\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.987 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 |
|---|---|---|---|---|---|
| 1205.5935v1_FO0001 | 3 | 1.000 | u | | |
| 1205.5935v1_FO0002 | 3 | 1.000 | v | | |
| 1205.5935v1_FO0003 | 3 | 1.000 | u \cdot v | | |
| 1205.5935v1_FO0004 | 3 | 1.000 | |u|^{2}=u \cdot u | | |
| 1205.5935v1_FO0005 | 3 | 1.000 | u v | | |
| 1205.5935v1_FO0006 | 4 | 1.000 | u^{2}=u \cdot u=|u|^{2} | | |
| 1205.5935v1_FO0007 | 4 | 1.000 | u u^{-1}=u^{2} / u^{2}=1 | | |
| 1205.5935v1_FO0008 | 4 | 0.997 | \wedge | | |
| 1205.5935v1_FO0009 | 4 | 1.000 | u \wedge v | | |
| 1205.5935v1_FO0010 | 4 | 0.997 | v v=|v|^{2} | | |
| 1205.5935v1_FO0011 | 4 | 0.997 | u \cdot v=|u||v| \cos \theta | | |
| 1205.5935v1_FO0012 | 4 | 1.000 | \lambda | | |
| 1205.5935v1_FO0013 | 5 | 1.000 | r | | |
| 1205.5935v1_FO0014 | 5 | 1.000 | a | | |
| 1205.5935v1_FO0015 | 5 | 1.000 | b | | |
| 1205.5935v1_FO0016 | 5 | 1.000 | x | | |
| 1205.5935v1_FO0017 | 5 | 1.000 | \alpha | | |
| 1205.5935v1_FO0018 | 5 | 1.000 | \beta | | |
| 1205.5935v1_FO0019 | 5 | 1.000 | a \wedge a=0 | | |
| 1205.5935v1_FO0020 | 5 | 1.000 | a \wedge x | | |
| 1205.5935v1_FO0021 | 5 | 1.000 | a \wedge b | | |
| 1205.5935v1_FO0022 | 5 | 0.948 | (a \wedge x)(a \wedge b)^{-1} | | |
| 1205.5935v1_FO0023 | 5 | 0.948 | (a \wedge b)^{-1}(a \wedge x) | | |
| 1205.5935v1_FO0024 | 5 | 1.000 | \alpha=(x \wedge b) /(a \wedge b) | | |
| 1205.5935v1_FO0025 | 5 | 1.000 | a \wedge b \neq 0 | | |
| 1205.5935v1_FO0026 | 5 | 0.960 | a, b | | |
| 1205.5935v1_FO0027 | 5 | 0.960 | c | | |
| 1205.5935v1_FO0028 | 5 | 1.000 | p | | |
| 1205.5935v1_FO0029 | 5 | 1.000 | q | | |
| 1205.5935v1_FO0030 | 6 | 1.000 | a \wedge x=a \wedge p | | |
| 1205.5935v1_FO0031 | 6 | 0.999 | x \wedge b=q \wedge b | | |
| 1205.5935v1_FO0032 | 6 | 1.000 | n | | |
| 1205.5935v1_FO0033 | 6 | 1.000 | v^{\prime} | | |
| 1205.5935v1_FO0034 | 6 | 1.000 | n^{-1} | | |
| 1205.5935v1_FO0035 | 6 | 1.000 | \theta | | |
| 1205.5935v1_FO0036 | 6 | 1.000 | \theta / 2 | | |
| 1205.5935v1_FO0037 | 7 | 1.000 | \phi | | |
| 1205.5935v1_FO0038 | 7 | 1.000 | m | | |
| 1205.5935v1_FO0039 | 7 | 1.000 | v^{\prime \prime} | | |
| 1205.5935v1_FO0040 | 7 | 0.516 | R=m n | | |
| 1205.5935v1_FO0041 | 7 | 0.516 | R | | |
| 1205.5935v1_FO0042 | 7 | 1.000 | m=m^{-1} | | |
| 1205.5935v1_FO0043 | 7 | 1.000 | n=n^{-1} | | |
| 1205.5935v1_FO0044 | 7 | 1.000 | R^{-1}=n m | | |
| 1205.5935v1_FO0045 | 7 | 1.000 | \theta / 2, m \cdot n=\cos (\theta / 2) | | |
| 1205.5935v1_FO0046 | 7 | 1.000 | (n \wedge m)^{2}=-\sin ^{2}(\theta / 2) | | |
| 1205.5935v1_FO0047 | 7 | 1.000 | B=(n \wedge m) / \sin (\theta / 2) | | |
| 1205.5935v1_FO0048 | 7 | 1.000 | B^{2}=-1 | | |
| 1205.5935v1_FO0049 | 8 | 1.000 | B | | |
| 1205.5935v1_FO0050 | 8 | 1.000 | z^{\prime}=e^{i \theta} z | | |
| 1205.5935v1_FO0051 | 8 | 1.000 | (a \wedge b)^{-1} | | |
| 1205.5935v1_FO0052 | 8 | 1.000 | n v n^{-1} | | |
| 1205.5935v1_FO0053 | 8 | 1.000 | (v \wedge n) n^{-1} | | |
| 1205.5935v1_FO0054 | 10 | 1.000 | \mathbb{R} | | |
| 1205.5935v1_FO0055 | 10 | 1.000 | i | | |
| 1205.5935v1_FO0056 | 10 | 1.000 | \mathcal{G} | | |
| 1205.5935v1_FO0057 | 10 | 1.000 | A, B | | |
| 1205.5935v1_FO0058 | 10 | 0.874 | \mathcal{G}_{0} | | |
| 1205.5935v1_FO0059 | 11 | 0.558 | \left(\lambda, \mu\right. | | |
| 1205.5935v1_FO0060 | 11 | 0.991 | 1+1=0 | | |
| 1205.5935v1_FO0061 | 11 | 1.000 | \mathcal{G}_{1} | | |
| 1205.5935v1_FO0062 | 11 | 1.000 | \lambda \in \mathcal{G}_{0}, v \in \mathcal{G}_{1} | | |
| 1205.5935v1_FO0063 | 11 | 1.000 | \lambda v=v \lambda \in \mathcal{G}_{1} | | |
| 1205.5935v1_FO0064 | 11 | 0.592 | \left(a, b, u, v\right. | | |
| 1205.5935v1_FO0065 | 11 | 0.969 | \mathbb{R}^{3} | | |
| 1205.5935v1_FO0066 | 11 | 0.992 | 0 v=0 | | |
| 1205.5935v1_FO0067 | 11 | 0.979 | u\rfloor v | | |
| 1205.5935v1_FO0068 | 11 | 0.979 | u\lfloor v | | |
| 1205.5935v1_FO0069 | 11 | 0.896 | u \downharpoonleft v=0, u | | |
| 1205.5935v1_FO0070 | 11 | 0.896 | u^{2}= \pm 1 | | |
| 1205.5935v1_FO0071 | 11 | 0.896 | u^{2}=0 | | |
