Subalgebra \(A^{5}_2+A^{1}_1\) ↪ \(E^{1}_6\)
84 out of 119
Computations done by the calculator project.

Subalgebra type: \(\displaystyle A^{5}_2+A^{1}_1\) (click on type for detailed printout).
Subalgebra is (parabolically) induced from \(\displaystyle A^{5}_2\) .
Centralizer: 0
The semisimple part of the centralizer of the semisimple part of my centralizer: \(\displaystyle E^{1}_6\)

Elements Cartan subalgebra scaled to act by two by components: \(\displaystyle A^{5}_2\): (3, 4, 5, 7, 5, 3): 10, (-1, -2, 0, -2, -2, -2): 10, \(\displaystyle A^{1}_1\): (0, 0, 0, 1, 1, 0): 2
Dimension of subalgebra generated by predefined or computed generators: 11.
Negative simple generators: \(\displaystyle g_{-22}+g_{-24}+g_{-28}\), \(\displaystyle g_{11}+2g_{8}+g_{1}\), \(\displaystyle g_{-10}\)
Positive simple generators: \(\displaystyle 2g_{28}+g_{24}+2g_{22}\), \(\displaystyle g_{-1}+g_{-8}+2g_{-11}\), \(\displaystyle g_{10}\)
Cartan symmetric matrix: \(\displaystyle \begin{pmatrix}2/5 & -1/5 & 0\\ -1/5 & 2/5 & 0\\ 0 & 0 & 2\\ \end{pmatrix}\)
Scalar products of elements of Cartan subalgebra scaled to act by 2 (co-symmetric Cartan matrix): \(\displaystyle \begin{pmatrix}10 & -5 & 0\\ -5 & 10 & 0\\ 0 & 0 & 2\\ \end{pmatrix}\)
Decomposition of ambient Lie algebra: \(\displaystyle V_{3\omega_{2}+\omega_{3}}\oplus V_{3\omega_{1}+\omega_{3}}\oplus V_{2\omega_{1}+2\omega_{2}}\oplus V_{2\omega_{3}}\oplus V_{\omega_{1}+\omega_{2}}\)
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.
Highest vectors of representations (total 5) ; the vectors are over the primal subalgebra.\(g_{21}-2g_{19}+2g_{12}\)\(g_{10}\)\(g_{29}\)\(g_{35}\)\(g_{15}\)
weight\(\omega_{1}+\omega_{2}\)\(2\omega_{3}\)\(2\omega_{1}+2\omega_{2}\)\(3\omega_{1}+\omega_{3}\)\(3\omega_{2}+\omega_{3}\)
Isotypic module decomposition over primal subalgebra (total 5 isotypic components).
Isotypical components + highest weight\(\displaystyle V_{\omega_{1}+\omega_{2}} \) → (1, 1, 0)\(\displaystyle V_{2\omega_{3}} \) → (0, 0, 2)\(\displaystyle V_{2\omega_{1}+2\omega_{2}} \) → (2, 2, 0)\(\displaystyle V_{3\omega_{1}+\omega_{3}} \) → (3, 0, 1)\(\displaystyle V_{3\omega_{2}+\omega_{3}} \) → (0, 3, 1)
Module label \(W_{1}\)\(W_{2}\)\(W_{3}\)\(W_{4}\)\(W_{5}\)
Module elements (weight vectors). In blue - corresp. F element. In red -corresp. H element. Semisimple subalgebra component.
\(-1/2g_{21}+g_{19}-g_{12}\)
\(-1/2g_{-1}-1/2g_{-8}-g_{-11}\)
\(g_{28}+1/2g_{24}+g_{22}\)
\(-h_{6}-h_{5}-h_{4}-h_{2}-1/2h_{1}\)
\(-3/2h_{6}-5/2h_{5}-7/2h_{4}-5/2h_{3}-2h_{2}-3/2h_{1}\)
\(-1/2g_{-22}-1/2g_{-24}-1/2g_{-28}\)
\(g_{11}+2g_{8}+g_{1}\)
\(-1/2g_{-12}+1/2g_{-19}-1/2g_{-21}\)
Semisimple subalgebra component.
