} x_{18} x_{19} x_{21} x_{24} x_{26} x_{27} -x_{16} x_{17} x_{19} x_{21} x_{24} x_{26} x_{27}
+4x_{15} x_{17} x_{19} x_{21} x_{24} x_{26} x_{27} -3x_{15} x_{16} x_{19} x_{21} x_{24} x_{26} x_{27}
-2x_{17} x_{18} x_{19} x_{20} x_{24} x_{26} x_{27} +6x_{15} x_{18} x_{19} x_{20} x_{24} x_{26} x_{27}
+x_{17}^{2}x_{19} x_{20} x_{24} x_{26} x_{27} -3x_{15} x_{17} x_{19} x_{20} x_{24} x_{26} x_{27} +4x_{17} x_{18} x_{19}^{2}x_{24} x_{26} x_{27}
-6x_{16} x_{18} x_{19}^{2}x_{24} x_{26} x_{27} -2x_{17}^{2}x_{19}^{2}x_{24} x_{26} x_{27} +3x_{16} x_{17} x_{19}^{2}x_{24} x_{26} x_{27}
-3/2x_{16} x_{17} x_{21} x_{22} x_{23} x_{26} x_{27} +3x_{15} x_{17} x_{21} x_{22} x_{23} x_{26} x_{27}
+2x_{16}^{2}x_{21} x_{22} x_{23} x_{26} x_{27} -4x_{15} x_{16} x_{21} x_{22} x_{23} x_{26} x_{27} +3/2x_{17}^{2}x_{20} x_{22} x_{23} x_{26} x_{27}
-2x_{16} x_{17} x_{20} x_{22} x_{23} x_{26} x_{27} -4x_{15} x_{17} x_{20} x_{22} x_{23} x_{26} x_{27}
+6x_{15} x_{16} x_{20} x_{22} x_{23} x_{26} x_{27} -3x_{17}^{2}x_{19} x_{22} x_{23} x_{26} x_{27} +8x_{16} x_{17} x_{19} x_{22} x_{23} x_{26} x_{27}
-6x_{16}^{2}x_{19} x_{22} x_{23} x_{26} x_{27} +3/2x_{16} x_{18} x_{21}^{2}x_{23} x_{26} x_{27} -3x_{15} x_{18} x_{21}^{2}x_{23} x_{26} x_{27}
-x_{16}^{2}x_{21}^{2}x_{23} x_{26} x_{27} +2x_{15} x_{16} x_{21}^{2}x_{23} x_{26} x_{27} -3/2x_{17} x_{18} x_{20} x_{21} x_{23} x_{26} x_{27}
-2x_{16} x_{18} x_{20} x_{21} x_{23} x_{26} x_{27} +8x_{15} x_{18} x_{20} x_{21} x_{23} x_{26} x_{27}
+2x_{16} x_{17} x_{20} x_{21} x_{23} x_{26} x_{27} -2x_{15} x_{17} x_{20} x_{21} x_{23} x_{26} x_{27}
-3x_{15} x_{16} x_{20} x_{21} x_{23} x_{26} x_{27} +3x_{17} x_{18} x_{19} x_{21} x_{23} x_{26} x_{27}
-4x_{16} x_{18} x_{19} x_{21} x_{23} x_{26} x_{27} -2x_{16} x_{17} x_{19} x_{21} x_{23} x_{26} x_{27}
+3x_{16}^{2}x_{19} x_{21} x_{23} x_{26} x_{27} +2x_{17} x_{18} x_{20}^{2}x_{23} x_{26} x_{27} -6x_{15} x_{18} x_{20}^{2}x_{23} x_{26} x_{27}
-x_{17}^{2}x_{20}^{2}x_{23} x_{26} x_{27} +3x_{15} x_{17} x_{20}^{2}x_{23} x_{26} x_{27} -4x_{17} x_{18} x_{19} x_{20} x_{23} x_{26} x_{27}
+6x_{16} x_{18} x_{19} x_{20} x_{23} x_{26} x_{27} +2x_{17}^{2}x_{19} x_{20} x_{23} x_{26} x_{27} -3x_{16} x_{17} x_{19} x_{20} x_{23} x_{26} x_{27}
+1/2x_{16}^{2}x_{22}^{2}x_{25}^{2}x_{27} -3/2x_{15} x_{16} x_{22}^{2}x_{25}^{2}x_{27} +3/2x_{15}^{2}x_{22}^{2}x_{25}^{2}x_{27}
-x_{16} x_{18} x_{20} x_{22} x_{25}^{2}x_{27} +3/2x_{15} x_{18} x_{20} x_{22} x_{25}^{2}x_{27} +x_{15} x_{16} x_{20} x_{22} x_{25}^{2}x_{27}
-2x_{15}^{2}x_{20} x_{22} x_{25}^{2}x_{27} +3/2x_{16} x_{18} x_{19} x_{22} x_{25}^{2}x_{27} -3x_{15} x_{18} x_{19} x_{22} x_{25}^{2}x_{27}
-x_{16}^{2}x_{19} x_{22} x_{25}^{2}x_{27} +2x_{15} x_{16} x_{19} x_{22} x_{25}^{2}x_{27} +1/2x_{18}^{2}x_{20}^{2}x_{25}^{2}x_{27}
-x_{15} x_{18} x_{20}^{2}x_{25}^{2}x_{27} +x_{15}^{2}x_{20}^{2}x_{25}^{2}x_{27} -3/2x_{18}^{2}x_{19} x_{20} x_{25}^{2}x_{27}
+x_{16} x_{18} x_{19} x_{20} x_{25}^{2}x_{27} +2x_{15} x_{18} x_{19} x_{20} x_{25}^{2}x_{27} -2x_{15} x_{16} x_{19} x_{20} x_{25}^{2}x_{27}
+3/2x_{18}^{2}x_{19}^{2}x_{25}^{2}x_{27} -2x_{16} x_{18} x_{19}^{2}x_{25}^{2}x_{27} +x_{16}^{2}x_{19}^{2}x_{25}^{2}x_{27}
-x_{16} x_{17} x_{22}^{2}x_{24} x_{25} x_{27} +3/2x_{15} x_{17} x_{22}^{2}x_{24} x_{25} x_{27} +2x_{15} x_{16} x_{22}^{2}x_{24} x_{25} x_{27}
-4x_{15}^{2}x_{22}^{2}x_{24} x_{25} x_{27} +x_{16} x_{18} x_{21} x_{22} x_{24} x_{25} x_{27} -3/2x_{15} x_{18} x_{21} x_{22} x_{24} x_{25} x_{27}
-x_{15} x_{16} x_{21} x_{22} x_{24} x_{25} x_{27} +2x_{15}^{2}x_{21} x_{22} x_{24} x_{25} x_{27} +x_{17} x_{18} x_{20} x_{22} x_{24} x_{25} x_{27}