| 1205.5935v1_FO0072 | 11 | 1.000 | v^{-1}=v / v^{2} | | |
| 1205.5935v1_FO0073 | 11 | 0.401 | \lfloor | | |
| 1205.5935v1_FO0074 | 12 | 1.000 | r>1 | | |
| 1205.5935v1_FO0075 | 12 | 1.000 | \mathcal{G}_{r} | | |
| 1205.5935v1_FO0076 | 12 | 1.000 | A \in \mathcal{G}_{r} | | |
| 1205.5935v1_FO0077 | 12 | 0.998 | 0 \in \mathcal{G}_{r} | | |
| 1205.5935v1_FO0078 | 12 | 1.000 | \mathcal{G}_{0}=\mathcal{G}_{1} | | |
| 1205.5935v1_FO0079 | 12 | 1.000 | \mathcal{G}=\mathcal{G}_{0} | | |
| 1205.5935v1_FO0080 | 12 | 1.000 | A \in \mathcal{G} | | |
| 1205.5935v1_FO0081 | 12 | 1.000 | A=\sum_{r} A_{r} | | |
| 1205.5935v1_FO0082 | 12 | 1.000 | A_{r} \in \mathcal{G}_{r} | | |
| 1205.5935v1_FO0083 | 12 | 1.000 | A_{r} | | |
| 1205.5935v1_FO0084 | 12 | 1.000 | A \neq 0 | | |
| 1205.5935v1_FO0085 | 12 | 1.000 | \left\rangle_{r}: \mathcal{G} \rightarrow \mathcal{G}_{r}\right. | | |
| 1205.5935v1_FO0086 | 12 | 1.000 | A | | |
| 1205.5935v1_FO0087 | 12 | 1.000 | A=\langle A\rangle_{r} | | |
| 1205.5935v1_FO0088 | 12 | 1.000 | \langle A+B\rangle_{r}=\langle A\rangle_{r}+\langle B\rangle_{r} | | |
| 1205.5935v1_FO0089 | 12 | 1.000 | \langle\lambda A\rangle_{r}=\langle A \lambda\rangle_{r}=\lambda\langle A\rangle_{r} | | |
| 1205.5935v1_FO0090 | 12 | 1.000 | \left\langle\langle A\rangle_{r}\right\rangle_{s}=\langle A\rangle_{r} \delta_{r s} | | |
| 1205.5935v1_FO0091 | 12 | 1.000 | \left\rangle_{r}\right. | | |
| 1205.5935v1_FO0092 | 12 | 1.000 | \sum_{r}\langle A\rangle_{r}=A | | |
| 1205.5935v1_FO0093 | 12 | 1.000 | \langle A\rangle_{r}=0 | | |
| 1205.5935v1_FO0094 | 12 | 1.000 | r<0 | | |
| 1205.5935v1_FO0095 | 12 | 1.000 | \left\rangle\right. | | |
| 1205.5935v1_FO0096 | 12 | 1.000 | \left\rangle_{0}\right. | | |
| 1205.5935v1_FO0097 | 12 | 1.000 | a_{1}, a_{2} | | |
| 1205.5935v1_FO0098 | 12 | 1.000 | \langle A\rangle_{r} | | |
| 1205.5935v1_FO0099 | 13 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}} | | |
| 1205.5935v1_FO0100 | 13 | 1.000 | \lambda A=A \lambda | | |
| 1205.5935v1_FO0101 | 13 | 1.000 | \mathcal{G}_{+} | | |
| 1205.5935v1_FO0102 | 13 | 1.000 | \mathcal{G}_{-} | | |
| 1205.5935v1_FO0103 | 13 | 1.000 | (-1)^{r} | | |
| 1205.5935v1_FO0104 | 13 | 1.000 | A_{+} | | |
| 1205.5935v1_FO0105 | 13 | 1.000 | A_{-} | | |
| 1205.5935v1_FO0106 | 13 | 1.000 | A,\langle A\rangle_{+} | | |
| 1205.5935v1_FO0107 | 13 | 1.000 | \langle A\rangle_{-} | | |
| 1205.5935v1_FO0108 | 13 | 1.000 | \left\{a_{i}\right\}_{i=1, \ldots, r} | | |
| 1205.5935v1_FO0109 | 13 | 0.870 | \sigma | | |
| 1205.5935v1_FO0110 | 13 | 0.870 | r, \operatorname{sgn} \sigma | | |
| 1205.5935v1_FO0111 | 13 | 0.996 | r! | | |
| 1205.5935v1_FO0112 | 13 | 0.996 | r=2 | | |
| 1205.5935v1_FO0113 | 13 | 1.000 | a_{i} | | |
| 1205.5935v1_FO0114 | 13 | 1.000 | \left\{e_{i}\right\}_{i=1, \ldots, r} | | |
| 1205.5935v1_FO0115 | 13 | 1.000 | e_{i} | | |
| 1205.5935v1_FO0116 | 13 | 1.000 | \operatorname{sgn} \sigma | | |
| 1205.5935v1_FO0117 | 14 | 0.358 | e_{1} \cdot e_{2}=0 | | |
| 1205.5935v1_FO0118 | 14 | 0.358 | \left.e_{1}\right\rfloor e_{2}=0 | | |
| 1205.5935v1_FO0119 | 14 | 0.553 | M | | |
| 1205.5935v1_FO0120 | 14 | 0.553 | M_{i j}=a_{i} \downharpoonleft a_{j} | | |
| 1205.5935v1_FO0121 | 14 | 0.679 | \operatorname{det}(R)= \pm 1 | | |
| 1205.5935v1_FO0122 | 14 | 0.679 | e_{1} | | |
| 1205.5935v1_FO0123 | 14 | 0.679 | e_{2} | | |
| 1205.5935v1_FO0125 | 14 | 1.000 | a_{1} \wedge a_{2} \wedge \cdots \wedge a_{r}=0 | | |
| 1205.5935v1_FO0126 | 14 | 1.000 | a \wedge \boldsymbol{A}_{\boldsymbol{r}} | | |
| 1205.5935v1_FO0127 | 14 | 1.000 | r \geq 1 | | |
| 1205.5935v1_FO0128 | 14 | 1.000 | a \wedge \boldsymbol{A}_{\boldsymbol{r}}=0 | | |
| 1205.5935v1_FO0129 | 15 | 1.000 | a \wedge \boldsymbol{A}_{\boldsymbol{r}} \neq 0 | | |
| 1205.5935v1_FO0130 | 15 | 1.000 | r+1 | | |
| 1205.5935v1_FO0131 | 15 | 0.998 | \boldsymbol{B}_{\boldsymbol{r}} | | |
| 1205.5935v1_FO0132 | 15 | 0.999 | \boldsymbol{A}_{\boldsymbol{r}}=\lambda \boldsymbol{B}_{\boldsymbol{r}} | | |
| 1205.5935v1_FO0133 | 15 | 0.999 | a \wedge \boldsymbol{B}_{\boldsymbol{r}}=0 | | |