\(-g_{10}\)
\(h_{5}+h_{4}\)
\(2g_{-10}\)
\(g_{29}\)
\(-g_{9}\)
\(-g_{34}\)
\(g_{-20}\)
\(g_{21}-g_{12}\)
\(g_{21}+g_{19}\)
\(-2g_{36}\)
\(g_{-8}-2g_{-11}\)
\(-g_{-1}+g_{-8}-g_{-11}\)
\(-2g_{28}+2g_{24}\)
\(-2g_{28}+g_{24}+g_{22}\)
\(-g_{-30}\)
\(-2h_{6}-2h_{5}+2h_{4}+2h_{2}\)
\(-h_{6}-h_{5}+2h_{4}+2h_{2}-h_{1}\)
\(-6g_{30}\)
\(h_{6}+2h_{4}+h_{2}-2h_{1}\)
\(-2g_{-24}+g_{-28}\)
\(6g_{11}-12g_{8}\)
\(-g_{-22}-4g_{-24}+3g_{-28}\)
\(4g_{11}-10g_{8}+2g_{1}\)
\(-g_{-36}\)
\(-2g_{-12}+4g_{-21}\)
\(24g_{20}\)
\(-4g_{-12}+g_{-19}+10g_{-21}\)
\(2g_{-34}\)
\(6g_{-9}\)
\(2g_{-29}\)
\(g_{35}\)
\(-g_{23}-g_{18}\)
\(g_{32}\)
\(g_{-2}-2g_{-6}\)
\(g_{31}+g_{26}\)
\(g_{13}+g_{7}\)
\(3g_{-27}\)
\(-2g_{5}-2g_{4}\)
\(g_{-14}+2g_{-16}\)
\(-g_{25}-g_{17}\)
\(3g_{-17}-3g_{-25}\)
\(3g_{-33}\)
\(2g_{16}-4g_{14}\)
\(2g_{-4}-2g_{-5}\)
\(6g_{-7}-6g_{-13}\)
\(3g_{-26}-3g_{-31}\)
\(2g_{6}+4g_{2}\)
\(-18g_{-3}\)
\(6g_{-18}-6g_{-23}\)
\(-18g_{-15}\)
\(g_{15}\)
\(-2g_{23}+g_{18}\)
\(-g_{3}\)
\(-g_{-2}-g_{-6}\)
\(2g_{31}-4g_{26}\)
\(2g_{13}-g_{7}\)
\(-g_{5}+2g_{4}\)
\(-g_{-14}+g_{-16}\)
\(6g_{33}\)
\(-2g_{25}+4g_{17}\)
\(g_{-17}+2g_{-25}\)
\(-2g_{16}-2g_{14}\)
\(g_{-4}+2g_{-5}\)
\(-6g_{27}\)
\(2g_{-7}+g_{-13}\)
\(g_{-26}+2g_{-31}\)
\(-2g_{6}+2g_{2}\)
\(-3g_{-32}\)
\(2g_{-18}+g_{-23}\)
\(3g_{-35}\)
Weights of elements in fundamental coords w.r.t. Cartan of subalgebra in same order as above\(\omega_{1}+\omega_{2}\)
\(-\omega_{1}+2\omega_{2}\)
\(2\omega_{1}-\omega_{2}\)
\(0\)
\(0\)
\(-2\omega_{1}+\omega_{2}\)
\(\omega_{1}-2\omega_{2}\)
\(-\omega_{1}-\omega_{2}\)		\(2\omega_{3}\)
\(0\)
\(-2\omega_{3}\)		\(2\omega_{1}+2\omega_{2}\)
\(3\omega_{2}\)
\(3\omega_{1}\)
\(-2\omega_{1}+4\omega_{2}\)
\(\omega_{1}+\omega_{2}\)
\(\omega_{1}+\omega_{2}\)
\(4\omega_{1}-2\omega_{2}\)
\(-\omega_{1}+2\omega_{2}\)
\(-\omega_{1}+2\omega_{2}\)
\(2\omega_{1}-\omega_{2}\)
\(2\omega_{1}-\omega_{2}\)
\(-3\omega_{1}+3\omega_{2}\)
\(0\)
\(0\)
\(3\omega_{1}-3\omega_{2}\)
\(0\)
\(-2\omega_{1}+\omega_{2}\)
\(\omega_{1}-2\omega_{2}\)
\(-2\omega_{1}+\omega_{2}\)
\(\omega_{1}-2\omega_{2}\)
\(-4\omega_{1}+2\omega_{2}\)
\(-\omega_{1}-\omega_{2}\)
\(2\omega_{1}-4\omega_{2}\)
\(-\omega_{1}-\omega_{2}\)
\(-3\omega_{1}\)
\(-3\omega_{2}\)
\(-2\omega_{1}-2\omega_{2}\)		\(3\omega_{1}+\omega_{3}\)
