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三洋三洋
2024-02-07 12:18:23 +00:00
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src/models/tokenizer/test_long_formulas.txt
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@@ -26,4 +26,6 @@
&&&\times\prod_{\overset{1\leq i\leq k-1}{i\notin S}}\frac{(Q+(Q+r)X_k+X_i+X_iX_k)(X_iX_k-Q)}{(Q+rX_k+QX_k)(Q+rX_i+QX_i)} \\
&&&\times\prod_{\overset{k+1\leq i\leq n}{i\notin S}}\frac{(Q+(Q+r)X_k+X_i+X_iX_k)(Q-X_iX_k)}{(Q+rX_k+QX_k)(Q+rX_i+QX_i)} \\
&&&&\times\prod_{1\leq i<j\leq n,i,j\notin S\cup\{k\}}\left(\frac{X_j(1+X_j)}{Q+rX_j+QX_j}-\frac{X_i(1+X_i)}{Q+rX_i+QX_i}\right).
\end{aligned}
\end{aligned}
\[w_{\mathbb{A}}\left(\begin{bmatrix}T_{1}&T_{2}&T_{3}\\ T_{2}&T_{3}&iT_{1}\\ T_{3}&iT_{1}&iT_{2}\end{bmatrix}\right)=w_{\mathbb{A}}\left(\mathbb{V}^{\#_{ \mathbb{A}}}\begin{bmatrix}T_{1}&T_{2}&T_{3}\\ T_{2}&T_{3}&iT_{1}\\ T_{3}&iT_{1}&iT_{2}\end{bmatrix}\mathbb{V}\right)\] \[=\frac{1}{2}w_{\mathbb{A}}\left(\begin{bmatrix}T_{1}^{\#_{A}}- iT_{2}^{\#_{A}}&-i\sqrt{2}(T_{1}^{\#_{A}}+T_{2}^{\#_{A}})&2T_{3}^{\#_{A}}- iT_{1}^{\#_{A}}+T_{2}^{\#_{A}}\\ i\sqrt{2}(T_{2}^{\#_{A}}-T_{1}^{\#_{A}})&2T_{3}^{\#_{A}}&\sqrt{2}(T_{1}^{\#_{A} }+T_{2}^{\#_{A}})\\ 2T_{3}^{\#_{A}}-(-iT_{1}^{\#_{A}}+T_{2}^{\#_{A}})&\sqrt{2}(T_{2}^{\#_{A}}-T_{ 1}^{\#_{A}})&T_{1}^{\#_{A}}-iT_{2}^{\#_{A}}\end{bmatrix}\right)\] \[\leq w_{\mathbb{A}}\left(\begin{bmatrix}O&O&T_{3}\\ O&T_{3}&O\\ T_{3}&O&O\end{bmatrix}^{\#_{\mathbb{A}}}\right)+\frac{1}{2}w_{\mathbb{A}}\left( \begin{bmatrix}T_{1}+iT_{2}&O&-(iT_{1}+T_{2})\\ O&O&O\\ iT_{1}+T_{2}&O&T_{1}+iT_{2}\end{bmatrix}^{\#_{\mathbb{A}}}\right)\] \[+\frac{1}{\sqrt{2}}w_{\mathbb{A}}\left(\begin{bmatrix}O&-i(T_{2} -T_{1})&O\\ i(T_{1}+T_{2})&O&O\\ O&O&O\end{bmatrix}^{\#_{\mathbb{A}}}\right)+\frac{1}{\sqrt{2}}w_{\mathbb{A}} \left(\begin{bmatrix}O&O&O\\ O&O&(T_{2}-T_{1})\\ O&T_{1}+T_{2}&O\end{bmatrix}^{\#_{\mathbb{A}}}\right)\] \[=w_{\mathbb{A}}\left(\begin{bmatrix}O&O&T_{3}\\ O&T_{3}&O\\ T_{3}&O&O\end{bmatrix}\right)+\frac{1}{2}w_{\mathbb{A}}\left(\begin{bmatrix}T_{ 1}+iT_{2}&O&-(iT_{1}+T_{2})\\ O&O&O\\ iT_{1}+T_{2}&O&T_{1}+iT_{2}\end{bmatrix}\right)\] \[+\frac{1}{\sqrt{2}}w_{\mathbb{A}}\left(\begin{bmatrix}O&-i(T_{2} -T_{1})&O\\ i(T_{1}+T_{2})&O&O\\ O&O&O\end{bmatrix}\right)+\frac{1}{\sqrt{2}}w_{\mathbb{A}}\left(\begin{bmatrix} O&O&O\\ O&O&(T_{2}-T_{1})\\ O&T_{1}+T_{2}&O\end{bmatrix}\right)\] \[\leq w_{A}(T_{3})+\max\{w_{A}(T_{1}),w_{A}(T_{2})\}+\frac{1}{ \sqrt{2}}w_{\mathbb{A}}\left(\begin{bmatrix}O&-i(T_{2}-T_{1})&O\\ O&O&O\\ O&O&O\end{bmatrix}\right)+\frac{1}{\sqrt{2}}w_{\mathbb{A}}\left(\begin{bmatrix} O&O&O\\ i(T_{1}+T_{2})&O&O\\ O&O&O\end{bmatrix}\right)\] \[+\frac{1}{\sqrt{2}}w_{\mathbb{A}}\left(\begin{bmatrix}O&O&O\\ O&O&(T_{2}-T_{1})\\ O&O&O\end{bmatrix}\right)+\frac{1}{\sqrt{2}}w_{\mathbb{A}}\left(\begin{bmatrix} O&O&O\\ O&O&O\\ O&T_{1}+T_{2}&O\end{bmatrix}\right)\] \[=w_{A}(T_{3})+\max\{w_{A}(T_{1}),w_{A}(T_{2})\}+\frac{1}{\sqrt{2 }}\left(\|T_{1}-T_{2}\|_{A}+\|T_{1}+T_{2}\|_{A}\right),\]