| 1205.5935v1_FO0134 | 15 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}}=a_{1} \wedge a_{2} \wedge \cdots \wedge a_{r} | | |
| 1205.5935v1_FO0135 | 15 | 1.000 | \boldsymbol{B}_{\boldsymbol{r}}=b_{1} \wedge b_{2} \wedge \cdots \wedge b_{r} | | |
| 1205.5935v1_FO0136 | 15 | 1.000 | \left\{b_{j}\right\}_{j=1, \ldots, r} | | |
| 1205.5935v1_FO0137 | 15 | 1.000 | b_{j} | | |
| 1205.5935v1_FO0138 | 15 | 1.000 | \boldsymbol{A}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0139 | 15 | 1.000 | \boldsymbol{A}_{\boldsymbol{s}-\boldsymbol{r}} | | |
| 1205.5935v1_FO0140 | 15 | 1.000 | \boldsymbol{A}_{\boldsymbol{s}}=\boldsymbol{A}_{\boldsymbol{r}} \wedge \boldsymbol{A}_{\boldsymbol{s}-\boldsymbol{r}} | | |
| 1205.5935v1_FO0141 | 15 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}}=a_{1} \wedge \cdots \wedge a_{r} | | |
| 1205.5935v1_FO0142 | 15 | 1.000 | \left\{a_{j}\right\}_{j=1, \ldots, r} | | |
| 1205.5935v1_FO0143 | 15 | 1.000 | \left\{a_{j}\right\}_{j=1, \ldots, s} | | |
| 1205.5935v1_FO0144 | 15 | 1.000 | a_{1} \wedge \cdots \wedge a_{s} | | |
| 1205.5935v1_FO0145 | 15 | 0.996 | A_{r} \wedge B_{s}=(-1)^{r s} B_{s} \wedge A_{r} | | |
| 1205.5935v1_FO0146 | 15 | 0.996 | s | | |
| 1205.5935v1_FO0147 | 15 | 0.537 | a\rfloor \boldsymbol{A}_{\boldsymbol{r}} | | |
| 1205.5935v1_FO0148 | 15 | 0.713 | r \geq 1, a | | |
| 1205.5935v1_FO0149 | 15 | 0.713 | \rfloor \boldsymbol{A}_{\boldsymbol{r}}=0 | | |
| 1205.5935v1_FO0150 | 15 | 1.000 | a_{j} | | |
| 1205.5935v1_FO0151 | 15 | 0.528 | a\rfloor \boldsymbol{A}_{\boldsymbol{r}}=0 | | |
| 1205.5935v1_FO0152 | 15 | 0.528 | a \downharpoonleft \boldsymbol{A}_{\boldsymbol{r}} | | |
| 1205.5935v1_FO0153 | 15 | 0.986 | a \downharpoonleft \boldsymbol{A}_{\boldsymbol{r}} \neq 0 | | |
| 1205.5935v1_FO0154 | 15 | 0.973 | 1<s \leq r | | |
| 1205.5935v1_FO0155 | 15 | 0.973 | a \leq a_{j} \neq 0 | | |
| 1205.5935v1_FO0156 | 15 | 0.973 | j=2, \ldots, s | | |
| 1205.5935v1_FO0157 | 16 | 0.978 | a \downharpoonleft b_{j}=0 | | |
| 1205.5935v1_FO0158 | 16 | 1.000 | a_{1} | | |
| 1205.5935v1_FO0159 | 16 | 0.999 | a \downharpoonleft \boldsymbol{A}_{\boldsymbol{r}}=0 | | |
| 1205.5935v1_FO0160 | 16 | 0.728 | r-1 | | |
| 1205.5935v1_FO0161 | 16 | 0.679 | \boldsymbol{A}_{r} | | |
| 1205.5935v1_FO0162 | 16 | 1.000 | -a | | |
| 1205.5935v1_FO0163 | 16 | 1.000 | -b | | |
| 1205.5935v1_FO0164 | 17 | 0.512 | { }^{\text {v }} | | |
| 1205.5935v1_FO0165 | 17 | 0.512 | a_{1} a_{2} \cdots \check{a}_{j} \cdots a_{r} | | |
| 1205.5935v1_FO0166 | 17 | 1.000 | r=1 | | |
| 1205.5935v1_FO0167 | 17 | 0.939 | a \downharpoonleft A_{r} | | |
| 1205.5935v1_FO0168 | 17 | 0.939 | A_{r}\lfloor a | | |
| 1205.5935v1_FO0169 | 17 | 1.000 | a, a_{1}, a_{2}, \ldots, a_{r} | | |
| 1205.5935v1_FO0170 | 18 | 1.000 | e_{1} e_{2} \cdots e_{r} | | |
| 1205.5935v1_FO0171 | 18 | 0.999 | \frac{1}{2}\left[a A_{r}-(-1)^{r} A_{r} a\right] | | |
| 1205.5935v1_FO0172 | 18 | 1.000 | r=0 | | |
| 1205.5935v1_FO0173 | 18 | 1.000 | A_{r}=\lambda | | |
| 1205.5935v1_FO0174 | 18 | 0.963 | a \wedge A_{r} | | |
| 1205.5935v1_FO0175 | 18 | 1.000 | a_{1} \wedge a_{2} \wedge \cdots \wedge a_{r}=e_{1} e_{2} \cdots e_{r} | | |
| 1205.5935v1_FO0176 | 18 | 0.959 | (r+1) | | |
| 1205.5935v1_FO0177 | 19 | 0.998 | \pi | | |
| 1205.5935v1_FO0178 | 19 | 0.998 | \pi_{i} | | |
| 1205.5935v1_FO0179 | 19 | 0.999 | a_{\pi_{j}(i)} | | |
| 1205.5935v1_FO0180 | 19 | 0.999 | e_{j} | | |
| 1205.5935v1_FO0181 | 19 | 0.999 | e_{\pi(i)} | | |
| 1205.5935v1_FO0182 | 19 | 0.672 | \operatorname{sgn} \pi | | |
| 1205.5935v1_FO0183 | 19 | 1.000 | \pi_{j} | | |
| 1205.5935v1_FO0184 | 19 | 1.000 | (-1)^{j} | | |
| 1205.5935v1_FO0185 | 19 | 1.000 | j+1 | | |
| 1205.5935v1_FO0186 | 19 | 1.000 | j-1 e_{i} | | |
| 1205.5935v1_FO0187 | 20 | 1.000 | a_{1} \wedge a_{2} \wedge \cdots \wedge a_{r} | | |
| 1205.5935v1_FO0188 | 20 | 1.000 | \frac{1}{2}\left[a A_{r}+(-1)^{r} A_{r} a\right] | | |
| 1205.5935v1_FO0189 | 20 | 1.000 | A_{r} a | | |
| 1205.5935v1_FO0190 | 20 | 1.000 | B=\sum_{s} B_{s} | | |
| 1205.5935v1_FO0191 | 20 | 1.000 | A B=\sum_{r, s} A_{r} B_{s} | | |
