\usepackage or this document’s own macros. Corpus-wide, \bm occurs 327 times, \Perp is defined by no package and spans 10 documents, and 11,088 of 11,624 undefined occurrences are the source document’s own macros. A row that looks wrong here may be correct, and one that looks right here may not compile. The LaTeX report renders through the document’s own preamble and is the surface to judge from.476 rows
The page, the confidence and the picture of an inline formula are its HOST LINE's --- a formula has none of its own. A line's confidence is not a formula's.
| Identifier | Page | Conf. | LaTeX source | Rendered | Image |
|---|---|---|---|---|---|
| rph8-g15q_FO0001 | 1 | 0.280 | { }^{\text {® }} | | |
| rph8-g15q_FO0002 | 1 | 0.280 | { }^{1,2, *} | | |
| rph8-g15q_FO0003 | 1 | 0.280 | { }^{3,4, \dagger} | | |
| rph8-g15q_FO0004 | 1 | 0.280 | { }^{5, \ddagger} | | |
| rph8-g15q_FO0005 | 1 | 1.000 | { }^{\dagger} | | |
| rph8-g15q_FO0006 | 1 | 1.000 | { }^{\ddagger} | | |
| rph8-g15q_FO0007 | 3 | 1.000 | x | | |
| rph8-g15q_FO0008 | 3 | 1.000 | \theta | | |
| rph8-g15q_FO0009 | 3 | 0.466 | \rangle | | |
| rph8-g15q_FO0010 | 3 | 1.000 | v=\left(v_{1}, \ldots, v_{d}\right) | | |
| rph8-g15q_FO0011 | 3 | 1.000 | \mathbb{R}^{d} | | |
| rph8-g15q_FO0012 | 3 | 1.000 | \mathcal{H} | | |
| rph8-g15q_FO0013 | 3 | 1.000 | \mathscr{S}(\mathcal{H}) | | |
| rph8-g15q_FO0014 | 3 | 1.000 | \mathscr{U}(\mathcal{H}) | | |
| rph8-g15q_FO0015 | 3 | 1.000 | \mathcal{X} | | |
| rph8-g15q_FO0016 | 3 | 1.000 | X | | |
| rph8-g15q_FO0017 | 3 | 1.000 | \rho: \mathcal{X} \rightarrow \mathscr{S}(\mathcal{H}) | | |
| rph8-g15q_FO0018 | 3 | 1.000 | U: \mathcal{X} \rightarrow \mathscr{U}(\mathcal{H}) | | |
| rph8-g15q_FO0019 | 3 | 1.000 | \left|\psi_{0}\right\rangle \in \mathcal{H} | | |
| rph8-g15q_FO0020 | 3 | 1.000 | \rho: \mathcal{X} \rightarrow | | |
| rph8-g15q_FO0021 | 4 | 1.000 | G | | |
| rph8-g15q_FO0022 | 4 | 1.000 | \alpha: G \rightarrow \operatorname{Aut}(\mathcal{X}) | | |
| rph8-g15q_FO0023 | 4 | 1.000 | \operatorname{Aut}(\mathcal{X}) | | |
| rph8-g15q_FO0024 | 4 | 1.000 | \alpha | | |
| rph8-g15q_FO0025 | 4 | 1.000 | (\mathcal{X}, \alpha) | | |
| rph8-g15q_FO0026 | 4 | 1.000 | g \in G | | |
| rph8-g15q_FO0027 | 4 | 1.000 | \alpha_{g}: \mathcal{X} \rightarrow \mathcal{X} | | |
| rph8-g15q_FO0028 | 4 | 1.000 | x \in \mathcal{X} | | |
| rph8-g15q_FO0029 | 4 | 1.000 | \alpha_{g}(x) | | |
| rph8-g15q_FO0030 | 4 | 1.000 | \alpha_{g h}(x)=\alpha_{g}\left(\alpha_{h}(x)\right) | | |
| rph8-g15q_FO0031 | 4 | 1.000 | g, h \in G | | |
| rph8-g15q_FO0032 | 4 | 0.987 | \alpha_{1_{G}}=\mathrm{id}_{\mathcal{X}} | | |
| rph8-g15q_FO0033 | 4 | 0.987 | 1_{G} | | |
| rph8-g15q_FO0034 | 4 | 1.000 | V: G \rightarrow | | |
| rph8-g15q_FO0035 | 4 | 1.000 | \operatorname{Aut}(\mathcal{H}) | | |
| rph8-g15q_FO0036 | 4 | 1.000 | \operatorname{Ad}_{V_{g}} \in \operatorname{Aut}(\mathscr{S}(\mathcal{H})) | | |
| rph8-g15q_FO0041 | 4 | 1.000 | \sigma \in \mathscr{S}(\mathcal{H}) | | |
| rph8-g15q_FO0042 | 4 | 0.987 | \left(\mathscr{S}(\mathcal{H}), \operatorname{Ad}_{V}\right) | | |
| rph8-g15q_FO0043 | 4 | 1.000 | V: G \rightarrow \mathscr{U}(\mathcal{H}) | | |
| rph8-g15q_FO0044 | 4 | 1.000 | \rho | | |
| rph8-g15q_FO0045 | 4 | 0.616 | \mathcal{X}, \alpha | | |
| rph8-g15q_FO0046 | 4 | 0.616 | \mathcal{Y}, \beta | | |
| rph8-g15q_FO0047 | 4 | 0.999 | (\mathcal{Y}, \beta) | | |
| rph8-g15q_FO0048 | 4 | 0.999 | f: \mathcal{X} \rightarrow | | |
| rph8-g15q_FO0049 | 4 | 1.000 | \mathcal{Y} | | |
| rph8-g15q_FO0050 | 5 | 1.000 | \mathcal{X}=\mathbb{R}^{2} | | |
| rph8-g15q_FO0051 | 5 | 1.000 | y: \mathcal{X} \rightarrow \mathbb{R} | | |
| rph8-g15q_FO0052 | 5 | 0.998 | y(x)>0 | | |
| rph8-g15q_FO0053 | 5 | 0.516 | y(x)<0 | | |
| rph8-g15q_FO0054 | 5 | 1.000 | G \rightarrow \operatorname{Aut}\left(\mathbb{R}^{2}\right) | | |
| rph8-g15q_FO0055 | 5 | 1.000 | \mathcal{H}=\mathbb{C}^{2} \otimes \mathbb{C}^{2} | | |
| rph8-g15q_FO0056 | 5 | 0.998 | X=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right], \mathbb{1}_{2} | | |
| rph8-g15q_FO0057 | 5 | 0.998 | 2 \times 2 | | |
| rph8-g15q_FO0058 | 5 | 0.994 | \operatorname{SWAP}(|\psi\rangle \otimes|\phi\rangle)=|\phi\rangle \otimes|\psi\rangle | | |