-2x_{15} x_{18} x_{20} x_{22} x_{24} x_{25} x_{27} -x_{15} x_{17} x_{20} x_{22} x_{24} x_{25} x_{27}
+3x_{15}^{2}x_{20} x_{22} x_{24} x_{25} x_{27} -3/2x_{17} x_{18} x_{19} x_{22} x_{24} x_{25} x_{27} -2x_{16} x_{18} x_{19} x_{22} x_{24} x_{25} x_{27}
+8x_{15} x_{18} x_{19} x_{22} x_{24} x_{25} x_{27} +2x_{16} x_{17} x_{19} x_{22} x_{24} x_{25} x_{27}
-2x_{15} x_{17} x_{19} x_{22} x_{24} x_{25} x_{27} -3x_{15} x_{16} x_{19} x_{22} x_{24} x_{25} x_{27}
-x_{18}^{2}x_{20} x_{21} x_{24} x_{25} x_{27} +2x_{15} x_{18} x_{20} x_{21} x_{24} x_{25} x_{27} -2x_{15}^{2}x_{20} x_{21} x_{24} x_{25} x_{27}
+3/2x_{18}^{2}x_{19} x_{21} x_{24} x_{25} x_{27} -x_{16} x_{18} x_{19} x_{21} x_{24} x_{25} x_{27} -2x_{15} x_{18} x_{19} x_{21} x_{24} x_{25} x_{27}
+2x_{15} x_{16} x_{19} x_{21} x_{24} x_{25} x_{27} +2x_{18}^{2}x_{19} x_{20} x_{24} x_{25} x_{27} -x_{17} x_{18} x_{19} x_{20} x_{24} x_{25} x_{27}
-3x_{15} x_{18} x_{19} x_{20} x_{24} x_{25} x_{27} +2x_{15} x_{17} x_{19} x_{20} x_{24} x_{25} x_{27}
-4x_{18}^{2}x_{19}^{2}x_{24} x_{25} x_{27} +2x_{17} x_{18} x_{19}^{2}x_{24} x_{25} x_{27} +3x_{16} x_{18} x_{19}^{2}x_{24} x_{25} x_{27}
-2x_{16} x_{17} x_{19}^{2}x_{24} x_{25} x_{27} +3/2x_{16} x_{17} x_{22}^{2}x_{23} x_{25} x_{27} -3x_{15} x_{17} x_{22}^{2}x_{23} x_{25} x_{27}
-2x_{16}^{2}x_{22}^{2}x_{23} x_{25} x_{27} +4x_{15} x_{16} x_{22}^{2}x_{23} x_{25} x_{27} -3/2x_{16} x_{18} x_{21} x_{22} x_{23} x_{25} x_{27}
+3x_{15} x_{18} x_{21} x_{22} x_{23} x_{25} x_{27} +x_{16}^{2}x_{21} x_{22} x_{23} x_{25} x_{27} -2x_{15} x_{16} x_{21} x_{22} x_{23} x_{25} x_{27}
-3/2x_{17} x_{18} x_{20} x_{22} x_{23} x_{25} x_{27} +4x_{16} x_{18} x_{20} x_{22} x_{23} x_{25} x_{27}
-4x_{15} x_{18} x_{20} x_{22} x_{23} x_{25} x_{27} -x_{16} x_{17} x_{20} x_{22} x_{23} x_{25} x_{27}
+4x_{15} x_{17} x_{20} x_{22} x_{23} x_{25} x_{27} -3x_{15} x_{16} x_{20} x_{22} x_{23} x_{25} x_{27}
+3x_{17} x_{18} x_{19} x_{22} x_{23} x_{25} x_{27} -4x_{16} x_{18} x_{19} x_{22} x_{23} x_{25} x_{27}
-2x_{16} x_{17} x_{19} x_{22} x_{23} x_{25} x_{27} +3x_{16}^{2}x_{19} x_{22} x_{23} x_{25} x_{27} +3/2x_{18}^{2}x_{20} x_{21} x_{23} x_{25} x_{27}
-x_{16} x_{18} x_{20} x_{21} x_{23} x_{25} x_{27} -2x_{15} x_{18} x_{20} x_{21} x_{23} x_{25} x_{27}
+2x_{15} x_{16} x_{20} x_{21} x_{23} x_{25} x_{27} -3x_{18}^{2}x_{19} x_{21} x_{23} x_{25} x_{27} +4x_{16} x_{18} x_{19} x_{21} x_{23} x_{25} x_{27}
-2x_{16}^{2}x_{19} x_{21} x_{23} x_{25} x_{27} -2x_{18}^{2}x_{20}^{2}x_{23} x_{25} x_{27} +x_{17} x_{18} x_{20}^{2}x_{23} x_{25} x_{27}
+3x_{15} x_{18} x_{20}^{2}x_{23} x_{25} x_{27} -2x_{15} x_{17} x_{20}^{2}x_{23} x_{25} x_{27} +4x_{18}^{2}x_{19} x_{20} x_{23} x_{25} x_{27}
-2x_{17} x_{18} x_{19} x_{20} x_{23} x_{25} x_{27} -3x_{16} x_{18} x_{19} x_{20} x_{23} x_{25} x_{27}
+2x_{16} x_{17} x_{19} x_{20} x_{23} x_{25} x_{27} +1/2x_{17}^{2}x_{22}^{2}x_{24}^{2}x_{27} -2x_{15} x_{17} x_{22}^{2}x_{24}^{2}x_{27}
+3x_{15}^{2}x_{22}^{2}x_{24}^{2}x_{27} -x_{17} x_{18} x_{21} x_{22} x_{24}^{2}x_{27} +2x_{15} x_{18} x_{21} x_{22} x_{24}^{2}x_{27}
+x_{15} x_{17} x_{21} x_{22} x_{24}^{2}x_{27} -3x_{15}^{2}x_{21} x_{22} x_{24}^{2}x_{27} +2x_{17} x_{18} x_{19} x_{22} x_{24}^{2}x_{27}
-6x_{15} x_{18} x_{19} x_{22} x_{24}^{2}x_{27} -x_{17}^{2}x_{19} x_{22} x_{24}^{2}x_{27} +3x_{15} x_{17} x_{19} x_{22} x_{24}^{2}x_{27}
+1/2x_{18}^{2}x_{21}^{2}x_{24}^{2}x_{27} -x_{15} x_{18} x_{21}^{2}x_{24}^{2}x_{27} +x_{15}^{2}x_{21}^{2}x_{24}^{2}x_{27}