| 1205.5935v1_FO0192 | 20 | 0.993 | A_{r} B_{s} | | |
| 1205.5935v1_FO0193 | 20 | 0.993 | \min \{r, s\}+1 | | |
| 1205.5935v1_FO0194 | 20 | 0.993 | |r-s|,|r-s|+2,|r-s|+4, \ldots, r+s | | |
| 1205.5935v1_FO0195 | 20 | 1.000 | s=0 | | |
| 1205.5935v1_FO0196 | 20 | 1.000 | 0<r \leq s | | |
| 1205.5935v1_FO0197 | 20 | 0.988 | a \boldsymbol{A}_{\boldsymbol{r}-\mathbf{1}} | | |
| 1205.5935v1_FO0198 | 20 | 0.988 | \boldsymbol{A}_{\boldsymbol{r}-\mathbf{1}} | | |
| 1205.5935v1_FO0199 | 21 | 1.000 | r \leq s | | |
| 1205.5935v1_FO0200 | 21 | 1.000 | s-r=|r-s|, \boldsymbol{A}_{\boldsymbol{r}} B_{s} | | |
| 1205.5935v1_FO0201 | 21 | 1.000 | |r-s|,|r-s|+2 | | |
| 1205.5935v1_FO0202 | 21 | 1.000 | |r-s|+4, \ldots, r+s | | |
| 1205.5935v1_FO0203 | 21 | 1.000 | 0<s \leq r | | |
| 1205.5935v1_FO0204 | 21 | 1.000 | \boldsymbol{A}_{\mathbf{2}}=e_{1} e_{2} | | |
| 1205.5935v1_FO0205 | 21 | 0.999 | \boldsymbol{A}_{\mathbf{2}} B_{s}=e_{1} e_{2} B_{s} | | |
| 1205.5935v1_FO0206 | 21 | 0.999 | e_{2} B_{s} | | |
| 1205.5935v1_FO0207 | 21 | 1.000 | s-2 | | |
| 1205.5935v1_FO0208 | 21 | 1.000 | B_{s} | | |
| 1205.5935v1_FO0209 | 21 | 1.000 | s+2 | | |
| 1205.5935v1_FO0210 | 21 | 1.000 | r+s | | |
| 1205.5935v1_FO0211 | 21 | 1.000 | r+s-2 j | | |
| 1205.5935v1_FO0212 | 21 | 1.000 | j | | |
| 1205.5935v1_FO0213 | 21 | 1.000 | (-1)^{r+s-2 j}=(-1)^{r+s} | | |
| 1205.5935v1_FO0214 | 22 | 1.000 | \frac{1}{2}(-1)^{r} A_{r} a B_{s} | | |
| 1205.5935v1_FO0215 | 22 | 1.000 | j-1 | | |
| 1205.5935v1_FO0216 | 22 | 1.000 | (-1)^{j-1} | | |
| 1205.5935v1_FO0217 | 22 | 1.000 | a_{1} a_{2} \cdots a_{r} | | |
| 1205.5935v1_FO0218 | 22 | 0.899 | r=0,1 | | |
| 1205.5935v1_FO0219 | 22 | 1.000 | r-2 | | |
| 1205.5935v1_FO0220 | 23 | 0.635 | \left.A_{r}\right\rfloor B_{r}=A_{r}\left\lfloor B_{r}=\left\langle A_{r} B_{r}\right\rangle\right. | | |
| 1205.5935v1_FO0221 | 23 | 0.995 | r>s | | |
| 1205.5935v1_FO0222 | 23 | 0.995 | \left.A_{r}\right\rfloor B_{s}=B_{s}\left\lfloor A_{r}=0\right. | | |
| 1205.5935v1_FO0223 | 23 | 0.983 | A_{r}\left\lfloor B_{s}\right. | | |
| 1205.5935v1_FO0224 | 23 | 0.983 | r \geq s | | |
| 1205.5935v1_FO0225 | 23 | 1.000 | A_{r} \wedge B_{s} | | |
| 1205.5935v1_FO0226 | 23 | 0.924 | \lambda, \lambda A=\lambda\rfloor A=\lambda \wedge A | | |
| 1205.5935v1_FO0227 | 23 | 0.924 | A \lambda=A\lfloor\lambda=A \wedge \lambda | | |
| 1205.5935v1_FO0228 | 23 | 0.846 | B_{s} A_{r} | | |
| 1205.5935v1_FO0229 | 23 | 0.846 | \left.A_{r}\right\rfloor B_{s} | | |
| 1205.5935v1_FO0230 | 23 | 0.846 | B_{s}\left\lfloor A_{r}\right. | | |
| 1205.5935v1_FO0231 | 23 | 1.000 | B_{s} \wedge A_{r} | | |
| 1205.5935v1_FO0232 | 23 | 1.000 | r+s-1 | | |
| 1205.5935v1_FO0233 | 23 | 1.000 | r-s+1 | | |
| 1205.5935v1_FO0234 | 23 | 1.000 | s-r+1 | | |
| 1205.5935v1_FO0235 | 24 | 0.999 | \left\rangle_{s+t}\right. | | |
| 1205.5935v1_FO0236 | 24 | 1.000 | A_{r} B_{s} C_{t} | | |
| 1205.5935v1_FO0237 | 24 | 1.000 | r+s+t | | |
| 1205.5935v1_FO0238 | 24 | 1.000 | B_{s} C_{t} | | |
| 1205.5935v1_FO0239 | 24 | 1.000 | A \wedge(B \wedge C)=(A \wedge B) \wedge C | | |
| 1205.5935v1_FO0240 | 24 | 1.000 | C | | |
| 1205.5935v1_FO0241 | 24 | 1.000 | r \leq s-t | | |
| 1205.5935v1_FO0242 | 24 | 1.000 | s-(r+t) | | |
| 1205.5935v1_FO0243 | 24 | 1.000 | A\rfloor(B\lfloor C)=(A\rfloor B)\lfloor C | | |
| 1205.5935v1_FO0244 | 25 | 1.000 | r+s \leq t | | |
| 1205.5935v1_FO0245 | 25 | 0.930 | A\rfloor(B\rfloor C)= | | |
| 1205.5935v1_FO0246 | 25 | 0.585 | (A \wedge B)\rfloor C | | |
| 1205.5935v1_FO0247 | 25 | 0.585 | A\lfloor B)\lfloor C=A\lfloor(B \wedge C) | | |
| 1205.5935v1_FO0248 | 25 | 1.000 | \left.\boldsymbol{B}_{\boldsymbol{s}}, \boldsymbol{A}_{\boldsymbol{r}}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0249 | 25 | 1.000 | \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0251 | 25 | 0.887 | \left\{a_{i_{j}}\right\}_{j=1, \ldots, r} | | |
| 1205.5935v1_FO0252 | 25 | 0.887 | \left\{a_{i}\right\}_{i=1, \ldots, s} | | |
| 1205.5935v1_FO0253 | 25 | 0.887 | i_{1} | | |
| 1205.5935v1_FO0254 | 25 | 1.000 | i_{r} | | |
| 1205.5935v1_FO0255 | 25 | 1.000 | i_{r+1} | | |