| rph8-g15q_FO0059 | 5 | 0.994 | |\psi\rangle,|\phi\rangle \in \mathbb{C}^{2} | | |
| rph8-g15q_FO0060 | 5 | 1.000 | V_{g} \rho(x) V_{g}^{\dagger}=\rho\left(\alpha_{g}(x)\right) | | |
| rph8-g15q_FO0061 | 5 | 1.000 | x=\left(x_{1}, x_{2}\right) \in \mathcal{X} | | |
| rph8-g15q_FO0062 | 5 | 1.000 | Z | | |
| rph8-g15q_FO0063 | 5 | 1.000 | Z=\left[\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right] | | |
| rph8-g15q_FO0064 | 5 | 1.000 | 0<p<1 | | |
| rph8-g15q_FO0065 | 5 | 1.000 | p | | |
| rph8-g15q_FO0066 | 5 | 1.000 | | \pm, \pm\rangle:=| \pm\rangle \otimes| \pm\rangle | | |
| rph8-g15q_FO0067 | 5 | 0.994 | x=\left(x_{1}, x_{2}\right) | | |
| rph8-g15q_FO0068 | 5 | 1.000 | \mathcal{L}: \mathbb{R}^{2} \rightarrow \mathbb{M}_{4} | | |
| rph8-g15q_FO0069 | 5 | 1.000 | \mathcal{L}(x) \in \mathbb{M}_{4} | | |
| rph8-g15q_FO0070 | 5 | 1.000 | \mathbb{M}_{4} | | |
| rph8-g15q_FO0071 | 5 | 0.968 | -i \mathcal{L}(x) \in \mathfrak{s u}(4) | | |
| rph8-g15q_FO0072 | 5 | 0.968 | 4 \times 4 | | |
| rph8-g15q_FO0073 | 5 | 1.000 | \mathcal{L} | | |
| rph8-g15q_FO0074 | 5 | 1.000 | e_{1}=(1,0) | | |
| rph8-g15q_FO0075 | 5 | 1.000 | e_{2}=(0,1) | | |
| rph8-g15q_FO0076 | 5 | 1.000 | 2\left(4^{2}-1\right)=30 | | |
| rph8-g15q_FO0077 | 5 | 1.000 | \mathcal{L}(x) | | |
| rph8-g15q_FO0078 | 5 | 1.000 | V_{g} | | |
| rph8-g15q_FO0079 | 5 | 1.000 | g=(1,0) | | |
| rph8-g15q_FO0080 | 5 | 0.983 | \mathrm{SWAP} L_{1} \mathrm{SWAP}=L_{2} | | |
| rph8-g15q_FO0081 | 5 | 0.983 | \mathrm{SWAP} L_{2} \mathrm{SWAP}=L_{1} | | |
| rph8-g15q_FO0082 | 5 | 1.000 | g=(0,1) | | |
| rph8-g15q_FO0083 | 5 | 1.000 | (X \otimes X) L_{1}(X \otimes X)=-L_{1} | | |
| rph8-g15q_FO0084 | 5 | 1.000 | (X \otimes X) L_{2}(X \otimes | | |
| rph8-g15q_FO0085 | 5 | 1.000 | X)=-L_{2} | | |
| rph8-g15q_FO0086 | 5 | 0.538 | \left(L_{1}, L_{2}\right) | | |
| rph8-g15q_FO0087 | 5 | 0.912 | L_{1} | | |
| rph8-g15q_FO0088 | 6 | 1.000 | \tau_{\mathcal{X}} | | |
| rph8-g15q_FO0089 | 6 | 0.999 | \left(\mathcal{X}, \tau_{\mathcal{X}}\right) | | |
| rph8-g15q_FO0090 | 6 | 1.000 | \mathcal{A} | | |
| rph8-g15q_FO0091 | 6 | 1.000 | \left(\mathcal{X}, \tau_{\mathcal{X}}, \mathcal{A}\right) | | |
| rph8-g15q_FO0092 | 6 | 0.755 | \mathcal{H}=\mathbb{C}^{d} | | |
| rph8-g15q_FO0093 | 6 | 0.755 | \mathbb{C P}^{d-1} | | |
| rph8-g15q_FO0094 | 6 | 1.000 | \mathcal{X}=\mathbb{R}^{d} | | |
| rph8-g15q_FO0095 | 6 | 1.000 | x=\left(x_{1}, \ldots, x_{d}\right) \in | | |
| rph8-g15q_FO0096 | 6 | 1.000 | X_{k} | | |
| rph8-g15q_FO0097 | 6 | 1.000 | k | | |
| rph8-g15q_FO0098 | 6 | 0.975 | \rho: \mathbb{R}^{d} \rightarrow \mathscr{S}\left(\mathbb{C}^{2^{d}}\right) | | |
| rph8-g15q_FO0099 | 6 | 1.000 | Y | | |
| rph8-g15q_FO0100 | 6 | 1.000 | \vec{n} \cdot \vec{\sigma} | | |
| rph8-g15q_FO0101 | 6 | 1.000 | \vec{n} | | |
| rph8-g15q_FO0102 | 6 | 1.000 | \mathbb{R}^{3} | | |
| rph8-g15q_FO0103 | 6 | 1.000 | \vec{\sigma}=(X, Y, Z) | | |
| rph8-g15q_FO0104 | 6 | 1.000 | d | | |
| rph8-g15q_FO0105 | 7 | 1.000 | x \in \mathbb{R}^{2^{d}} \backslash\{0\} | | |
| rph8-g15q_FO0106 | 7 | 0.999 | \chi(x) | | |
| rph8-g15q_FO0107 | 7 | 0.999 | \mathbb{C}^{2^{d}} | | |
| rph8-g15q_FO0108 | 7 | 1.000 | |\Phi(x)\rangle | | |
| rph8-g15q_FO0109 | 7 | 1.000 | x=\left(x_{0}, x_{1}, \ldots, x_{2^{d}-1}\right) \in \mathbb{R}^{2^{d}} | | |
| rph8-g15q_FO0110 | 7 | 0.998 | n | | |
| rph8-g15q_FO0111 | 7 | 0.998 | d 0 \mathrm{~s} | | |
| rph8-g15q_FO0112 | 7 | 0.998 | d=2 | | |
| rph8-g15q_FO0113 | 7 | 0.999 | n \in\{00,01,10,11\} | | |
| rph8-g15q_FO0114 | 7 | 1.000 | \|\chi(x)\| | | |
| rph8-g15q_FO0115 | 7 | 1.000 | S^{2^{d}-1} | | |
| rph8-g15q_FO0116 | 7 | 1.000 | \mathbb{R}^{2^{d}} | | |
| rph8-g15q_FO0117 | 7 | 0.999 | \log _{2}\left(2^{d}\right)=d | | |
| rph8-g15q_FO0118 | 7 | 1.000 | S^{2^{d}} | | |
| rph8-g15q_FO0119 | 7 | 1.000 | \frac{\pi}{4} | | |
| rph8-g15q_FO0120 | 7 | 0.999 | \frac{\pi}{2} | | |
| rph8-g15q_FO0124 | 8 | 0.978 | \mathbb{R} | | |
| rph8-g15q_FO0125 | 8 | 0.706 | \left(\mathcal{X}, d_{\mathcal{X}}\right) | | |
| rph8-g15q_FO0126 | 8 | 1.000 | d_{\mathcal{X}}: \mathcal{X} \times \mathcal{X} \rightarrow \mathbb{R} | | |
| rph8-g15q_FO0127 | 8 | 1.000 | d_{\mathcal{X}}\left(x_{1}, x_{2}\right)=0 | | |