\(\omega_{1}+\omega_{2}+\omega_{3}\)
\(3\omega_{1}-\omega_{3}\)
\(-\omega_{1}+2\omega_{2}+\omega_{3}\)
\(2\omega_{1}-\omega_{2}+\omega_{3}\)
\(\omega_{1}+\omega_{2}-\omega_{3}\)
\(-3\omega_{1}+3\omega_{2}+\omega_{3}\)
\(\omega_{3}\)
\(-\omega_{1}+2\omega_{2}-\omega_{3}\)
\(2\omega_{1}-\omega_{2}-\omega_{3}\)
\(-2\omega_{1}+\omega_{2}+\omega_{3}\)
\(-3\omega_{1}+3\omega_{2}-\omega_{3}\)
\(\omega_{1}-2\omega_{2}+\omega_{3}\)
\(-\omega_{3}\)
\(-\omega_{1}-\omega_{2}+\omega_{3}\)
\(-2\omega_{1}+\omega_{2}-\omega_{3}\)
\(\omega_{1}-2\omega_{2}-\omega_{3}\)
\(-3\omega_{2}+\omega_{3}\)
\(-\omega_{1}-\omega_{2}-\omega_{3}\)
\(-3\omega_{2}-\omega_{3}\)		\(3\omega_{2}+\omega_{3}\)
\(\omega_{1}+\omega_{2}+\omega_{3}\)
\(3\omega_{2}-\omega_{3}\)
\(-\omega_{1}+2\omega_{2}+\omega_{3}\)
\(2\omega_{1}-\omega_{2}+\omega_{3}\)
\(\omega_{1}+\omega_{2}-\omega_{3}\)
\(\omega_{3}\)
\(-\omega_{1}+2\omega_{2}-\omega_{3}\)
\(3\omega_{1}-3\omega_{2}+\omega_{3}\)
\(2\omega_{1}-\omega_{2}-\omega_{3}\)
\(-2\omega_{1}+\omega_{2}+\omega_{3}\)
\(\omega_{1}-2\omega_{2}+\omega_{3}\)
\(-\omega_{3}\)
\(3\omega_{1}-3\omega_{2}-\omega_{3}\)
\(-\omega_{1}-\omega_{2}+\omega_{3}\)
\(-2\omega_{1}+\omega_{2}-\omega_{3}\)
\(\omega_{1}-2\omega_{2}-\omega_{3}\)
\(-3\omega_{1}+\omega_{3}\)
\(-\omega_{1}-\omega_{2}-\omega_{3}\)
\(-3\omega_{1}-\omega_{3}\)
Weights of elements in (fundamental coords w.r.t. Cartan of subalgebra) + Cartan centralizer\(\omega_{1}+\omega_{2}\)
\(-\omega_{1}+2\omega_{2}\)
\(2\omega_{1}-\omega_{2}\)
\(0\)
\(0\)
\(-2\omega_{1}+\omega_{2}\)
\(\omega_{1}-2\omega_{2}\)
\(-\omega_{1}-\omega_{2}\)		\(2\omega_{3}\)
\(0\)
\(-2\omega_{3}\)		\(2\omega_{1}+2\omega_{2}\)
\(3\omega_{2}\)
\(3\omega_{1}\)
\(-2\omega_{1}+4\omega_{2}\)
\(\omega_{1}+\omega_{2}\)
\(\omega_{1}+\omega_{2}\)
\(4\omega_{1}-2\omega_{2}\)
\(-\omega_{1}+2\omega_{2}\)
\(-\omega_{1}+2\omega_{2}\)
\(2\omega_{1}-\omega_{2}\)
\(2\omega_{1}-\omega_{2}\)
\(-3\omega_{1}+3\omega_{2}\)
\(0\)
\(0\)
\(3\omega_{1}-3\omega_{2}\)
\(0\)
\(-2\omega_{1}+\omega_{2}\)
\(\omega_{1}-2\omega_{2}\)
\(-2\omega_{1}+\omega_{2}\)
\(\omega_{1}-2\omega_{2}\)
\(-4\omega_{1}+2\omega_{2}\)
\(-\omega_{1}-\omega_{2}\)
\(2\omega_{1}-4\omega_{2}\)
\(-\omega_{1}-\omega_{2}\)
\(-3\omega_{1}\)