| 1205.5935v1_FO0256 | 25 | 1.000 | i_{s} | | |
| 1205.5935v1_FO0257 | 25 | 1.000 | B_{r} | | |
| 1205.5935v1_FO0258 | 25 | 0.987 | \binom{s}{r} | | |
| 1205.5935v1_FO0259 | 25 | 1.000 | \boldsymbol{B}_{\boldsymbol{r}}=a \wedge \boldsymbol{B}_{\boldsymbol{r}-\mathbf{1}} | | |
| 1205.5935v1_FO0260 | 25 | 1.000 | \boldsymbol{B}_{\boldsymbol{r}-\mathbf{1}} | | |
| 1205.5935v1_FO0261 | 26 | 0.991 | i_{r-1} | | |
| 1205.5935v1_FO0262 | 26 | 0.880 | (s-r+1)\binom{s}{r-1}=r\binom{s}{r} | | |
| 1205.5935v1_FO0263 | 26 | 1.000 | s-r | | |
| 1205.5935v1_FO0264 | 26 | 1.000 | C\left(a_{i_{1}}, \ldots, a_{i_{r}}\right) | | |
| 1205.5935v1_FO0265 | 26 | 1.000 | a_{i_{1}} | | |
| 1205.5935v1_FO0266 | 26 | 1.000 | a_{i_{r}} | | |
| 1205.5935v1_FO0267 | 26 | 1.000 | a_{i_{j}} | | |
| 1205.5935v1_FO0268 | 26 | 1.000 | \epsilon_{j} | | |
| 1205.5935v1_FO0269 | 26 | 0.982 | a_{i_{k}} | | |
| 1205.5935v1_FO0270 | 26 | 0.982 | k<j | | |
| 1205.5935v1_FO0271 | 26 | 1.000 | i_{k} | | |
| 1205.5935v1_FO0272 | 26 | 1.000 | k | | |
| 1205.5935v1_FO0273 | 26 | 1.000 | i_{k}-k | | |
| 1205.5935v1_FO0274 | 26 | 1.000 | k>j | | |
| 1205.5935v1_FO0275 | 26 | 1.000 | k-1 | | |
| 1205.5935v1_FO0276 | 26 | 1.000 | i_{k}-k+1 | | |
| 1205.5935v1_FO0277 | 26 | 1.000 | a_{i_{j+1}} | | |
| 1205.5935v1_FO0278 | 26 | 1.000 | i_{j} | | |
| 1205.5935v1_FO0279 | 26 | 1.000 | i_{j}-j+r | | |
| 1205.5935v1_FO0280 | 26 | 1.000 | i_{j}-j | | |
| 1205.5935v1_FO0281 | 27 | 1.000 | v \wedge n n^{-1} | | |
| 1205.5935v1_FO0282 | 27 | 1.000 | n v n | | |
| 1205.5935v1_FO0283 | 27 | 1.000 | n \wedge v \wedge n | | |
| 1205.5935v1_FO0284 | 27 | 1.000 | v \wedge n n | | |
| 1205.5935v1_FO0285 | 27 | 1.000 | v \wedge n \wedge n | | |
| 1205.5935v1_FO0286 | 27 | 0.996 | \left.\left(v \wedge n n^{-1}\right)\right\rfloor n | | |
| 1205.5935v1_FO0287 | 27 | 1.000 | v \wedge n | | |
| 1205.5935v1_FO0288 | 27 | 1.000 | r, s \geq 1 | | |
| 1205.5935v1_FO0289 | 27 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}} \wedge \boldsymbol{B}_{\boldsymbol{s}}=0 | | |
| 1205.5935v1_FO0290 | 27 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}} \wedge \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0291 | 28 | 1.000 | a \wedge \boldsymbol{A}_{\boldsymbol{r}} \wedge \boldsymbol{B}_{\boldsymbol{s}}=0 | | |
| 1205.5935v1_FO0292 | 28 | 0.592 | a \wedge \boldsymbol{B}_{\boldsymbol{s}}=0 | | |
| 1205.5935v1_FO0293 | 28 | 0.977 | \left.\boldsymbol{A}_{\boldsymbol{r}}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}}=0 | | |
| 1205.5935v1_FO0294 | 28 | 0.585 | r<s | | |
| 1205.5935v1_FO0295 | 28 | 0.585 | \left.\boldsymbol{A}_{\boldsymbol{r}}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0296 | 28 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}}=\boldsymbol{A}_{\boldsymbol{r}-\mathbf{1}} \wedge a_{1} | | |
| 1205.5935v1_FO0297 | 28 | 0.749 | a_{1} \downharpoonleft \boldsymbol{B}_{\boldsymbol{s}}=0 | | |
| 1205.5935v1_FO0298 | 28 | 0.413 | \boldsymbol{A}_{\boldsymbol{r}} \downharpoonleft \boldsymbol{B}_{\boldsymbol{s}}=0 | | |
| 1205.5935v1_FO0299 | 28 | 0.413 | \left.\left.\boldsymbol{A}_{\boldsymbol{r}-\mathbf{1}}\right\rfloor\left(a_{1}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}}\right)=0 | | |
| 1205.5935v1_FO0300 | 28 | 0.925 | \left.a_{1}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}}=0 | | |
| 1205.5935v1_FO0301 | 28 | 0.994 | a_{2} | | |
| 1205.5935v1_FO0302 | 28 | 0.994 | \left.a_{1}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0303 | 28 | 0.993 | b_{1} \wedge \cdots \wedge b_{s} | | |
| 1205.5935v1_FO0304 | 28 | 0.993 | a_{1} \downharpoonleft b_{1} \neq 0 | | |
| 1205.5935v1_FO0305 | 28 | 0.470 | a_{2} \downarrow b_{1} \neq 0 | | |
| 1205.5935v1_FO0306 | 28 | 0.999 | b_{1} | | |
| 1205.5935v1_FO0307 | 28 | 0.997 | \left.\boldsymbol{A}_{\boldsymbol{r}}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}}= | | |
| 1205.5935v1_FO0308 | 28 | 0.301 | \left.\left.\boldsymbol{A}_{\boldsymbol{r}-\mathbf{1}}\right\rfloor\left(a_{1}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}}\right) \neq 0 | | |