| rph8-g15q_FO0128 | 8 | 1.000 | x_{1}=x_{2} | | |
| rph8-g15q_FO0129 | 8 | 1.000 | d_{\mathcal{X}}\left(x_{1}, x_{2}\right)=d_{\mathcal{X}}\left(x_{2}, x_{1}\right) | | |
| rph8-g15q_FO0130 | 8 | 1.000 | x_{1}, x_{2} \in \mathcal{X} | | |
| rph8-g15q_FO0131 | 8 | 1.000 | d_{\mathcal{X}}\left(x_{1}, x_{2}\right) \leqslant d_{\mathcal{X}}\left(x_{1}, x_{3}\right)+d_{\mathcal{X}}\left(x_{2}, x_{3}\right) | | |
| rph8-g15q_FO0132 | 8 | 1.000 | x_{1}, x_{2}, x_{3} | | |
| rph8-g15q_FO0133 | 8 | 1.000 | \in \mathcal{X} | | |
| rph8-g15q_FO0134 | 8 | 1.000 | d_{\mathcal{X}} | | |
| rph8-g15q_FO0135 | 8 | 1.000 | X \subseteq \mathcal{X} | | |
| rph8-g15q_FO0137 | 8 | 0.969 | K_{\bullet}\left(X, d_{X}\right) | | |
| rph8-g15q_FO0138 | 8 | 1.000 | H_{\bullet}\left(X, d_{X}\right) | | |
| rph8-g15q_FO0139 | 8 | 1.000 | d_{X} | | |
| rph8-g15q_FO0140 | 8 | 1.000 | d_{X}\left(x_{1}, x_{2}\right)=d_{\mathcal{X}}\left(x_{1}, x_{2}\right) | | |
| rph8-g15q_FO0141 | 8 | 1.000 | x_{1}, x_{2} \in X | | |
| rph8-g15q_FO0142 | 8 | 0.953 | X, d_{X} | | |
| rph8-g15q_FO0143 | 8 | 0.829 | H_{\bullet}\left(X, d_{X}\right)[45,86,87] | | |
| rph8-g15q_FO0144 | 8 | 0.920 | \operatorname{dgm}_{\bullet}\left(X, d_{X}\right) | | |
| rph8-g15q_FO0145 | 8 | 1.000 | S | | |
| rph8-g15q_FO0146 | 8 | 1.000 | \epsilon | | |
| rph8-g15q_FO0147 | 8 | 1.000 | s \in S | | |
| rph8-g15q_FO0148 | 8 | 1.000 | k+1 | | |
| rph8-g15q_FO0149 | 8 | 1.000 | v_{1}, v_{2}, \ldots, v_{n} | | |
| rph8-g15q_FO0150 | 8 | 1.000 | s | | |
| rph8-g15q_FO0151 | 8 | 1.000 | s=\left\{v_{i_{1}}, \ldots, v_{i_{k+1}}\right\} | | |
| rph8-g15q_FO0152 | 8 | 0.863 | i_{1}<\cdots<i_{k+1} | | |
| rph8-g15q_FO0153 | 8 | 0.863 | v_{i_{1}}, \ldots, v_{i_{k+1}} | | |
| rph8-g15q_FO0154 | 8 | 1.000 | |s\rangle | | |
| rph8-g15q_FO0155 | 8 | 1.000 | i_{1}, \ldots, i_{k+1} | | |
| rph8-g15q_FO0156 | 8 | 1.000 | |1\rangle | | |
| rph8-g15q_FO0157 | 8 | 1.000 | |0\rangle | | |
| rph8-g15q_FO0158 | 8 | 1.000 | n=7 | | |
| rph8-g15q_FO0159 | 8 | 1.000 | k=3 | | |
| rph8-g15q_FO0160 | 8 | 1.000 | s=\left\{v_{2}, v_{4}, v_{5}\right\} | | |
| rph8-g15q_FO0161 | 8 | 1.000 | |s\rangle=|0101100\rangle | | |
| rph8-g15q_FO0162 | 8 | 1.000 | f | | |
| rph8-g15q_FO0163 | 8 | 1.000 | \left(\mathcal{X}, d_{\mathcal{X}}\right) \rightarrow\left(\mathcal{Y}, d_{\mathcal{Y}}\right) | | |
| rph8-g15q_FO0164 | 8 | 1.000 | \left(\mathcal{Y}, d_{\mathcal{Y}}\right) | | |
| rph8-g15q_FO0165 | 8 | 1.000 | f: \mathcal{X} \rightarrow \mathcal{Y} | | |
| rph8-g15q_FO0166 | 8 | 0.780 | d_{\mathcal{Y}}\left(f\left(x_{1}\right), f\left(x_{2}\right)\right) \leqslant d_{\mathcal{X}}\left(x_{1}, x_{2}\right) | | |
| rph8-g15q_FO0167 | 9 | 1.000 | d_{\mathcal{Y}}\left(f\left(x_{1}\right), f\left(x_{2}\right)\right)=d_{\mathcal{X}}\left(x_{1}, x_{2}\right) | | |
| rph8-g15q_FO0168 | 9 | 1.000 | f:\left(X, d_{X}\right) \rightarrow\left(\mathcal{Y}, d_{\mathcal{Y}}\right) | | |
| rph8-g15q_FO0169 | 9 | 1.000 | Y:=f(X) | | |
| rph8-g15q_FO0170 | 9 | 1.000 | d_{Y} | | |
| rph8-g15q_FO0171 | 9 | 1.000 | d_{\mathcal{Y}} | | |
| rph8-g15q_FO0172 | 9 | 1.000 | K_{\bullet}\left(Y, d_{Y}\right) | | |
| rph8-g15q_FO0173 | 9 | 1.000 | H_{\bullet}\left(Y, d_{Y}\right) | | |
| rph8-g15q_FO0174 | 9 | 1.000 | \operatorname{dgm}_{\bullet}\left(Y, d_{Y}\right) | | |
| rph8-g15q_FO0175 | 9 | 0.988 | \mathcal{X} \xrightarrow{f} \mathcal{Y} | | |
| rph8-g15q_FO0176 | 9 | 1.000 | d_{\mathcal{X}}: \mathcal{X} \times \mathcal{X} \rightarrow[0, \infty) | | |
| rph8-g15q_FO0177 | 9 | 1.000 | \left(\mathcal{X}, d_{\mathcal{X}}\right) \xrightarrow{f}\left(\mathcal{Y}, d_{\mathcal{Y}}\right) | | |
| rph8-g15q_FO0178 | 9 | 1.000 | L_{p} | | |
| rph8-g15q_FO0179 | 10 | 0.999 | \left(\mathcal{X}, d_{\mathcal{X}_{\text {true }}}\right) | | |
| rph8-g15q_FO0180 | 10 | 0.999 | d_{\mathcal{X}_{\text {true }}} | | |
| rph8-g15q_FO0181 | 10 | 1.000 | \sigma | | |
| rph8-g15q_FO0182 | 10 | 0.518 | \ell_{1} | | |
| rph8-g15q_FO0183 | 10 | 1.000 | \ell_{2} | | |
| rph8-g15q_FO0184 | 10 | 1.000 | \rho, \sigma \in \mathscr{S}(\mathcal{H}) | | |
| rph8-g15q_FO0185 | 10 | 1.000 | d_{\mathcal{H}} | | |
| rph8-g15q_FO0186 | 10 | 1.000 | \Theta | | |