\(-3\omega_{2}\)
\(-2\omega_{1}-2\omega_{2}\)		\(3\omega_{1}+\omega_{3}\)
\(\omega_{1}+\omega_{2}+\omega_{3}\)
\(3\omega_{1}-\omega_{3}\)
\(-\omega_{1}+2\omega_{2}+\omega_{3}\)
\(2\omega_{1}-\omega_{2}+\omega_{3}\)
\(\omega_{1}+\omega_{2}-\omega_{3}\)
\(-3\omega_{1}+3\omega_{2}+\omega_{3}\)
\(\omega_{3}\)
\(-\omega_{1}+2\omega_{2}-\omega_{3}\)
\(2\omega_{1}-\omega_{2}-\omega_{3}\)
\(-2\omega_{1}+\omega_{2}+\omega_{3}\)
\(-3\omega_{1}+3\omega_{2}-\omega_{3}\)
\(\omega_{1}-2\omega_{2}+\omega_{3}\)
\(-\omega_{3}\)
\(-\omega_{1}-\omega_{2}+\omega_{3}\)
\(-2\omega_{1}+\omega_{2}-\omega_{3}\)
\(\omega_{1}-2\omega_{2}-\omega_{3}\)
\(-3\omega_{2}+\omega_{3}\)
\(-\omega_{1}-\omega_{2}-\omega_{3}\)
\(-3\omega_{2}-\omega_{3}\)		\(3\omega_{2}+\omega_{3}\)
\(\omega_{1}+\omega_{2}+\omega_{3}\)
\(3\omega_{2}-\omega_{3}\)
\(-\omega_{1}+2\omega_{2}+\omega_{3}\)
\(2\omega_{1}-\omega_{2}+\omega_{3}\)
\(\omega_{1}+\omega_{2}-\omega_{3}\)
\(\omega_{3}\)
\(-\omega_{1}+2\omega_{2}-\omega_{3}\)
\(3\omega_{1}-3\omega_{2}+\omega_{3}\)
\(2\omega_{1}-\omega_{2}-\omega_{3}\)
\(-2\omega_{1}+\omega_{2}+\omega_{3}\)
\(\omega_{1}-2\omega_{2}+\omega_{3}\)
\(-\omega_{3}\)
\(3\omega_{1}-3\omega_{2}-\omega_{3}\)
\(-\omega_{1}-\omega_{2}+\omega_{3}\)
\(-2\omega_{1}+\omega_{2}-\omega_{3}\)
\(\omega_{1}-2\omega_{2}-\omega_{3}\)
\(-3\omega_{1}+\omega_{3}\)
\(-\omega_{1}-\omega_{2}-\omega_{3}\)
\(-3\omega_{1}-\omega_{3}\)
Single module character over Cartan of s.a.+ Cartan of centralizer of s.a.\(\displaystyle M_{\omega_{1}+\omega_{2}}\oplus M_{-\omega_{1}+2\omega_{2}}\oplus M_{2\omega_{1}-\omega_{2}}\oplus 2M_{0}\oplus M_{-2\omega_{1}+\omega_{2}}
\oplus M_{\omega_{1}-2\omega_{2}}\oplus M_{-\omega_{1}-\omega_{2}}\)		\(\displaystyle M_{2\omega_{3}}\oplus M_{0}\oplus M_{-2\omega_{3}}\)\(\displaystyle M_{2\omega_{1}+2\omega_{2}}\oplus M_{3\omega_{2}}\oplus M_{3\omega_{1}}\oplus M_{-2\omega_{1}+4\omega_{2}}\oplus 2M_{\omega_{1}+\omega_{2}}
\oplus M_{4\omega_{1}-2\omega_{2}}\oplus 2M_{-\omega_{1}+2\omega_{2}}\oplus 2M_{2\omega_{1}-\omega_{2}}\oplus M_{-3\omega_{1}+3\omega_{2}}
\oplus 3M_{0}\oplus M_{3\omega_{1}-3\omega_{2}}\oplus 2M_{-2\omega_{1}+\omega_{2}}\oplus 2M_{\omega_{1}-2\omega_{2}}\oplus M_{-4\omega_{1}+2\omega_{2}}