| 1205.5935v1_FO0309 | 29 | 0.975 | r>s ; \boldsymbol{A}_{\boldsymbol{r}} \downharpoonleft \boldsymbol{B}_{\boldsymbol{s}}=0 | | |
| 1205.5935v1_FO0310 | 29 | 0.958 | \left.\boldsymbol{B}_{\boldsymbol{s}}\right\rfloor \boldsymbol{A}_{\boldsymbol{r}} | | |
| 1205.5935v1_FO0311 | 29 | 1.000 | \boldsymbol{B}_{\boldsymbol{p}} | | |
| 1205.5935v1_FO0312 | 29 | 0.997 | p=s | | |
| 1205.5935v1_FO0313 | 29 | 0.998 | p<s | | |
| 1205.5935v1_FO0314 | 29 | 0.998 | \boldsymbol{B}_{\boldsymbol{s}}=\boldsymbol{B}_{\boldsymbol{p}} \wedge \boldsymbol{B}_{\boldsymbol{s}-\boldsymbol{p}} | | |
| 1205.5935v1_FO0315 | 29 | 0.998 | \boldsymbol{B}_{\boldsymbol{s}-\boldsymbol{p}} | | |
| 1205.5935v1_FO0316 | 29 | 0.680 | \left.\boldsymbol{B}_{\boldsymbol{s}-\boldsymbol{p}}\right\rfloor \boldsymbol{A}_{\boldsymbol{r}} \neq 0 | | |
| 1205.5935v1_FO0317 | 29 | 0.680 | \boldsymbol{B}_{\boldsymbol{s}-\boldsymbol{p}} \downharpoonleft \boldsymbol{A}_{\boldsymbol{r}} | | |
| 1205.5935v1_FO0318 | 29 | 1.000 | A_{r}\left\lfloor B_{s}=(-1)^{r(s-1)} B_{s}\right\rfloor A_{r} | | |
| 1205.5935v1_FO0319 | 29 | 1.000 | \boldsymbol{A} | | |
| 1205.5935v1_FO0320 | 29 | 1.000 | \boldsymbol{A}^{2} | | |
| 1205.5935v1_FO0321 | 29 | 1.000 | \boldsymbol{A}^{2} \neq 0 | | |
| 1205.5935v1_FO0322 | 29 | 1.000 | \boldsymbol{A}^{-1}=\boldsymbol{A} / \boldsymbol{A}^{2} | | |
| 1205.5935v1_FO0323 | 29 | 1.000 | \boldsymbol{A}^{-1} | | |
| 1205.5935v1_FO0324 | 29 | 1.000 | 1 \leq r \leq s | | |
| 1205.5935v1_FO0325 | 29 | 0.978 | \left.\boldsymbol{A}_{\boldsymbol{r}} \boldsymbol{B}_{\boldsymbol{s}}=\boldsymbol{A}_{\boldsymbol{r}}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0326 | 29 | 1.000 | s=1 | | |
| 1205.5935v1_FO0327 | 29 | 0.986 | a \boldsymbol{B}_{\boldsymbol{s}}=a \downharpoonleft \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0328 | 29 | 0.960 | \boldsymbol{B}_{\boldsymbol{s}} ; \mathrm{I} | | |
| 1205.5935v1_FO0329 | 29 | 0.960 | \boldsymbol{A}_{\boldsymbol{r}}=\boldsymbol{A}_{\boldsymbol{r}-\mathbf{1}} a | | |
| 1205.5935v1_FO0330 | 29 | 0.659 | a\rfloor \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0331 | 29 | 0.659 | a \downharpoonleft \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0332 | 29 | 0.389 | a\rfloor \boldsymbol{B}_{\boldsymbol{s}}=0 | | |
| 1205.5935v1_FO0333 | 29 | 0.969 | \left.\boldsymbol{B}_{\boldsymbol{s}}=\boldsymbol{A}_{\boldsymbol{r}}^{-1} \boldsymbol{A}_{\boldsymbol{r}}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0334 | 29 | 0.826 | \boldsymbol{B}_{\boldsymbol{s}} \neq 0 | | |
| 1205.5935v1_FO0335 | 29 | 0.826 | \left.\boldsymbol{A}_{\boldsymbol{r}}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}} \neq 0 | | |
| 1205.5935v1_FO0336 | 29 | 0.826 | r=s | | |
| 1205.5935v1_FO0337 | 29 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}}^{-1} | | |
| 1205.5935v1_FO0338 | 29 | 0.763 | \left.\boldsymbol{A}_{\boldsymbol{r}}^{-1} \boldsymbol{A}_{\boldsymbol{r}}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0339 | 29 | 0.386 | \boldsymbol{B}_{\boldsymbol{s}}=\boldsymbol{A}_{\boldsymbol{r}}^{-1} \wedge\left(\boldsymbol{A}_{\boldsymbol{r}} \downharpoonleft \boldsymbol{B}_{\boldsymbol{s}}\right) | | |
| 1205.5935v1_FO0340 | 29 | 0.386 | \boldsymbol{A}_{\boldsymbol{r}} \downharpoonleft \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0341 | 30 | 0.951 | \left.\boldsymbol{A}_{\boldsymbol{r}}=\boldsymbol{A}_{\boldsymbol{r}}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}} \boldsymbol{B}_{\boldsymbol{s}}^{-1} | | |
| 1205.5935v1_FO0342 | 30 | 0.951 | r=s, \boldsymbol{A}_{\boldsymbol{r}} | | |
| 1205.5935v1_FO0343 | 30 | 0.996 | \left.\boldsymbol{A}_{\boldsymbol{r}}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}} \boldsymbol{B}_{\boldsymbol{s}}^{-1} | | |
| 1205.5935v1_FO0344 | 30 | 0.986 | \left.\left.\boldsymbol{A}_{\boldsymbol{r}}=\left(\boldsymbol{A}_{\boldsymbol{r}}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}}\right)\right\rfloor \boldsymbol{B}_{\boldsymbol{s}}^{-1} | | |
| 1205.5935v1_FO0345 | 30 | 0.986 | \boldsymbol{B}_{\boldsymbol{s}}^{-1} | | |