-2x_{18}^{2}x_{19} x_{21} x_{24}^{2}x_{27} +x_{17} x_{18} x_{19} x_{21} x_{24}^{2}x_{27} +3x_{15} x_{18} x_{19} x_{21} x_{24}^{2}x_{27}
-2x_{15} x_{17} x_{19} x_{21} x_{24}^{2}x_{27} +3x_{18}^{2}x_{19}^{2}x_{24}^{2}x_{27} -3x_{17} x_{18} x_{19}^{2}x_{24}^{2}x_{27}
+x_{17}^{2}x_{19}^{2}x_{24}^{2}x_{27} -3/2x_{17}^{2}x_{22}^{2}x_{23} x_{24} x_{27} +2x_{16} x_{17} x_{22}^{2}x_{23} x_{24} x_{27}
+4x_{15} x_{17} x_{22}^{2}x_{23} x_{24} x_{27} -6x_{15} x_{16} x_{22}^{2}x_{23} x_{24} x_{27} +3x_{17} x_{18} x_{21} x_{22} x_{23} x_{24} x_{27}
-2x_{16} x_{18} x_{21} x_{22} x_{23} x_{24} x_{27} -4x_{15} x_{18} x_{21} x_{22} x_{23} x_{24} x_{27}
-x_{16} x_{17} x_{21} x_{22} x_{23} x_{24} x_{27} -2x_{15} x_{17} x_{21} x_{22} x_{23} x_{24} x_{27}
+6x_{15} x_{16} x_{21} x_{22} x_{23} x_{24} x_{27} -2x_{17} x_{18} x_{20} x_{22} x_{23} x_{24} x_{27}
+6x_{15} x_{18} x_{20} x_{22} x_{23} x_{24} x_{27} +x_{17}^{2}x_{20} x_{22} x_{23} x_{24} x_{27} -3x_{15} x_{17} x_{20} x_{22} x_{23} x_{24} x_{27}
-4x_{17} x_{18} x_{19} x_{22} x_{23} x_{24} x_{27} +6x_{16} x_{18} x_{19} x_{22} x_{23} x_{24} x_{27}
+2x_{17}^{2}x_{19} x_{22} x_{23} x_{24} x_{27} -3x_{16} x_{17} x_{19} x_{22} x_{23} x_{24} x_{27} -3/2x_{18}^{2}x_{21}^{2}x_{23} x_{24} x_{27}
+x_{16} x_{18} x_{21}^{2}x_{23} x_{24} x_{27} +2x_{15} x_{18} x_{21}^{2}x_{23} x_{24} x_{27} -2x_{15} x_{16} x_{21}^{2}x_{23} x_{24} x_{27}
+2x_{18}^{2}x_{20} x_{21} x_{23} x_{24} x_{27} -x_{17} x_{18} x_{20} x_{21} x_{23} x_{24} x_{27} -3x_{15} x_{18} x_{20} x_{21} x_{23} x_{24} x_{27}
+2x_{15} x_{17} x_{20} x_{21} x_{23} x_{24} x_{27} +4x_{18}^{2}x_{19} x_{21} x_{23} x_{24} x_{27} -2x_{17} x_{18} x_{19} x_{21} x_{23} x_{24} x_{27}
-3x_{16} x_{18} x_{19} x_{21} x_{23} x_{24} x_{27} +2x_{16} x_{17} x_{19} x_{21} x_{23} x_{24} x_{27}
-6x_{18}^{2}x_{19} x_{20} x_{23} x_{24} x_{27} +6x_{17} x_{18} x_{19} x_{20} x_{23} x_{24} x_{27} -2x_{17}^{2}x_{19} x_{20} x_{23} x_{24} x_{27}
+3/2x_{17}^{2}x_{22}^{2}x_{23}^{2}x_{27} -4x_{16} x_{17} x_{22}^{2}x_{23}^{2}x_{27} +3x_{16}^{2}x_{22}^{2}x_{23}^{2}x_{27}
-3x_{17} x_{18} x_{21} x_{22} x_{23}^{2}x_{27} +4x_{16} x_{18} x_{21} x_{22} x_{23}^{2}x_{27} +2x_{16} x_{17} x_{21} x_{22} x_{23}^{2}x_{27}
-3x_{16}^{2}x_{21} x_{22} x_{23}^{2}x_{27} +4x_{17} x_{18} x_{20} x_{22} x_{23}^{2}x_{27} -6x_{16} x_{18} x_{20} x_{22} x_{23}^{2}x_{27}
-2x_{17}^{2}x_{20} x_{22} x_{23}^{2}x_{27} +3x_{16} x_{17} x_{20} x_{22} x_{23}^{2}x_{27} +3/2x_{18}^{2}x_{21}^{2}x_{23}^{2}x_{27}
-2x_{16} x_{18} x_{21}^{2}x_{23}^{2}x_{27} +x_{16}^{2}x_{21}^{2}x_{23}^{2}x_{27} -4x_{18}^{2}x_{20} x_{21} x_{23}^{2}x_{27}
+2x_{17} x_{18} x_{20} x_{21} x_{23}^{2}x_{27} +3x_{16} x_{18} x_{20} x_{21} x_{23}^{2}x_{27} -2x_{16} x_{17} x_{20} x_{21} x_{23}^{2}x_{27}
+3x_{18}^{2}x_{20}^{2}x_{23}^{2}x_{27} -3x_{17} x_{18} x_{20}^{2}x_{23}^{2}x_{27} +x_{17}^{2}x_{20}^{2}x_{23}^{2}x_{27}
-1= 0
3x_{7} x_{14} +3x_{6} x_{13} +2x_{5} x_{12} +4x_{4} x_{11} +2x_{3} x_{10} +x_{2} x_{9} +x_{1} x_{8} -4= 0
2x_{7} x_{14} +2x_{6} x_{13} +2x_{5} x_{12} +3x_{4} x_{11} +x_{3} x_{10} +x_{2} x_{9} +x_{1} x_{8} -3= 0
x_{7} x_{14} +x_{6} x_{13} +x_{5} x_{12} +2x_{4} x_{11} +x_{3} x_{10} +x_{2} x_{9} +x_{1} x_{8} -2= 0
x_{7} x_{13} +x_{2} x_{8} = 0
x_{7} x_{12} -x_{3} x_{8} = 0
x_{7} x_{11} +x_{4} x_{8} = 0
x_{7} x_{10} -x_{5} x_{8} = 0
x_{7} x_{9} +x_{6} x_{8} = 0
x_{6} x_{14} +x_{1} x_{9} = 0
2x_{7} x_{14} +x_{6} x_{13} +x_{5} x_{12} +2x_{4} x_{11} +x_{3} x_{10} +x_{2} x_{9} -2= 0
x_{6} x_{12} +x_{3} x_{9} = 0
x_{6} x_{11} -x_{4} x_{9} = 0
x_{6} x_{10} +x_{5} x_{9} = 0