| rph8-g15q_FO0187 | 10 | 1.000 | \rho: \mathcal{X} \times \Theta \rightarrow \mathscr{S}(\mathcal{H}) | | |
| rph8-g15q_FO0188 | 10 | 1.000 | \theta \in \Theta | | |
| rph8-g15q_FO0189 | 10 | 1.000 | \mathcal{X}^{\prime} | | |
| rph8-g15q_FO0190 | 10 | 1.000 | \mathscr{S}(\mathcal{H})^{\prime} | | |
| rph8-g15q_FO0191 | 10 | 1.000 | \rho^{\prime}: \mathcal{X}^{\prime} \rightarrow \mathscr{S}(\mathcal{H})^{\prime} | | |
| rph8-g15q_FO0192 | 10 | 1.000 | \rho^{\prime} | | |
| rph8-g15q_FO0193 | 11 | 1.000 | \mathcal{X}=[-2,2] | | |
| rph8-g15q_FO0199 | 11 | 0.679 | f: | | |
| rph8-g15q_FO0200 | 11 | 1.000 | \mathcal{X} \rightarrow \mathcal{Y} | | |
| rph8-g15q_FO0201 | 11 | 1.000 | g: \mathcal{Y} \rightarrow \mathcal{Z} | | |
| rph8-g15q_FO0202 | 11 | 1.000 | g \circ f: \mathcal{X} \rightarrow \mathcal{Z} | | |
| rph8-g15q_FO0203 | 11 | 1.000 | f: \mathcal{X} \rightarrow \mathcal{Y}, g: \mathcal{Y} \rightarrow \mathcal{Z} | | |
| rph8-g15q_FO0204 | 11 | 1.000 | h: \mathcal{Z} \rightarrow \mathcal{W} | | |
| rph8-g15q_FO0205 | 11 | 1.000 | h \circ(g \circ f) | | |
| rph8-g15q_FO0206 | 11 | 1.000 | (h \circ g) \circ f | | |
| rph8-g15q_FO0207 | 11 | 1.000 | \operatorname{id}_{\mathcal{X}}: \mathcal{X} \rightarrow \mathcal{X} | | |
| rph8-g15q_FO0208 | 11 | 0.996 | \operatorname{id}_{\mathcal{X}}(x)=x | | |
| rph8-g15q_FO0209 | 11 | 0.612 | \operatorname{id}_{\mathcal{Y}} \circ f=f \circ \mathrm{id}_{\mathcal{X}}=f | | |
| rph8-g15q_FO0210 | 11 | 1.000 | \mathbf{C} | | |
| rph8-g15q_FO0211 | 11 | 0.996 | \mathcal{X}, \mathcal{Y}, \ldots | | |
| rph8-g15q_FO0212 | 11 | 1.000 | \mathcal{X}, \mathcal{Y} | | |
| rph8-g15q_FO0213 | 11 | 0.957 | f: \mathcal{X} \rightarrow \mathcal{Y}, \quad g: \mathcal{Y} \rightarrow \mathcal{Z}, \quad | | |
| rph8-g15q_FO0214 | 12 | 0.737 | f \circ \operatorname{id}_{\mathcal{X}}= | | |
| rph8-g15q_FO0215 | 12 | 0.994 | \operatorname{id}_{\mathcal{Y}} \circ f=f | | |
| rph8-g15q_FO0216 | 12 | 0.932 | \operatorname{id}_{\mathcal{X}} | | |
| rph8-g15q_FO0217 | 12 | 0.985 | { }^{\text {emb }} | | |
| rph8-g15q_FO0218 | 12 | 0.958 | { }^{\mathrm{nif}} | | |
| rph8-g15q_FO0219 | 12 | 0.738 | \mathbf{M e t}^{\mathrm{nif}} | | |
| rph8-g15q_FO0220 | 12 | 0.982 | { }^{\mathrm{inf}} | | |
| rph8-g15q_FO0221 | 12 | 0.876 | { }^{\text {nif }} | | |
| rph8-g15q_FO0222 | 12 | 1.000 | \rho:(\mathcal{X}, \alpha) \rightarrow\left(\mathscr{S}(\mathcal{H}), \operatorname{Ad}_{V}\right) | | |
| rph8-g15q_FO0223 | 12 | 0.999 | F: G | | |
| rph8-g15q_FO0224 | 13 | 1.000 | F(\mathcal{X}, \alpha)=\mathcal{X} | | |
| rph8-g15q_FO0225 | 13 | 1.000 | F(f)=f | | |
| rph8-g15q_FO0226 | 13 | 1.000 | F | | |
| rph8-g15q_FO0227 | 13 | 1.000 | g | | |
| rph8-g15q_FO0228 | 13 | 1.000 | x \mapsto x | | |
| rph8-g15q_FO0229 | 13 | 1.000 | F: \mathbf{C} \rightarrow \mathbf{D} | | |
| rph8-g15q_FO0230 | 13 | 0.582 | F(\mathcal{X}) | | |
| rph8-g15q_FO0231 | 13 | 0.582 | \mathbf{D} | | |
| rph8-g15q_FO0232 | 13 | 0.988 | F(f): F(\mathcal{X}) \rightarrow F(\mathcal{Y}) | | |
| rph8-g15q_FO0233 | 13 | 1.000 | F(g \circ f)= | | |
| rph8-g15q_FO0234 | 13 | 1.000 | F(g) \circ F(f) | | |
| rph8-g15q_FO0235 | 13 | 0.452 | F\left(\mathrm{id}_{\mathcal{X}}\right)=\operatorname{id}_{F(\mathcal{X})} | | |
| rph8-g15q_FO0236 | 13 | 1.000 | \mathbf{C}(\mathcal{X}, \mathcal{Y}) | | |
| rph8-g15q_FO0237 | 13 | 1.000 | \mathbf{C}(\mathcal{X}, \mathcal{Y}) \rightarrow \mathbf{D}(F(\mathcal{X}), F(\mathcal{Y})) | | |
| rph8-g15q_FO0238 | 13 | 1.000 | f \mapsto F(f) | | |
| rph8-g15q_FO0239 | 13 | 0.808 | \mathbf{C} \rightarrow \mathbf{D} | | |
| rph8-g15q_FO0240 | 14 | 1.000 | F\left(\mathcal{X}^{\prime}\right)=\mathcal{X} | | |
| rph8-g15q_FO0241 | 14 | 1.000 | F\left(\mathscr{S}(\mathcal{H})^{\prime}\right)=\mathscr{S}(\mathcal{H}) | | |
| rph8-g15q_FO0242 | 14 | 0.880 | F: \mathbf{C} \rightarrow | | |
| rph8-g15q_FO0243 | 14 | 1.000 | F\left(\rho^{\prime}\right)=\rho | | |
| rph8-g15q_FO0244 | 14 | 0.999 | \mathcal{X}^{\prime}:=(\mathcal{X}, \alpha) | | |
| rph8-g15q_FO0245 | 14 | 1.000 | G \ni g \mapsto V_{g} \in \mathscr{U}(\mathcal{H}) | | |
| rph8-g15q_FO0246 | 14 | 1.000 | G \ni g \mapsto \operatorname{Ad}_{V_{g}} | | |
| rph8-g15q_FO0247 | 14 | 1.000 | \mathscr{S}(\mathcal{H})^{\prime}:= | | |