| 1205.5935v1_FO0346 | 30 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}} \boldsymbol{B}_{\boldsymbol{s}}=\boldsymbol{A}_{\boldsymbol{r}} \wedge \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0347 | 30 | 1.000 | b_{1} b_{2} \cdots b_{s} | | |
| 1205.5935v1_FO0348 | 30 | 0.893 | a \boldsymbol{B}_{\boldsymbol{s}}=a \wedge \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0349 | 30 | 0.893 | \left.a\right\rfloor \boldsymbol{B}_{\boldsymbol{s}}=0 | | |
| 1205.5935v1_FO0350 | 30 | 0.995 | \boldsymbol{B}_{\boldsymbol{s}}= | | |
| 1205.5935v1_FO0351 | 30 | 0.987 | \boldsymbol{A}_{\boldsymbol{r}}^{-1} \boldsymbol{A}_{\boldsymbol{r}} \wedge \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0352 | 30 | 0.998 | \left.\boldsymbol{B}_{\boldsymbol{s}}=\boldsymbol{A}_{\boldsymbol{r}}^{-1}\right\rfloor\left(\boldsymbol{A}_{\boldsymbol{r}} \wedge \boldsymbol{B}_{\boldsymbol{s}}\right) | | |
| 1205.5935v1_FO0353 | 30 | 0.999 | e_{1}, e_{2}, e_{3} | | |
| 1205.5935v1_FO0354 | 30 | 0.999 | e_{4} | | |
| 1205.5935v1_FO0355 | 30 | 0.979 | \boldsymbol{A}_{\mathbf{3}}=e_{1} e_{2} e_{3} | | |
| 1205.5935v1_FO0356 | 30 | 0.979 | \boldsymbol{B}_{\mathbf{3}}=e_{2} e_{3} e_{4} | | |
| 1205.5935v1_FO0357 | 30 | 0.979 | e_{2}^{2}=0 | | |
| 1205.5935v1_FO0358 | 30 | 0.979 | \boldsymbol{A}_{\mathbf{3}} \boldsymbol{B}_{\mathbf{3}}=0 | | |
| 1205.5935v1_FO0359 | 30 | 0.979 | \left.\boldsymbol{A}_{\mathbf{3}}\right\rfloor \boldsymbol{B}_{\mathbf{3}}=\boldsymbol{A}_{\mathbf{3}} \wedge \boldsymbol{B}_{\mathbf{3}}=0 | | |
| 1205.5935v1_FO0360 | 30 | 1.000 | \boldsymbol{A}_{\mathbf{3}} | | |
| 1205.5935v1_FO0361 | 30 | 1.000 | \boldsymbol{B}_{\mathbf{3}} | | |
| 1205.5935v1_FO0362 | 30 | 1.000 | e_{3} | | |
| 1205.5935v1_FO0363 | 30 | 1.000 | \left.A_{r} B_{s}=A_{r}\right\rfloor B_{s} | | |
| 1205.5935v1_FO0364 | 30 | 1.000 | B_{s} A_{r}=B_{s}\left\lfloor A_{r}\right. | | |
| 1205.5935v1_FO0365 | 30 | 1.000 | z | | |
| 1205.5935v1_FO0366 | 30 | 0.838 | x y | | |
| 1205.5935v1_FO0367 | 30 | 0.838 | \boldsymbol{B}_{\boldsymbol{s}}=\boldsymbol{A}_{\boldsymbol{r}} \wedge\left(\boldsymbol{A}_{\boldsymbol{r}} \downharpoonleft \boldsymbol{B}_{\boldsymbol{s}}\right) | | |
| 1205.5935v1_FO0368 | 30 | 0.637 | \boldsymbol{B}_{\boldsymbol{s}}=\boldsymbol{A}_{\boldsymbol{r}} \wedge\left(\boldsymbol{A}_{\boldsymbol{r}}^{-1} \downharpoonleft \boldsymbol{B}_{\boldsymbol{s}}\right) | | |
| 1205.5935v1_FO0369 | 30 | 0.657 | \boldsymbol{A}_{\boldsymbol{r}}^{2} \boldsymbol{B}_{\boldsymbol{s}}= | | |
| 1205.5935v1_FO0370 | 30 | 0.804 | \boldsymbol{A}_{\boldsymbol{r}} \wedge\left(\boldsymbol{A}_{\boldsymbol{r}} \downharpoonleft \boldsymbol{B}_{\boldsymbol{s}}\right) | | |
| 1205.5935v1_FO0371 | 31 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}}^{2} | | |
| 1205.5935v1_FO0372 | 31 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}}^{2} \neq 0 | | |
| 1205.5935v1_FO0373 | 31 | 0.804 | \left.\boldsymbol{B}_{\boldsymbol{s}}=\boldsymbol{A}_{\boldsymbol{r}} \wedge\left(\boldsymbol{A}_{\boldsymbol{r}}^{-1}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}}\right) | | |
| 1205.5935v1_FO0374 | 31 | 0.991 | \left.\boldsymbol{A}_{\boldsymbol{r}} \wedge\left(\boldsymbol{A}_{\boldsymbol{r}}\right\rfloor \boldsymbol{B}_{\boldsymbol{s}}\right)=0 | | |
| 1205.5935v1_FO0375 | 31 | 0.991 | \boldsymbol{A}_{\boldsymbol{r}}^{2}=0 | | |
| 1205.5935v1_FO0376 | 31 | 1.000 | \left(A^{-1}\right)^{*} A^{*}= | | |
| 1205.5935v1_FO0377 | 31 | 1.000 | \left(A^{-1} A\right)^{*}=1^{*}=1 | | |
| 1205.5935v1_FO0378 | 32 | 1.000 | A\lfloor a | | |
| 1205.5935v1_FO0379 | 32 | 1.000 | A \wedge a | | |
| 1205.5935v1_FO0380 | 32 | 0.999 | { }^{* r} | | |
| 1205.5935v1_FO0381 | 32 | 0.999 | A^{* r} | | |
| 1205.5935v1_FO0382 | 32 | 0.999 | A^{*} | | |
| 1205.5935v1_FO0383 | 32 | 0.995 | { }^{\dagger} | | |
| 1205.5935v1_FO0384 | 33 | 1.000 | r(r-1) / 2 | | |
| 1205.5935v1_FO0385 | 33 | 1.000 | \left(A^{-1}\right)^{\dagger} A^{\dagger}=\left(A A^{-1}\right)^{\dagger}=1^{\dagger}=1 | | |
| 1205.5935v1_FO0386 | 33 | 1.000 | \left\langle A_{r} B_{s}\right\rangle=\left\langle B_{s} A_{r}\right\rangle=0 | | |