x_{5} x_{14} -x_{1} x_{10} = 0
x_{5} x_{13} +x_{2} x_{10} = 0
x_{5} x_{11} +x_{4} x_{10} = 0
x_{4} x_{14} +x_{1} x_{11} = 0
x_{4} x_{13} -x_{2} x_{11} = 0
x_{4} x_{12} +x_{3} x_{11} = 0
x_{3} x_{14} -x_{1} x_{12} = 0
x_{3} x_{13} +x_{2} x_{12} = 0
x_{2} x_{14} +x_{1} x_{13} = 0
x_{1} x_{18} -x_{1} x_{15} = 0
x_{2} x_{18} -x_{2} x_{16} +x_{2} x_{15} = 0
x_{3} x_{18} -x_{3} x_{17} +x_{3} x_{16} = 0
x_{4} x_{18} = 0
x_{5} x_{17} -x_{5} x_{16} = 0
x_{6} x_{16} -x_{6} x_{15} = 0
x_{7} x_{15} = 0
x_{8} x_{18} -x_{8} x_{15} = 0
x_{9} x_{18} -x_{9} x_{16} +x_{9} x_{15} = 0
x_{10} x_{18} -x_{10} x_{17} +x_{10} x_{16} = 0
x_{11} x_{18} = 0
x_{12} x_{17} -x_{12} x_{16} = 0
x_{13} x_{16} -x_{13} x_{15} = 0
x_{14} x_{15} = 0
x_{1} x_{22} -x_{1} x_{19} = 0
x_{2} x_{22} -x_{2} x_{20} +x_{2} x_{19} = 0
x_{3} x_{22} -x_{3} x_{21} +x_{3} x_{20} = 0
x_{4} x_{22} = 0
x_{5} x_{21} -x_{5} x_{20} = 0
x_{6} x_{20} -x_{6} x_{19} = 0
x_{7} x_{19} = 0
x_{8} x_{22} -x_{8} x_{19} = 0
x_{9} x_{22} -x_{9} x_{20} +x_{9} x_{19} = 0
x_{10} x_{22} -x_{10} x_{21} +x_{10} x_{20} = 0
x_{11} x_{22} = 0
x_{12} x_{21} -x_{12} x_{20} = 0
x_{13} x_{20} -x_{13} x_{19} = 0
x_{14} x_{19} = 0
x_{1} x_{26} -x_{1} x_{23} = 0
x_{2} x_{26} -x_{2} x_{24} +x_{2} x_{23} = 0
x_{3} x_{26} -x_{3} x_{25} +x_{3} x_{24} = 0
x_{4} x_{26} = 0
x_{5} x_{25} -x_{5} x_{24} = 0
x_{6} x_{24} -x_{6} x_{23} = 0
x_{7} x_{23} = 0
x_{8} x_{26} -x_{8} x_{23} = 0
x_{9} x_{26} -x_{9} x_{24} +x_{9} x_{23} = 0
x_{10} x_{26} -x_{10} x_{25} +x_{10} x_{24} = 0
x_{11} x_{26} = 0
x_{12} x_{25} -x_{12} x_{24} = 0
x_{13} x_{24} -x_{13} x_{23} = 0
x_{14} x_{23} = 0
For the calculator:
(DynkinType =A^{2}_1; ElementsCartan =((2, 4, 6, 4)); generators =(x_{1} g_{-16}+x_{2} g_{-18}+x_{3} g_{-20}+x_{4} g_{-21}+x_{5} g_{-22}+x_{6} g_{-23}+x_{7} g_{-24}, x_{14} g_{24}+x_{13} g_{23}+x_{12} g_{22}+x_{11} g_{21}+x_{10} g_{20}+x_{9} g_{18}+x_{8} g_{16}) );
FindOneSolutionSerreLikePolynomialSystem{}( 1/2x_{16}^{2}x_{21}^{2}x_{26}^{2}x_{27} -3/2x_{15} x_{16} x_{21}^{2}x_{26}^{2}x_{27} +3/2x_{15}^{2}x_{21}^{2}x_{26}^{2}x_{27} -x_{16} x_{17} x_{20} x_{21} x_{26}^{2}x_{27} +3/2x_{15} x_{17} x_{20} x_{21} x_{26}^{2}x_{27} +2x_{15} x_{16} x_{20} x_{21} x_{26}^{2}x_{27} -4x_{15}^{2}x_{20} x_{21} x_{26}^{2}x_{27} +3/2x_{16} x_{17} x_{19} x_{21} x_{26}^{2}x_{27} -3x_{15} x_{17} x_{19} x_{21} x_{26}^{2}x_{27} -2x_{16}^{2}x_{19} x_{21} x_{26}^{2}x_{27} +4x_{15} x_{16} x_{19} x_{21} x_{26}^{2}x_{27} +1/2x_{17}^{2}x_{20}^{2}x_{26}^{2}x_{27} -2x_{15} x_{17} x_{20}^{2}x_{26}^{2}x_{27} +3x_{15}^{2}x_{20}^{2}x_{26}^{2}x_{27} -3/2x_{17}^{2}x_{19} x_{20} x_{26}^{2}x_{27} +2x_{16} x_{17} x_{19} x_{20} x_{26}^{2}x_{27} +4x_{15} x_{17} x_{19} x_{20} x_{26}^{2}x_{27} -6x_{15} x_{16} x_{19} x_{20} x_{26}^{2}x_{27} +3/2x_{17}^{2}x_{19}^{2}x_{26}^{2}x_{27} -4x_{16} x_{17} x_{19}^{2}x_{26}^{2}x_{27} +3x_{16}^{2}x_{19}^{2}x_{26}^{2}x_{27} -x_{16}^{2}x_{21} x_{22} x_{25} x_{26} x_{27} +3x_{15} x_{16} x_{21} x_{22} x_{25} x_{26} x_{27} -3x_{15}^{2}x_{21} x_{22} x_{25} x_{26} x_{27} +x_{16} x_{17} x_{20} x_{22} x_{25} x_{26} x_{27} -3/2x_{15} x_{17} x_{20} x_{22} x_{25} x_{26} x_{27} -2x_{15} x_{16} x_{20} x_{22} x_{25} x_{26} x_{27} +4x_{15}^{2}x_{20} x_{22} x_{25} x_{26} x_{27} -3/2x_{16} x_{17} x_{19} x_{22} x_{25} x_{26} x_{27} +3x_{15} x_{17} x_{19} x_{22} x_{25} x_{26} x_{27} +2x_{16}^{2}x_{19} x_{22} x_{25} x_{26} x_{27} -4x_{15} x_{16} x_{19} x_{22} x_{25} x_{26} x_{27} +x_{16} x_{18} x_{20} x_{21} x_{25} x_{26} x_{27} -3/2x_{15} x_{18} x_{20} x_{21} x_{25} x_{26} x_{27} -x_{15} x_{16} x_{20} x_{21} x_{25} x_{26} x_{27} +2x_{15}^{2}x_{20} x_{21} x_{25} x_{26} x_{27} -3/2x_{16} x_{18} x_{19} x_{21} x_{25} x_{26} x_{27} +3x_{15} x_{18} x_{19} x_{21} x_{25} x_{26} x_{27} +x_{16}^{2}x_{19} x_{21} x_{25} x_{26} x_{27} -2x_{15} x_{16} x_{19} x_{21} x_{25} x_{26} x_{27} -x_{17} x_{18} x_{20}^{2}x_{25} x_{26} x_{27} +2x_{15} x_{18} x_{20}^{2}x_{25} x_{26} x_{27} +x_{15} x_{17} x_{20}^{2}x_{25} x_{26} x_{27} -3x_{15}^{2}x_{20}^{2}x_{25} x_{26} x_{27} +3x_{17} x_{18} x_{19} x_{20} x_{25} x_{26} x_{27} -2x_{16} x_{18} x_{19} x_{20} x_{25} x_{26} x_{27} -4x_{15} x_{18} x_{19} x_{20} x_{25} x_{26} x_{27} -x_{16} x_{17} x_{19} x_{20} x_{25} x_{26} x_{27} -2x_{15} x_{17} x_{19} x_{20} x_{25} x_{26} x_{27} +6x_{15} x_{16} x_{19} x_{20} x_{25} x_{26} x_{27} -3x_{17} x_{18} x_{19}^{2}x_{25} x_{26} x_{27} +4x_{16} x_{18} x_{19}^{2}x_{25} x_{26} x_{27} +2x_{16} x_{17} x_{19}^{2}x_{25} x_{26} x_{27} -3x_{16}^{2}x_{19}^{2}x_{25} x_{26} x_{27} +x_{16} x_{17} x_{21} x_{22} x_{24} x_{26} x_{27} -3/2x_{15} x_{17} x_{21} x_{22} x_{24} x_{26} x_{27} -2x_{15} x_{16} x_{21} x_{22} x_{24} x_{26} x_{27} +4x_{15}^{2}x_{21} x_{22} x_{24} x_{26} x_{27} -x_{17}^{2}x_{20} x_{22} x_{24} x_{26} x_{27} +4x_{15} x_{17} x_{20} x_{22} x_{24} x_{26} x_{27} -6x_{15}^{2}x_{20} x_{22} x_{24} x_{26} x_{27} +3/2x_{17}^{2}x_{19} x_{22} x_{24} x_{26} x_{27} -2x_{16} x_{17} x_{19} x_{22} x_{24} x_{26} x_{27} -4x_{15} x_{17} x_{19} x_{22} x_{24} x_{26} x_{27} +6x_{15} x_{16} x_{19} x_{22} x_{24} x_{26} x_{27} -x_{16} x_{18} x_{21}^{2}x_{24} x_{26} x_{27} +3/2x_{15} x_{18} x_{21}^{2}x_{24} x_{26} x_{27} +x_{15} x_{16} x_{21}^{2}x_{24} x_{26} x_{27} -2x_{15}^{2}x_{21}^{2}x_{24} x_{26} x_{27} +x_{17} x_{18} x_{20} x_{21} x_{24} x_{26} x_{27} -2x_{15} x_{18} x_{20} x_{21} x_{24} x_{26} x_{27} -x_{15} x_{17} x_{20} x_{21} x_{24} x_{26} x_{27} +3x_{15}^{2}x_{20} x_{21} x_{24} x_{26} x_{27} -3/2x_{17} x_{18} x_{19} x_{21} x_{24} x_{26} x_{27} +4x_{16} x_{18} x_{19} x_{21} x_{24} x_{26} x_{27} -4x_{15} x_{18} x_{19} x_{21} x_{24} x_{26} x_{27} -x_{16} x_{17} x_{19} x_{21} x_{24} x_{26} x_{27} +4x_{15} x_{17} x_{19} x_{21} x_{24} x_{26} x_{27} -3x_{15} x_{16} x_{19} x_{21} x_{24} x_{26} x_{27} -2x_{17} x_{18} x_{19} x_{20} x_{24} x_{26} x_{27} +6x_{15} x_{18} x_{19} x_{20} x_{24} x_{26} x_{27} +x_{17}^{2}x_{19} x_{20} x_{24} x_{26} x_{27} -3x_{15} x_{17} x_{19} x_{20} x_{24} x_{26} x_{27} +4x_{17} x_{18} x_{19}^{2}x_{24} x_{26} x_{27} -6x_{16} x_{18} x_{19}^{2}x_{24} x_{26} x_{27} -2x_{17}^{2}x_{19}^{2}x_{24} x_{26} x_{27} +3x_{16} x_{17} x_{19}^{2}x_{24} x_{26} x_{27} -3/2x_{16} x_{17} x_{21} x_{22} x_{23} x_{26} x_{27} +3x_{15} x_{17} x_{21} x_{22} x_{23} x_{26} x_{27} +2x_{16}^{2}x_{21} x_{22} x_{23} x_{26} x_{27} -4x_{15} x_{16} x_{21} x_{22} x_{23} x_{26} x_{27} +3/2x_{17}^{2}x_{20} x_{22} x_{23} x_{26} x_{27} -2x_{16} x_{17} x_{20} x_{22} x_{23} x_{26} x_{27} -4x_{15} x_{17} x_{20} x_{22} x_{23} x_{26} x_{27} +6x_{15} x_{16} x_{20} x_{22} x_{23} x_{26} x_{27} -3x_{17}^{2}x_{19} x_{22} x_{23} x_{26} x_{27} +8x_{16} x_{17} x_{19} x_{22} x_{23} x_{26} x_{27} -6x_{16}^{2}x_{19} x_{22} x_{23} x_{26} x_{27} +3/2x_{16} x_{18} x_{21}^{2}x_{23} x_{26} x_{27} -3x_{15} x_{18} x_{21}^{2}x_{23} x_{26} x_{27} -x_{16}^{2}x_{21}^{2}x_{23} x_{26} x_{27} +2x_{15} x_{16} x_{21}^{2}x_{23} x_{26} x_{27} -3/2x_{17} x_{18} x_{20} x_{21} x_{23} x_{26} x_{27} -2x_{16} x_{18} x_{20} x_{21} x_{23} x_{26} x_{27} +8x_{15} x_{18} x_{20} x_{21} x_{23} x_{26} x_{27} +2x_{16