| rph8-g15q_FO0248 | 14 | 0.902 | \rho^{\prime}: \mathcal{X}^{\prime} \rightarrow | | |
| rph8-g15q_FO0249 | 14 | 1.000 | U | | |
| rph8-g15q_FO0250 | 14 | 1.000 | \mathbb{R}^{d} \rightarrow \mathscr{U}(\mathcal{H}) | | |
| rph8-g15q_FO0251 | 14 | 1.000 | \mathcal{L}: \mathbb{R}^{d} \rightarrow \mathcal{B}(\mathcal{H}) | | |
| rph8-g15q_FO0252 | 14 | 1.000 | x \in \mathbb{R}^{d} | | |
| rph8-g15q_FO0253 | 14 | 1.000 | \mathcal{B}(\mathcal{H}) | | |
| rph8-g15q_FO0254 | 14 | 1.000 | U: \mathbb{R}^{d} \rightarrow \mathscr{U}(\mathcal{H}) | | |
| rph8-g15q_FO0255 | 15 | 1.000 | \rho: X \rightarrow \mathscr{S}(\mathcal{H}) | | |
| rph8-g15q_FO0256 | 15 | 1.000 | \rho_{\text {opt }} | | |
| rph8-g15q_FO0257 | 16 | 0.995 | \mathcal{L}: \mathcal{X} \rightarrow \mathcal{B}(\mathcal{H}) | | |
| rph8-g15q_FO0258 | 16 | 1.000 | \rho(x)=U(x)\left|\psi_{0}\right\rangle\left\langle\psi_{0}\right| U(x)^{\dagger} | | |
| rph8-g15q_FO0259 | 16 | 1.000 | \gamma: \mathbb{R} \rightarrow G | | |
| rph8-g15q_FO0260 | 16 | 1.000 | \gamma | | |
| rph8-g15q_FO0261 | 16 | 1.000 | \gamma(0)=1 | | |
| rph8-g15q_FO0262 | 16 | 1.000 | \gamma(s+t)=\gamma(s) \gamma(t) | | |
| rph8-g15q_FO0263 | 16 | 1.000 | s, t \in \mathbb{R} | | |
| rph8-g15q_FO0264 | 16 | 1.000 | M \in \mathfrak{g} | | |
| rph8-g15q_FO0265 | 16 | 0.999 | \mathfrak{g} | | |
| rph8-g15q_FO0266 | 16 | 0.999 | \exp : \mathfrak{g} \rightarrow G | | |
| rph8-g15q_FO0267 | 16 | 1.000 | t \in \mathbb{R} | | |
| rph8-g15q_FO0268 | 16 | 1.000 | t=0 | | |
| rph8-g15q_FO0269 | 16 | 1.000 | M=\left.\frac{d}{d t} \gamma\right|_{t=0} | | |
| rph8-g15q_FO0270 | 16 | 1.000 | \mathcal{X}=\mathbb{R} | | |
| rph8-g15q_FO0271 | 16 | 1.000 | x \mapsto e^{-i x L} | | |
| rph8-g15q_FO0272 | 16 | 0.999 | L \in \mathfrak{s u}\left(2^{n}\right) | | |
| rph8-g15q_FO0273 | 16 | 0.995 | \exp : \mathbb{R}^{d} \rightarrow \mathbb{R}^{d} | | |
| rph8-g15q_FO0274 | 16 | 1.000 | \exp (x)=x | | |
| rph8-g15q_FO0275 | 16 | 1.000 | [V, W]:=V W-W V | | |
| rph8-g15q_FO0276 | 16 | 1.000 | H | | |
| rph8-g15q_FO0277 | 16 | 1.000 | f: G \rightarrow H | | |
| rph8-g15q_FO0278 | 16 | 0.979 | \mathcal{M}: \mathfrak{g} \rightarrow \mathfrak{h} | | |
| rph8-g15q_FO0279 | 16 | 1.000 | W \in \mathfrak{g} | | |
| rph8-g15q_FO0280 | 16 | 1.000 | \mathcal{M} | | |
| rph8-g15q_FO0281 | 16 | 1.000 | W_{1}, W_{2} \in \mathfrak{g} | | |
| rph8-g15q_FO0282 | 17 | 1.000 | U: \mathcal{X} \rightarrow \mathscr{U}\left(\mathbb{C}^{2}\right) | | |
| rph8-g15q_FO0283 | 17 | 1.000 | (s, t) \in \mathbb{R}^{2} | | |
| rph8-g15q_FO0284 | 17 | 1.000 | \mathcal{M}: \mathbb{R}^{2} \rightarrow \mathfrak{s u}(2) | | |
| rph8-g15q_FO0285 | 17 | 1.000 | \mathcal{M}((1,0))=-i X | | |
| rph8-g15q_FO0286 | 17 | 1.000 | \mathcal{M}((0,1))=-i Y | | |
| rph8-g15q_FO0287 | 17 | 1.000 | \mathcal{M}((s, t))=-i s X-i t Y | | |
| rph8-g15q_FO0288 | 17 | 0.968 | \exp : \mathbb{R}^{2} \rightarrow \mathbb{R}^{2} | | |
| rph8-g15q_FO0289 | 17 | 1.000 | \mathbb{R}^{2} | | |
| rph8-g15q_FO0290 | 17 | 0.995 | \mathbb{R}_{\alpha} \subset \mathbb{R}^{2} | | |
| rph8-g15q_FO0291 | 17 | 1.000 | \left.U\right|_{\mathbb{R}_{\alpha}}: \mathbb{R}_{\alpha} \rightarrow \mathscr{U}\left(\mathbb{C}^{2}\right) | | |
| rph8-g15q_FO0292 | 17 | 1.000 | W:=\alpha \cdot(X, Y) | | |
| rph8-g15q_FO0293 | 17 | 0.993 | X, Y | | |
| rph8-g15q_FO0294 | 17 | 1.000 | W | | |
| rph8-g15q_FO0295 | 17 | 1.000 | \mathbb{R} \xrightarrow{\alpha} \mathbb{R}^{2} | | |
| rph8-g15q_FO0296 | 17 | 1.000 | r \in \mathbb{R} | | |
| rph8-g15q_FO0297 | 17 | 1.000 | \alpha(r):=r \alpha | | |
| rph8-g15q_FO0298 | 17 | 1.000 | \mathscr{U}\left(\mathbb{C}^{2}\right) | | |
| rph8-g15q_FO0299 | 17 | 1.000 | U(r \alpha) | | |
| rph8-g15q_FO0300 | 17 | 1.000 | f: G \rightarrow | | |
| rph8-g15q_FO0301 | 17 | 1.000 | \mathbb{R} \xrightarrow{\gamma} G | | |
| rph8-g15q_FO0302 | 17 | 1.000 | \mathbb{R} \xrightarrow{\gamma} G \xrightarrow{f} H | | |
| rph8-g15q_FO0303 | 17 | 1.000 | G \xrightarrow{f} H | | |
| rph8-g15q_FO0304 | 17 | 1.000 | x \in \mathfrak{g} | | |
| rph8-g15q_FO0305 | 17 | 1.000 | 1_{G} \in G | | |
| rph8-g15q_FO0306 | 17 | 1.000 | \mathcal{M}:= | | |
| rph8-g15q_FO0307 | 17 | 1.000 | \left.D f\right|_{1_{G}} | | |