\oplus 2M_{-\omega_{1}-\omega_{2}}\oplus M_{2\omega_{1}-4\omega_{2}}\oplus M_{-3\omega_{1}}\oplus M_{-3\omega_{2}}\oplus M_{-2\omega_{1}-2\omega_{2}}\)		\(\displaystyle M_{3\omega_{1}+\omega_{3}}\oplus M_{\omega_{1}+\omega_{2}+\omega_{3}}\oplus M_{-\omega_{1}+2\omega_{2}+\omega_{3}}\oplus M_{2\omega_{1}-\omega_{2}+\omega_{3}}
\oplus M_{3\omega_{1}-\omega_{3}}\oplus M_{-3\omega_{1}+3\omega_{2}+\omega_{3}}\oplus M_{\omega_{3}}\oplus M_{\omega_{1}+\omega_{2}-\omega_{3}}
\oplus M_{-2\omega_{1}+\omega_{2}+\omega_{3}}\oplus M_{\omega_{1}-2\omega_{2}+\omega_{3}}\oplus M_{-\omega_{1}+2\omega_{2}-\omega_{3}}
\oplus M_{2\omega_{1}-\omega_{2}-\omega_{3}}\oplus M_{-\omega_{1}-\omega_{2}+\omega_{3}}\oplus M_{-3\omega_{1}+3\omega_{2}-\omega_{3}}
\oplus M_{-\omega_{3}}\oplus M_{-3\omega_{2}+\omega_{3}}\oplus M_{-2\omega_{1}+\omega_{2}-\omega_{3}}\oplus M_{\omega_{1}-2\omega_{2}-\omega_{3}}
\oplus M_{-\omega_{1}-\omega_{2}-\omega_{3}}\oplus M_{-3\omega_{2}-\omega_{3}}\)		\(\displaystyle M_{3\omega_{2}+\omega_{3}}\oplus M_{\omega_{1}+\omega_{2}+\omega_{3}}\oplus M_{-\omega_{1}+2\omega_{2}+\omega_{3}}\oplus M_{2\omega_{1}-\omega_{2}+\omega_{3}}
\oplus M_{3\omega_{2}-\omega_{3}}\oplus M_{\omega_{3}}\oplus M_{3\omega_{1}-3\omega_{2}+\omega_{3}}\oplus M_{\omega_{1}+\omega_{2}-\omega_{3}}
\oplus M_{-2\omega_{1}+\omega_{2}+\omega_{3}}\oplus M_{\omega_{1}-2\omega_{2}+\omega_{3}}\oplus M_{-\omega_{1}+2\omega_{2}-\omega_{3}}
\oplus M_{2\omega_{1}-\omega_{2}-\omega_{3}}\oplus M_{-\omega_{1}-\omega_{2}+\omega_{3}}\oplus M_{-\omega_{3}}\oplus M_{3\omega_{1}-3\omega_{2}-\omega_{3}}
\oplus M_{-3\omega_{1}+\omega_{3}}\oplus M_{-2\omega_{1}+\omega_{2}-\omega_{3}}\oplus M_{\omega_{1}-2\omega_{2}-\omega_{3}}
\oplus M_{-\omega_{1}-\omega_{2}-\omega_{3}}\oplus M_{-3\omega_{1}-\omega_{3}}\)
Isotypic character\(\displaystyle M_{\omega_{1}+\omega_{2}}\oplus M_{-\omega_{1}+2\omega_{2}}\oplus M_{2\omega_{1}-\omega_{2}}\oplus 2M_{0}\oplus M_{-2\omega_{1}+\omega_{2}}
\oplus M_{\omega_{1}-2\omega_{2}}\oplus M_{-\omega_{1}-\omega_{2}}\)		\(\displaystyle M_{2\omega_{3}}\oplus M_{0}\oplus M_{-2\omega_{3}}\)\(\displaystyle M_{2\omega_{1}+2\omega_{2}}\oplus M_{3\omega_{2}}\oplus M_{3\omega_{1}}\oplus M_{-2\omega_{1}+4\omega_{2}}\oplus 2M_{\omega_{1}+\omega_{2}}