} x_{17} x_{20} x_{21} x_{23} x_{26} x_{27} -2x_{15} x_{17} x_{20} x_{21} x_{23} x_{26} x_{27} -3x_{15} x_{16} x_{20} x_{21} x_{23} x_{26} x_{27} +3x_{17} x_{18} x_{19} x_{21} x_{23} x_{26} x_{27} -4x_{16} x_{18} x_{19} x_{21} x_{23} x_{26} x_{27} -2x_{16} x_{17} x_{19} x_{21} x_{23} x_{26} x_{27} +3x_{16}^{2}x_{19} x_{21} x_{23} x_{26} x_{27} +2x_{17} x_{18} x_{20}^{2}x_{23} x_{26} x_{27} -6x_{15} x_{18} x_{20}^{2}x_{23} x_{26} x_{27} -x_{17}^{2}x_{20}^{2}x_{23} x_{26} x_{27} +3x_{15} x_{17} x_{20}^{2}x_{23} x_{26} x_{27} -4x_{17} x_{18} x_{19} x_{20} x_{23} x_{26} x_{27} +6x_{16} x_{18} x_{19} x_{20} x_{23} x_{26} x_{27} +2x_{17}^{2}x_{19} x_{20} x_{23} x_{26} x_{27} -3x_{16} x_{17} x_{19} x_{20} x_{23} x_{26} x_{27} +1/2x_{16}^{2}x_{22}^{2}x_{25}^{2}x_{27} -3/2x_{15} x_{16} x_{22}^{2}x_{25}^{2}x_{27} +3/2x_{15}^{2}x_{22}^{2}x_{25}^{2}x_{27} -x_{16} x_{18} x_{20} x_{22} x_{25}^{2}x_{27} +3/2x_{15} x_{18} x_{20} x_{22} x_{25}^{2}x_{27} +x_{15} x_{16} x_{20} x_{22} x_{25}^{2}x_{27} -2x_{15}^{2}x_{20} x_{22} x_{25}^{2}x_{27} +3/2x_{16} x_{18} x_{19} x_{22} x_{25}^{2}x_{27} -3x_{15} x_{18} x_{19} x_{22} x_{25}^{2}x_{27} -x_{16}^{2}x_{19} x_{22} x_{25}^{2}x_{27} +2x_{15} x_{16} x_{19} x_{22} x_{25}^{2}x_{27} +1/2x_{18}^{2}x_{20}^{2}x_{25}^{2}x_{27} -x_{15} x_{18} x_{20}^{2}x_{25}^{2}x_{27} +x_{15}^{2}x_{20}^{2}x_{25}^{2}x_{27} -3/2x_{18}^{2}x_{19} x_{20} x_{25}^{2}x_{27} +x_{16} x_{18} x_{19} x_{20} x_{25}^{2}x_{27} +2x_{15} x_{18} x_{19} x_{20} x_{25}^{2}x_{27} -2x_{15} x_{16} x_{19} x_{20} x_{25}^{2}x_{27} +3/2x_{18}^{2}x_{19}^{2}x_{25}^{2}x_{27} -2x_{16} x_{18} x_{19}^{2}x_{25}^{2}x_{27} +x_{16}^{2}x_{19}^{2}x_{25}^{2}x_{27} -x_{16} x_{17} x_{22}^{2}x_{24} x_{25} x_{27} +3/2x_{15} x_{17} x_{22}^{2}x_{24} x_{25} x_{27} +2x_{15} x_{16} x_{22}^{2}x_{24} x_{25} x_{27} -4x_{15}^{2}x_{22}^{2}x_{24} x_{25} x_{27} +x_{16} x_{18} x_{21} x_{22} x_{24} x_{25} x_{27} -3/2x_{15} x_{18} x_{21} x_{22} x_{24} x_{25} x_{27} -x_{15} x_{16} x_{21} x_{22} x_{24} x_{25} x_{27} +2x_{15}^{2}x_{21} x_{22} x_{24} x_{25} x_{27} +x_{17} x_{18} x_{20} x_{22} x_{24} x_{25} x_{27} -2x_{15} x_{18} x_{20} x_{22} x_{24} x_{25} x_{27} -x_{15} x_{17} x_{20} x_{22} x_{24} x_{25} x_{27} +3x_{15}^{2}x_{20} x_{22} x_{24} x_{25} x_{27} -3/2x_{17} x_{18} x_{19} x_{22} x_{24} x_{25} x_{27} -2x_{16} x_{18} x_{19} x_{22} x_{24} x_{25} x_{27} +8x_{15} x_{18} x_{19} x_{22} x_{24} x_{25} x_{27} +2x_{16} x_{17} x_{19} x_{22} x_{24} x_{25} x_{27} -2x_{15} x_{17} x_{19} x_{22} x_{24} x_{25} x_{27} -3x_{15} x_{16} x_{19} x_{22} x_{24} x_{25} x_{27} -x_{18}^{2}x_{20} x_{21} x_{24} x_{25} x_{27} +2x_{15} x_{18} x_{20} x_{21} x_{24} x_{25} x_{27} -2x_{15}^{2}x_{20} x_{21} x_{24} x_{25} x_{27} +3/2x_{18}^{2}x_{19} x_{21} x_{24} x_{25} x_{27} -x_{16} x_{18} x_{19} x_{21} x_{24} x_{25} x_{27} -2x_{15} x_{18} x_{19} x_{21} x_{24} x_{25} x_{27} +2x_{15} x_{16} x_{19} x_{21} x_{24} x_{25} x_{27} +2x_{18}^{2}x_{19} x_{20} x_{24} x_{25} x_{27} -x_{17} x_{18} x_{19} x_{20} x_{24} x_{25} x_{27} -3x_{15} x_{18} x_{19} x_{20} x_{24} x_{25} x_{27} +2x_{15} x_{17} x_{19} x_{20} x_{24} x_{25} x_{27} -4x_{18}^{2}x_{19}^{2}x_{24} x_{25} x_{27} +2x_{17} x_{18} x_{19}^{2}x_{24} x_{25} x_{27} +3x_{16} x_{18} x_{19}^{2}x_{24} x_{25} x_{27} -2x_{16} x_{17} x_{19}^{2}x_{24} x_{25} x_{27} +3/2x_{16} x_{17} x_{22}^{2}x_{23} x_{25} x_{27} -3x_{15} x_{17} x_{22}^{2}x_{23} x_{25} x_{27} -2x_{16}^{2}x_{22}^{2}x_{23} x_{25} x_{27} +4x_{15} x_{16} x_{22}^{2}x_{23} x_{25} x_{27} -3/2x_{16} x_{18} x_{21} x_{22} x_{23} x_