| rph8-g15q_FO0308 | 17 | 1.000 | \gamma(0)=1_{G} | | |
| rph8-g15q_FO0309 | 17 | 1.000 | \left.\frac{d}{d t} \gamma\right|_{t=0}=x \in \mathfrak{g} | | |
| rph8-g15q_FO0310 | 17 | 1.000 | \left.\frac{d}{d t}(f \circ \gamma)\right|_{t=0}=\mathcal{M}(x) | | |
| rph8-g15q_FO0311 | 17 | 1.000 | \left.\frac{d}{d t} \gamma\right|_{t=0}=x | | |
| rph8-g15q_FO0312 | 17 | 1.000 | f \circ \gamma | | |
| rph8-g15q_FO0313 | 17 | 1.000 | y \in \mathfrak{h} | | |
| rph8-g15q_FO0314 | 18 | 1.000 | G=\mathbb{R}^{d} | | |
| rph8-g15q_FO0315 | 18 | 1.000 | \mathfrak{g}=\mathbb{R}^{d} | | |
| rph8-g15q_FO0316 | 18 | 1.000 | \mathbb{R}^{d} \xrightarrow{f} G | | |
| rph8-g15q_FO0317 | 18 | 0.976 | \mathcal{M}: \mathbb{R}^{d} \rightarrow | | |
| rph8-g15q_FO0318 | 18 | 1.000 | f: \mathbb{R}^{d} \rightarrow G | | |
| rph8-g15q_FO0319 | 18 | 1.000 | \mathbb{R}^{d} \rightarrow \mathscr{U}\left(\mathbb{C}^{n}\right) | | |
| rph8-g15q_FO0320 | 18 | 0.999 | \mathcal{L}: \mathbb{R}^{d} \rightarrow \mathcal{B}\left(\mathbb{C}^{n}\right) | | |
| rph8-g15q_FO0321 | 18 | 1.000 | \mathbb{R}^{d} \xrightarrow{U} \mathscr{U}\left(\mathbb{C}^{n}\right) | | |
| rph8-g15q_FO0322 | 18 | 1.000 | U(x+y)=e^{-i \mathcal{L}(x+y)} | | |
| rph8-g15q_FO0323 | 18 | 1.000 | U(x) U(y)=e^{-i \mathcal{L}(x)} e^{-i \mathcal{L}(y)} | | |
| rph8-g15q_FO0324 | 18 | 1.000 | X \subseteq \mathbb{R}^{2} | | |
| rph8-g15q_FO0325 | 18 | 1.000 | c: \mathcal{X} \rightarrow\{-1,0,+1\} | | |
| rph8-g15q_FO0326 | 18 | 1.000 | O \in | | |
| rph8-g15q_FO0327 | 18 | 0.997 | O | | |
| rph8-g15q_FO0328 | 18 | 0.997 | \{-1,+1\} | | |
| rph8-g15q_FO0329 | 18 | 1.000 | \rho(x) | | |
| rph8-g15q_FO0330 | 18 | 1.000 | y | | |
| rph8-g15q_FO0331 | 18 | 1.000 | y^{-1}(0) \subseteq \mathcal{X} | | |
| rph8-g15q_FO0332 | 18 | 1.000 | x_{1}, x_{2} \in \mathbb{R} | | |
| rph8-g15q_FO0333 | 18 | 1.000 | \left|\psi_{0}\right\rangle \in \mathcal{H}=\mathbb{C}^{4} | | |
| rph8-g15q_FO0334 | 18 | 1.000 | p=0.99 | | |
| rph8-g15q_FO0335 | 18 | 0.969 | \left(x_{1}, x_{2}\right) | | |
| rph8-g15q_FO0336 | 18 | 1.000 | y\left(x_{1}, x_{2}\right)<0 | | |
| rph8-g15q_FO0337 | 18 | 0.999 | y\left(x_{1}, x_{2}\right)>0 | | |
| rph8-g15q_FO0338 | 18 | 0.965 | y\left(x_{1}, x_{2}\right)= | | |
| rph8-g15q_FO0339 | 18 | 1.000 | U: \mathbb{R}^{2} \rightarrow \mathscr{U}\left(\mathbb{C}^{4}\right) | | |
| rph8-g15q_FO0340 | 18 | 1.000 | U(x)=e^{-i \mathcal{L}(x)} | | |
| rph8-g15q_FO0341 | 18 | 1.000 | \mathcal{L}: \mathbb{R}^{2} \rightarrow \mathfrak{s u}(4) | | |
| rph8-g15q_FO0342 | 18 | 1.000 | e_{1}, e_{2} | | |
| rph8-g15q_FO0343 | 18 | 1.000 | L_{1}:=\mathcal{L}\left(e_{1}\right) | | |
| rph8-g15q_FO0344 | 18 | 1.000 | L_{2}:=\mathcal{L}\left(e_{2}\right) | | |
| rph8-g15q_FO0345 | 18 | 1.000 | a_{11}, a_{22}, a_{33}, a_{44} \in \mathbb{R}, a_{12}, a_{13}, a_{14}, a_{23}, a_{24}, a_{34} \in \mathbb{C} | | |
| rph8-g15q_FO0346 | 18 | 1.000 | a_{11}+a_{22}+a_{33}+a_{44}=0 | | |
| rph8-g15q_FO0347 | 18 | 0.994 | L_{2} | | |
| rph8-g15q_FO0348 | 18 | 0.994 | 2(4+2(6)-1)=30 | | |
| rph8-g15q_FO0349 | 18 | 1.000 | \mathbb{R}^{2} \rightarrow \mathscr{U}\left(\mathbb{C}^{4}\right) | | |
| rph8-g15q_FO0350 | 18 | 0.989 | L_{2}= | | |
| rph8-g15q_FO0351 | 19 | 1.000 | \left\{X \otimes X, L_{1}\right\}=0 | | |
| rph8-g15q_FO0352 | 19 | 1.000 | \mathbb{R}^{n} | | |
| rph8-g15q_FO0353 | 19 | 0.936 | \mathcal{X}=\mathbb{R}^{n} | | |
| rph8-g15q_FO0354 | 19 | 0.432 | \left(\mathcal{Y}=\mathbb{R}^{m}, d_{\mathcal{Y}}\right) | | |
| rph8-g15q_FO0355 | 19 | 1.000 | \mathbb{R}^{n} \xrightarrow{\varphi} \mathbb{R}^{m} | | |
| rph8-g15q_FO0356 | 19 | 1.000 | m \times n | | |
| rph8-g15q_FO0357 | 19 | 1.000 | V | | |
| rph8-g15q_FO0358 | 19 | 1.000 | V^{T} | | |
| rph8-g15q_FO0359 | 19 | 0.871 | \left(\mathbb{R}^{m}, A\right) | | |
| rph8-g15q_FO0360 | 19 | 0.871 | m \in \mathbb{N} | | |
| rph8-g15q_FO0361 | 19 | 0.871 | A | | |
| rph8-g15q_FO0362 | 19 | 0.871 | m \times m | | |
| rph8-g15q_FO0363 | 19 | 0.945 | \mathbb{R}^{m}, A | | |
| rph8-g15q_FO0364 | 19 | 0.945 | \mathbb{R}^{n}, B | | |
| rph8-g15q_FO0365 | 19 | 0.945 | n \times m | | |
| rph8-g15q_FO0366 | 19 | 1.000 | V^{T} B V=A | | |
| rph8-g15q_FO0367 | 19 | 1.000 | \mathbb{R}^{m} | | |