\oplus M_{4\omega_{1}-2\omega_{2}}\oplus 2M_{-\omega_{1}+2\omega_{2}}\oplus 2M_{2\omega_{1}-\omega_{2}}\oplus M_{-3\omega_{1}+3\omega_{2}}
\oplus 3M_{0}\oplus M_{3\omega_{1}-3\omega_{2}}\oplus 2M_{-2\omega_{1}+\omega_{2}}\oplus 2M_{\omega_{1}-2\omega_{2}}\oplus M_{-4\omega_{1}+2\omega_{2}}
\oplus 2M_{-\omega_{1}-\omega_{2}}\oplus M_{2\omega_{1}-4\omega_{2}}\oplus M_{-3\omega_{1}}\oplus M_{-3\omega_{2}}\oplus M_{-2\omega_{1}-2\omega_{2}}\)		\(\displaystyle M_{3\omega_{1}+\omega_{3}}\oplus M_{\omega_{1}+\omega_{2}+\omega_{3}}\oplus M_{-\omega_{1}+2\omega_{2}+\omega_{3}}\oplus M_{2\omega_{1}-\omega_{2}+\omega_{3}}
\oplus M_{3\omega_{1}-\omega_{3}}\oplus M_{-3\omega_{1}+3\omega_{2}+\omega_{3}}\oplus M_{\omega_{3}}\oplus M_{\omega_{1}+\omega_{2}-\omega_{3}}
\oplus M_{-2\omega_{1}+\omega_{2}+\omega_{3}}\oplus M_{\omega_{1}-2\omega_{2}+\omega_{3}}\oplus M_{-\omega_{1}+2\omega_{2}-\omega_{3}}
\oplus M_{2\omega_{1}-\omega_{2}-\omega_{3}}\oplus M_{-\omega_{1}-\omega_{2}+\omega_{3}}\oplus M_{-3\omega_{1}+3\omega_{2}-\omega_{3}}
\oplus M_{-\omega_{3}}\oplus M_{-3\omega_{2}+\omega_{3}}\oplus M_{-2\omega_{1}+\omega_{2}-\omega_{3}}\oplus M_{\omega_{1}-2\omega_{2}-\omega_{3}}
\oplus M_{-\omega_{1}-\omega_{2}-\omega_{3}}\oplus M_{-3\omega_{2}-\omega_{3}}\)		\(\displaystyle M_{3\omega_{2}+\omega_{3}}\oplus M_{\omega_{1}+\omega_{2}+\omega_{3}}\oplus M_{-\omega_{1}+2\omega_{2}+\omega_{3}}\oplus M_{2\omega_{1}-\omega_{2}+\omega_{3}}
\oplus M_{3\omega_{2}-\omega_{3}}\oplus M_{\omega_{3}}\oplus M_{3\omega_{1}-3\omega_{2}+\omega_{3}}\oplus M_{\omega_{1}+\omega_{2}-\omega_{3}}
\oplus M_{-2\omega_{1}+\omega_{2}+\omega_{3}}\oplus M_{\omega_{1}-2\omega_{2}+\omega_{3}}\oplus M_{-\omega_{1}+2\omega_{2}-\omega_{3}}
\oplus M_{2\omega_{1}-\omega_{2}-\omega_{3}}\oplus M_{-\omega_{1}-\omega_{2}+\omega_{3}}\oplus M_{-\omega_{3}}\oplus M_{3\omega_{1}-3\omega_{2}-\omega_{3}}
\oplus M_{-3\omega_{1}+\omega_{3}}\oplus M_{-2\omega_{1}+\omega_{2}-\omega_{3}}\oplus M_{\omega_{1}-2\omega_{2}-\omega_{3}}
\oplus M_{-\omega_{1}-\omega_{2}-\omega_{3}}\oplus M_{-3\omega_{1}-\omega_{3}}\)

Semisimple subalgebra: W_{1}+W_{2}
Centralizer extension: 0

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 812 arithmetic operations while solving the Serre relations polynomial system.