{25} x_{27} +3x_{15} x_{18} x_{21} x_{22} x_{23} x_{25} x_{27} +x_{16}^{2}x_{21} x_{22} x_{23} x_{25} x_{27} -2x_{15} x_{16} x_{21} x_{22} x_{23} x_{25} x_{27} -3/2x_{17} x_{18} x_{20} x_{22} x_{23} x_{25} x_{27} +4x_{16} x_{18} x_{20} x_{22} x_{23} x_{25} x_{27} -4x_{15} x_{18} x_{20} x_{22} x_{23} x_{25} x_{27} -x_{16} x_{17} x_{20} x_{22} x_{23} x_{25} x_{27} +4x_{15} x_{17} x_{20} x_{22} x_{23} x_{25} x_{27} -3x_{15} x_{16} x_{20} x_{22} x_{23} x_{25} x_{27} +3x_{17} x_{18} x_{19} x_{22} x_{23} x_{25} x_{27} -4x_{16} x_{18} x_{19} x_{22} x_{23} x_{25} x_{27} -2x_{16} x_{17} x_{19} x_{22} x_{23} x_{25} x_{27} +3x_{16}^{2}x_{19} x_{22} x_{23} x_{25} x_{27} +3/2x_{18}^{2}x_{20} x_{21} x_{23} x_{25} x_{27} -x_{16} x_{18} x_{20} x_{21} x_{23} x_{25} x_{27} -2x_{15} x_{18} x_{20} x_{21} x_{23} x_{25} x_{27} +2x_{15} x_{16} x_{20} x_{21} x_{23} x_{25} x_{27} -3x_{18}^{2}x_{19} x_{21} x_{23} x_{25} x_{27} +4x_{16} x_{18} x_{19} x_{21} x_{23} x_{25} x_{27} -2x_{16}^{2}x_{19} x_{21} x_{23} x_{25} x_{27} -2x_{18}^{2}x_{20}^{2}x_{23} x_{25} x_{27} +x_{17} x_{18} x_{20}^{2}x_{23} x_{25} x_{27} +3x_{15} x_{18} x_{20}^{2}x_{23} x_{25} x_{27} -2x_{15} x_{17} x_{20}^{2}x_{23} x_{25} x_{27} +4x_{18}^{2}x_{19} x_{20} x_{23} x_{25} x_{27} -2x_{17} x_{18} x_{19} x_{20} x_{23} x_{25} x_{27} -3x_{16} x_{18} x_{19} x_{20} x_{23} x_{25} x_{27} +2x_{16} x_{17} x_{19} x_{20} x_{23} x_{25} x_{27} +1/2x_{17}^{2}x_{22}^{2}x_{24}^{2}x_{27} -2x_{15} x_{17} x_{22}^{2}x_{24}^{2}x_{27} +3x_{15}^{2}x_{22}^{2}x_{24}^{2}x_{27} -x_{17} x_{18} x_{21} x_{22} x_{24}^{2}x_{27} +2x_{15} x_{18} x_{21} x_{22} x_{24}^{2}x_{27} +x_{15} x_{17} x_{21} x_{22} x_{24}^{2}x_{27} -3x_{15}^{2}x_{21} x_{22} x_{24}^{2}x_{27} +2x_{17} x_{18} x_{19} x_{22} x_{24}^{2}x_{27} -6x_{15} x_{18} x_{19} x_{22} x_{24}^{2}x_{27} -x_{17}^{2}x_{19} x_{22} x_{24}^{2}x_{27} +3x_{15} x_{17} x_{19} x_{22} x_{24}^{2}x_{27} +1/2x_{18}^{2}x_{21}^{2}x_{24}^{2}x_{27} -x_{15} x_{18} x_{21}^{2}x_{24}^{2}x_{27} +x_{15}^{2}x_{21}^{2}x_{24}^{2}x_{27} -2x_{18}^{2}x_{19} x_{21} x_{24}^{2}x_{27} +x_{17} x_{18} x_{19} x_{21} x_{24}^{2}x_{27} +3x_{15} x_{18} x_{19} x_{21} x_{24}^{2}x_{27} -2x_{15} x_{17} x_{19} x_{21} x_{24}^{2}x_{27} +3x_{18}^{2}x_{19}^{2}x_{24}^{2}x_{27} -3x_{17} x_{18} x_{19}^{2}x_{24}^{2}x_{27} +x_{17}^{2}x_{19}^{2}x_{24}^{2}x_{27} -3/2x_{17}^{2}x_{22}^{2}x_{23} x_{24} x_{27} +2x_{16} x_{17} x_{22}^{2}x_{23} x_{24} x_{27} +4x_{15} x_{17} x_{22}^{2}x_{23} x_{24} x_{27} -6x_{15} x_{16} x_{22}^{2}x_{23} x_{24} x_{27} +3x_{17} x_{18} x_{21} x_{22} x_{23} x_{24} x_{27} -2x_{16} x_{18} x_{21} x_{22} x_{23} x_{24} x_{27} -4x_{15} x_{18} x_{21} x_{22} x_{23} x_{24} x_{27} -x_{16} x_{17} x_{21} x_{22} x_{23} x_{24} x_{27} -2x_{15} x_{17} x_{21} x_{22} x_{23} x_{24} x_{27} +6x_{15} x_{16} x_{21} x_{22} x_{23} x_{24} x_{27} -2x_{17} x_{18} x_{20} x_{22} x_{23} x_{24} x_{27} +6x_{15} x_{18} x_{20} x_{22} x_{23} x_{24} x_{27} +x_{17}^{2}x_{20} x_{22} x_{23} x_{24} x_{27} -3x_{15} x_{17} x_{20} x_{22} x_{23} x_{24} x_{27} -4x_{17} x_{18} x_{19} x_{22} x_{23} x_{24} x_{27} +6x_{16} x_{18} x_{19} x_{22} x_{23} x_{24} x_{27} +2x_{17}^{2}x_{19} x_{22} x_{23} x_{24} x_{27} -3x_{16} x_{17} x_{19} x_{22} x_{23} x_{24} x_{27} -3/2x_{18}^{2}x_{21}^{2}x_{23} x_{24} x_{27} +x_{16} x_{18} x_{21}^{2}x_{23} x_{24} x_{27} +2x_{15} x_{18} x_{21}^{2}x_{23} x_{24} x_{27} -2x_{15} x_{16} x_{21}^{2}x_{23} x_{24} x_{27} +2x_{18}^{2}x_{20} x_{21} x_{23} x_{24} x_{27} -x_{17} x_{18} x_{20} x_{21} x_{23} x_{24} x_{27} -3x_{15} x_{18} x_{20