| rph8-g15q_FO0368 | 19 | 1.000 | \mathbb{R}^{m} \xrightarrow{V} \mathbb{R}^{n} | | |
| rph8-g15q_FO0369 | 19 | 1.000 | y \in \mathcal{Y} | | |
| rph8-g15q_FO0370 | 19 | 1.000 | x_{3} \in \mathcal{X} | | |
| rph8-g15q_FO0371 | 19 | 1.000 | d_{\mathcal{X}}(x, x)=0 | | |
| rph8-g15q_FO0372 | 19 | 1.000 | f\left(x_{1}\right)=f\left(x_{2}\right) | | |
| rph8-g15q_FO0373 | 19 | 1.000 | x_{1}, x_{2} | | |
| rph8-g15q_FO0374 | 19 | 1.000 | X \subset \mathcal{X} | | |
| rph8-g15q_FO0375 | 20 | 1.000 | \{A, B\} | | |
| rph8-g15q_FO0376 | 20 | 0.997 | B | | |
| rph8-g15q_FO0377 | 20 | 0.954 | c: \mathcal{X} \rightarrow\{-1,0,1\} | | |
| rph8-g15q_FO0378 | 20 | 0.965 | \# A | | |
| rph8-g15q_FO0379 | 20 | 0.965 | \# B | | |
| rph8-g15q_FO0380 | 20 | 1.000 | \mathcal{X} \rightarrow \mathscr{S}(\mathcal{H}) | | |
| rph8-g15q_FO0381 | 20 | 1.000 | \rho: \Theta \times \mathcal{X} \rightarrow \mathscr{S}(\mathcal{H}) | | |
| rph8-g15q_FO0382 | 20 | 1.000 | \Theta=[0,2 \pi)^{4} | | |
| rph8-g15q_FO0383 | 20 | 1.000 | \theta=\left(\theta_{1}, \theta_{2}, \theta_{3}, \theta_{4}\right) \in \Theta | | |
| rph8-g15q_FO0384 | 20 | 1.000 | \rho_{\theta}(x):=\rho(\theta, x) | | |
| rph8-g15q_FO0385 | 20 | 1.000 | U: \Theta \times \mathcal{X} \rightarrow \mathscr{U}(\mathcal{H}) | | |
| rph8-g15q_FO0386 | 20 | 1.000 | \rho_{A} | | |
| rph8-g15q_FO0387 | 20 | 1.000 | \rho_{B} | | |
| rph8-g15q_FO0388 | 20 | 0.999 | \lambda \in(0,1] | | |
| rph8-g15q_FO0389 | 20 | 1.000 | \rho_{A}-\rho_{B} | | |
| rph8-g15q_FO0390 | 20 | 1.000 | \{-\lambda,+\lambda\} | | |
| rph8-g15q_FO0391 | 20 | 1.000 | \lambda_{1} | | |
| rph8-g15q_FO0392 | 20 | 1.000 | \lambda_{2} | | |
| rph8-g15q_FO0393 | 20 | 0.955 | \rho_{A} \neq \rho_{B} | | |
| rph8-g15q_FO0394 | 20 | 0.982 | \lambda_{1}+\lambda_{2}=0 | | |
| rph8-g15q_FO0395 | 20 | 0.982 | \lambda_{2}=-\lambda_{1} | | |
| rph8-g15q_FO0396 | 20 | 0.982 | \lambda=\left|\lambda_{1}\right| | | |
| rph8-g15q_FO0397 | 20 | 1.000 | A \cup B=X | | |
| rph8-g15q_FO0398 | 20 | 1.000 | O=\rho_{A}-\rho_{B} | | |
| rph8-g15q_FO0399 | 20 | 1.000 | \lambda>0 | | |
| rph8-g15q_FO0400 | 20 | 1.000 | c | | |
| rph8-g15q_FO0401 | 20 | 0.856 | x \in X | | |
| rph8-g15q_FO0402 | 20 | 0.856 | \operatorname{sgn}:(-\infty, 0) \cup(0, \infty) \rightarrow\{-1,+1\} | | |
| rph8-g15q_FO0403 | 20 | 1.000 | \operatorname{sgn}(x)=\frac{x}{|x|} | | |
| rph8-g15q_FO0404 | 20 | 1.000 | \Pi_{+}-\Pi_{-} | | |
| rph8-g15q_FO0405 | 20 | 1.000 | \Pi_{+} | | |
| rph8-g15q_FO0406 | 20 | 1.000 | \Pi_{-} | | |
| rph8-g15q_FO0407 | 20 | 1.000 | \theta_{1}, \theta_{2}, \theta_{3} | | |
| rph8-g15q_FO0408 | 20 | 1.000 | \theta_{4} | | |
| rph8-g15q_FO0409 | 20 | 1.000 | \rho: \Theta \times \mathcal{X} \rightarrow \mathscr{S}\left(\mathbb{C}^{2}\right) | | |
| rph8-g15q_FO0410 | 20 | 1.000 | \mathcal{X} \times \mathcal{X} | | |
| rph8-g15q_FO0411 | 21 | 1.000 | G: \mathbf{D} \rightarrow \mathbf{E} | | |
| rph8-g15q_FO0412 | 21 | 1.000 | G \circ F: \mathbf{C} \rightarrow \mathbf{E} | | |
| rph8-g15q_FO0413 | 21 | 1.000 | G(F(\mathcal{X})) | | |
| rph8-g15q_FO0414 | 21 | 0.999 | G(F(f)) | | |
| rph8-g15q_FO0415 | 21 | 0.989 | F, G | | |
| rph8-g15q_FO0416 | 21 | 0.996 | \eta | | |
| rph8-g15q_FO0417 | 21 | 1.000 | \eta: F \Rightarrow G | | |
| rph8-g15q_FO0418 | 21 | 0.948 | \eta_{\mathcal{X}}: F(\mathcal{X}) \rightarrow G(\mathcal{X}) | | |
| rph8-g15q_FO0419 | 21 | 0.996 | G(f) \circ \eta_{\mathcal{X}}=\eta_{\mathcal{Y}} \circ F(f) | | |
| rph8-g15q_FO0420 | 21 | 1.000 | \mathcal{C} | | |
| rph8-g15q_FO0421 | 21 | 1.000 | \mathbb{C} | | |
| rph8-g15q_FO0422 | 21 | 1.000 | \left(\mathbb{C}_{\mathrm{fs}}^{\mathcal{X}}, 0,+, \cdot\right) | | |
| rph8-g15q_FO0423 | 21 | 1.000 | \mathbb{C}_{\mathrm{fs}}^{\mathcal{X}} \rightarrow \mathbb{C}_{\mathrm{fs}}^{\mathcal{Y}} | | |
| rph8-g15q_FO0424 | 21 | 0.995 | v | | |
| rph8-g15q_FO0425 | 21 | 0.995 | \mathbb{C}_{\mathrm{fs}}^{\mathcal{X}} | | |
| rph8-g15q_FO0426 | 21 | 1.000 | v: \mathcal{X} \rightarrow \mathbb{C} | | |
| rph8-g15q_FO0427 | 21 | 1.000 | v(x)=0 | | |
| rph8-g15q_FO0428 | 21 | 0.999 | v, w \in \mathbb{C}_{\mathrm{fs}}^{\mathcal{X}} | | |
| rph8-g15q_FO0429 | 21 | 1.000 | v+w | | |
| rph8-g15q_FO0430 | 21 | 1.000 | (v+w)(x):= | | |
| rph8-g15q_FO0431 | 21 | 1.000 | v(x)+w(x) | | |
| rph8-g15q_FO0432 | 21 | 1.000 | \lambda \in \mathbb{C} | | |
| rph8-g15q_FO0433 | 21 | 1.000 | \lambda \cdot v | | |
| rph8-g15q_FO0434 | 21 | 1.000 | \lambda v | | |
| rph8-g15q_FO0435 | 21 | 1.000 | \lambda v(x) | | |
| rph8-g15q_FO0436 | 21 | 1.000 | \delta_{x} | | |
| rph8-g15q_FO0437 | 21 | 0.998 | \delta_{x}\left(x^{\prime}\right)=\delta_{x x^{\prime}} | | |
| rph8-g15q_FO0438 | 21 | 0.998 | x^{\prime}=x | | |
| rph8-g15q_FO0439 | 21 | 0.998 | x^{\prime} \neq | | |
| rph8-g15q_FO0440 | 21 | 1.000 | |x\rangle | | |
| rph8-g15q_FO0441 | 21 | 1.000 | \left\langle x^{\prime} \mid x\right\rangle=\delta_{x x^{\prime}} | | |
| rph8-g15q_FO0442 | 21 | 1.000 | \mathcal{X}=\mathbb{Z}_{2}^{n}= | | |
| rph8-g15q_FO0443 | 21 | 1.000 | \{0,1\}^{n} | | |
| rph8-g15q_FO0444 | 21 | 1.000 | x=\left(x_{0}, x_{1}, \ldots, x_{n-1}\right) | | |
| rph8-g15q_FO0445 | 21 | 1.000 | \left\{0,1,2, \ldots, 2^{n}-1\right\} | | |
| rph8-g15q_FO0446 | 21 | 1.000 | \mathbb{C}^{\mathcal{X}} | | |
| rph8-g15q_FO0447 | 21 | 1.000 | 2^{n} | | |
| rph8-g15q_FO0448 | 21 | 1.000 | L_{f}: \mathbb{C}_{\mathrm{fs}}^{\mathcal{X}} \rightarrow | | |
| rph8-g15q_FO0449 | 21 | 0.995 | \mathbb{C}_{\mathrm{fs}}^{\mathcal{Y}} | | |
| rph8-g15q_FO0450 | 21 | 0.766 | |y\rangle | | |
| rph8-g15q_FO0451 | 21 | 0.766 | L_{f} | | |
| rph8-g15q_FO0452 | 21 | 1.000 | |f(x)\rangle | | |
| rph8-g15q_FO0453 | 21 | 1.000 | \mathbb{C}^{\mathcal{Y}} | | |
| rph8-g15q_FO0454 | 21 | 1.000 | L_{f}: \mathbb{C}_{\mathrm{fs}}^{\mathcal{X}} \rightarrow \mathbb{C}_{\mathrm{fs}}^{\mathcal{Y}} | | |
| rph8-g15q_FO0455 | 21 | 0.871 | (V, 0,+, \cdot) | | |
| rph8-g15q_FO0456 | 22 | 1.000 | F(\mathcal{X})= | | |
| rph8-g15q_FO0457 | 22 | 0.562 | G(F(\mathcal{X}))=\mathbb{C}_{\mathrm{fs}}^{\mathcal{X}} | | |
| rph8-g15q_FO0458 | 22 | 1.000 | G \circ F | | |
| rph8-g15q_FO0459 | 22 | 0.977 | \mathrm{id}_{\text {Set }} | | |
| rph8-g15q_FO0460 | 22 | 0.955 | \eta: \mathrm{id}_{\text {Set }} \Rightarrow | | |
| rph8-g15q_FO0461 | 22 | 0.877 | \eta_{\mathcal{X}}: \operatorname{id}_{\text {Set }}(\mathcal{X}) \rightarrow G(F(\mathcal{X})) | | |
| rph8-g15q_FO0462 | 22 | 1.000 | \eta_{\mathcal{X}}: \mathcal{X} \rightarrow \mathbb{C}_{\mathrm{fs}}^{\mathcal{X}} | | |
| rph8-g15q_FO0463 | 22 | 1.000 | \eta_{\mathcal{X}}(x)=|x\rangle \in \mathbb{C}_{\mathrm{fs}}^{\mathcal{X}} | | |
| rph8-g15q_FO0464 | 22 | 1.000 | \{|x\rangle\} | | |
| rph8-g15q_FO0465 | 22 | 1.000 | \eta_{\mathcal{Y}}(f(x))=L_{f}\left(\eta_{\mathcal{X}}(x)\right) | | |
| rph8-g15q_FO0466 | 22 | 1.000 | |f(x)\rangle=L_{f}|x\rangle | | |
| rph8-g15q_FO0467 | 22 | 1.000 | \mathbb{B} G | | |
| rph8-g15q_FO0468 | 22 | 1.000 | \alpha: \mathbb{B} G \rightarrow | | |
| rph8-g15q_FO0469 | 22 | 1.000 | g^{-1} | | |
| rph8-g15q_FO0470 | 22 | 1.000 | g g^{-1}=1_{G}=g^{-1} g | | |
| rph8-g15q_FO0471 | 22 | 0.987 | \operatorname{id}_{\mathcal{X}}=\alpha_{e}=\alpha_{g g^{-1}}=\alpha_{g} \circ \alpha_{g^{-1}} | | |
| rph8-g15q_FO0472 | 22 | 0.693 | \operatorname{id}_{\mathcal{X}}=\alpha_{g^{-1}} \circ \alpha_{g} | | |
| rph8-g15q_FO0473 | 22 | 0.693 | \alpha_{g} | | |
| rph8-g15q_FO0474 | 22 | 1.000 | \alpha_{g^{-1}} | | |
| rph8-g15q_FO0475 | 22 | 0.986 | \alpha, \beta | | |
| rph8-g15q_FO0476 | 22 | 0.939 | \mathbb{B} G \rightarrow | | |
| rph8-g15q_FO0477 | 22 | 0.939 | \mathcal{X}:=\alpha(\bullet) | | |
| rph8-g15q_FO0478 | 22 | 0.939 | \mathcal{Y}:=\beta(\bullet) | | |
| rph8-g15q_FO0479 | 22 | 0.949 | f: \alpha \Rightarrow \beta | | |
| rph8-g15q_FO0480 | 22 | 0.949 | \bullet | | |
| rph8-g15q_FO0481 | 25 | 1.000 | w^{*} | | |
| rph8-g15q_FO0482 | 25 | 1.000 | x, y, \ldots \in \mathbb{R} | | |
| rph8-g15q_FO0483 | 25 | 1.000 | x \rightarrow y | | |
| rph8-g15q_FO0484 | 25 | 1.000 | x \leqslant y | | |
| rph8-g15q_FO0485 | 25 | 1.000 | \alpha \in \mathbb{R}^{2} | | |
| rph8-g15q_FO0486 | 25 | 0.999 | \alpha: \mathbb{R} \rightarrow \mathbb{R}^{2} | | |
| rph8-g15q_FO0487 | 25 | 0.999 | 1 \in \mathbb{R} | | |
| rph8-g15q_FO0488 | 25 | 1.000 | \operatorname{Tr}[\sigma O] | | |
| rph8-g15q_FO0489 | 25 | 1.000 | \{\sigma \in \mathscr{S}(\mathcal{H}): \operatorname{Tr}[\sigma O]=0\} | |