} x_{21} x_{23} x_{24} x_{27} +2x_{15} x_{17} x_{20} x_{21} x_{23} x_{24} x_{27} +4x_{18}^{2}x_{19} x_{21} x_{23} x_{24} x_{27} -2x_{17} x_{18} x_{19} x_{21} x_{23} x_{24} x_{27} -3x_{16} x_{18} x_{19} x_{21} x_{23} x_{24} x_{27} +2x_{16} x_{17} x_{19} x_{21} x_{23} x_{24} x_{27} -6x_{18}^{2}x_{19} x_{20} x_{23} x_{24} x_{27} +6x_{17} x_{18} x_{19} x_{20} x_{23} x_{24} x_{27} -2x_{17}^{2}x_{19} x_{20} x_{23} x_{24} x_{27} +3/2x_{17}^{2}x_{22}^{2}x_{23}^{2}x_{27} -4x_{16} x_{17} x_{22}^{2}x_{23}^{2}x_{27} +3x_{16}^{2}x_{22}^{2}x_{23}^{2}x_{27} -3x_{17} x_{18} x_{21} x_{22} x_{23}^{2}x_{27} +4x_{16} x_{18} x_{21} x_{22} x_{23}^{2}x_{27} +2x_{16} x_{17} x_{21} x_{22} x_{23}^{2}x_{27} -3x_{16}^{2}x_{21} x_{22} x_{23}^{2}x_{27} +4x_{17} x_{18} x_{20} x_{22} x_{23}^{2}x_{27} -6x_{16} x_{18} x_{20} x_{22} x_{23}^{2}x_{27} -2x_{17}^{2}x_{20} x_{22} x_{23}^{2}x_{27} +3x_{16} x_{17} x_{20} x_{22} x_{23}^{2}x_{27} +3/2x_{18}^{2}x_{21}^{2}x_{23}^{2}x_{27} -2x_{16} x_{18} x_{21}^{2}x_{23}^{2}x_{27} +x_{16}^{2}x_{21}^{2}x_{23}^{2}x_{27} -4x_{18}^{2}x_{20} x_{21} x_{23}^{2}x_{27} +2x_{17} x_{18} x_{20} x_{21} x_{23}^{2}x_{27} +3x_{16} x_{18} x_{20} x_{21} x_{23}^{2}x_{27} -2x_{16} x_{17} x_{20} x_{21} x_{23}^{2}x_{27} +3x_{18}^{2}x_{20}^{2}x_{23}^{2}x_{27} -3x_{17} x_{18} x_{20}^{2}x_{23}^{2}x_{27} +x_{17}^{2}x_{20}^{2}x_{23}^{2}x_{27} -1, 3x_{7} x_{14} +3x_{6} x_{13} +2x_{5} x_{12} +4x_{4} x_{11} +2x_{3} x_{10} +x_{2} x_{9} +x_{1} x_{8} -4, 2x_{7} x_{14} +2x_{6} x_{13} +2x_{5} x_{12} +3x_{4} x_{11} +x_{3} x_{10} +x_{2} x_{9} +x_{1} x_{8} -3, x_{7} x_{14} +x_{6} x_{13} +x_{5} x_{12} +2x_{4} x_{11} +x_{3} x_{10} +x_{2} x_{9} +x_{1} x_{8} -2, x_{7} x_{13} +x_{2} x_{8} , x_{7} x_{12} -x_{3} x_{8} , x_{7} x_{11} +x_{4} x_{8} , x_{7} x_{10} -x_{5} x_{8} , x_{7} x_{9} +x_{6} x_{8} , x_{6} x_{14} +x_{1} x_{9} , 2x_{7} x_{14} +x_{6} x_{13} +x_{5} x_{12} +2x_{4} x_{11} +x_{3} x_{10} +x_{2} x_{9} -2, x_{6} x_{12} +x_{3} x_{9} , x_{6} x_{11} -x_{4} x_{9} , x_{6} x_{10} +x_{5} x_{9} , x_{5} x_{14} -x_{1} x_{10} , x_{5} x_{13} +x_{2} x_{10} , x_{5} x_{11} +x_{4} x_{10} , x_{4} x_{14} +x_{1} x_{11} , x_{4} x_{13} -x_{2} x_{11} , x_{4} x_{12} +x_{3} x_{11} , x_{3} x_{14} -x_{1} x_{12} , x_{3} x_{13} +x_{2} x_{12} , x_{2} x_{14} +x_{1} x_{13} , x_{1} x_{18} -x_{1} x_{15} , x_{2} x_{18} -x_{2} x_{16} +x_{2} x_{15} , x_{3} x_{18} -x_{3} x_{17} +x_{3} x_{16} , x_{4} x_{18} , x_{5} x_{17} -x_{5} x_{16} , x_{6} x_{16} -x_{6} x_{15} , x_{7} x_{15} , x_{8} x_{18} -x_{8} x_{15} , x_{9} x_{18} -x_{9} x_{16} +x_{9} x_{15} , x_{10} x_{18} -x_{10} x_{17} +x_{10} x_{16} , x_{11} x_{18} , x_{12} x_{17} -x_{12} x_{16} , x_{13} x_{16} -x_{13} x_{15} , x_{14} x_{15} , x_{1} x_{22} -x_{1} x_{19} , x_{2} x_{22} -x_{2} x_{20} +x_{2} x_{19} , x_{3} x_{22} -x_{3} x_{21} +x_{3} x_{20} , x_{4} x_{22} , x_{5} x_{21} -x_{5} x_{20} , x_{6} x_{20} -x_{6} x_{19} , x_{7} x_{19} , x_{8} x_{22} -x_{8} x_{19} , x_{9} x_{22} -x_{9} x_{20} +x_{9} x_{19} , x_{10} x_{22} -x_{10} x_{21} +x_{10} x_{20} , x_{11} x_{22} , x_{12} x_{21} -x_{12} x_{20} , x_{13} x_{20} -x_{13} x_{19} , x_{14} x_{19} , x_{1} x_{26} -x_{1} x_{23} , x_{2} x_{26} -x_{2} x_{24} +x_{2} x_{23} , x_{3} x_{26} -x_{3} x_{25} +x_{3} x_{24} , x_{4} x_{26} , x_{5} x_{25} -x_{5} x_{24} , x_{6} x_{24} -x_{6} x_{23} , x_{7} x_{23} , x_{8} x_{26} -x_{8} x_{23} , x_{9} x_{26} -x_{9} x_{24} +x_{9} x_{23} , x_{10} x_{26} -x_{10} x_{25} +x_{10} x_{24} , x_{11} x_{26} , x_{12} x_{25} -x_{12} x_{24} , x_{13} x_{24} -x_{13} x_{23} , x_{14} x_{23} )