| 1205.5935v1_FO0387 | 33 | 1.000 | r \neq s | | |
| 1205.5935v1_FO0388 | 33 | 1.000 | \left\langle A_{r} B_{s}\right\rangle=\left\langle B_{s} A_{r}\right\rangle | | |
| 1205.5935v1_FO0389 | 34 | 1.000 | j=r | | |
| 1205.5935v1_FO0390 | 34 | 1.000 | j=0 | | |
| 1205.5935v1_FO0391 | 34 | 0.951 | (n v n)^{\dagger}=n v n | | |
| 1205.5935v1_FO0392 | 34 | 1.000 | { }^{\ddagger} | | |
| 1205.5935v1_FO0393 | 35 | 1.000 | A * B=\langle A B\rangle | | |
| 1205.5935v1_FO0394 | 36 | 1.000 | \left\langle A B^{\dagger}\right\rangle | | |
| 1205.5935v1_FO0395 | 36 | 1.000 | A *(B \wedge C) | | |
| 1205.5935v1_FO0396 | 36 | 1.000 | |A|^{2}=0 | | |
| 1205.5935v1_FO0397 | 36 | 1.000 | |A|^{2}= \pm 1 | | |
| 1205.5935v1_FO0398 | 36 | 1.000 | |A|^{2} | | |
| 1205.5935v1_FO0399 | 36 | 1.000 | |A|^{n} | | |
| 1205.5935v1_FO0400 | 37 | 1.000 | A^{\dagger} A | | |
| 1205.5935v1_FO0401 | 37 | 1.000 | B=C | | |
| 1205.5935v1_FO0402 | 37 | 1.000 | |A| \neq 0 | | |
| 1205.5935v1_FO0403 | 37 | 0.998 | A B=1 | | |
| 1205.5935v1_FO0404 | 37 | 1.000 | B^{\dagger} A^{\dagger}=1 | | |
| 1205.5935v1_FO0405 | 37 | 1.000 | \left|A^{-1}\right|^{2} | | |
| 1205.5935v1_FO0406 | 38 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}}^{\dagger}=(-1)^{r(r-1) / 2} \boldsymbol{A}_{\boldsymbol{r}},|A|^{2}=A^{\dagger} A | | |
| 1205.5935v1_FO0407 | 38 | 1.000 | \left|\boldsymbol{A}_{\boldsymbol{r}}\right|^{2}=(-1)^{r(r-1) / 2} \boldsymbol{A}_{\boldsymbol{r}}^{2} | | |
| 1205.5935v1_FO0408 | 38 | 0.760 | \boldsymbol{A}_{\boldsymbol{r}}^{2}= \pm 1 | | |
| 1205.5935v1_FO0409 | 38 | 0.999 | (a \wedge b)^{2} | | |
| 1205.5935v1_FO0410 | 38 | 0.999 | -a^{2} b^{2} \sin ^{2} \theta | | |
| 1205.5935v1_FO0411 | 38 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}}=e_{1} e_{2} \cdots e_{r} | | |
| 1205.5935v1_FO0412 | 38 | 1.000 | e_{i}^{2}=0 | | |
| 1205.5935v1_FO0413 | 38 | 1.000 | \left\{e_{j}\right\}_{i=1, \ldots, r} | | |
| 1205.5935v1_FO0414 | 38 | 1.000 | e_{i}=0 | | |
| 1205.5935v1_FO0415 | 38 | 1.000 | e_{i} \neq 0 | | |
| 1205.5935v1_FO0416 | 38 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}} \neq 0 | | |
| 1205.5935v1_FO0417 | 38 | 1.000 | A_{r} B_{s}=0 | | |
| 1205.5935v1_FO0418 | 38 | 1.000 | \left|A_{r}\right|^{2} B_{s}=A_{r}^{\dagger} A_{r} B_{s}=0 | | |
| 1205.5935v1_FO0419 | 38 | 1.000 | \left|A_{r}\right|^{2}=0 | | |
| 1205.5935v1_FO0420 | 38 | 1.000 | B_{s}^{\dagger} | | |
| 1205.5935v1_FO0421 | 38 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}}\left(a \wedge \boldsymbol{A}_{\boldsymbol{r}}=0\right) | | |
| 1205.5935v1_FO0422 | 38 | 0.491 | \left.(a\rfloor \boldsymbol{A}_{\boldsymbol{r}}=0\right) | | |
| 1205.5935v1_FO0423 | 38 | 0.491 | a \boldsymbol{A}_{\boldsymbol{r}}=0 | | |
| 1205.5935v1_FO0424 | 39 | 1.000 | \left.B\right\rfloor \boldsymbol{A}_{\boldsymbol{r}}^{-1} | | |
| 1205.5935v1_FO0425 | 39 | 1.000 | s>r | | |
| 1205.5935v1_FO0426 | 39 | 1.000 | s=r | | |
| 1205.5935v1_FO0427 | 39 | 0.996 | s<r | | |
| 1205.5935v1_FO0428 | 39 | 0.996 | r-s | | |
| 1205.5935v1_FO0429 | 39 | 0.998 | \boldsymbol{B}_{\boldsymbol{s}} \boldsymbol{A}_{\boldsymbol{r}}^{-1} | | |
| 1205.5935v1_FO0430 | 39 | 1.000 | \boldsymbol{I} | | |
| 1205.5935v1_FO0431 | 39 | 1.000 | |\boldsymbol{I}|^{2} | | |
| 1205.5935v1_FO0432 | 39 | 0.635 | \boldsymbol{I}=e_{1} e_{2} \cdots e_{n} | | |
| 1205.5935v1_FO0433 | 39 | 0.999 | |\boldsymbol{I}|^{2}=1 | | |
| 1205.5935v1_FO0434 | 39 | 0.999 | |\boldsymbol{I}|^{2}=-1 | | |
| 1205.5935v1_FO0435 | 39 | 0.999 | |\boldsymbol{I}|^{2}=\boldsymbol{I}^{\dagger} \boldsymbol{I} | | |
| 1205.5935v1_FO0436 | 39 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}} \wedge \boldsymbol{A}_{\boldsymbol{s}-\boldsymbol{r}}=\boldsymbol{A}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0437 | 39 | 0.835 | A^{\perp} | | |
| 1205.5935v1_FO0438 | 39 | 1.000 | s>n | | |
| 1205.5935v1_FO0439 | 39 | 1.000 | \boldsymbol{B}_{\boldsymbol{n}}=\lambda \boldsymbol{I} | | |
| 1205.5935v1_FO0440 | 39 | 1.000 | \boldsymbol{B}_{\boldsymbol{n}} | | |
| 1205.5935v1_FO0441 | 40 | 1.000 | s<n | | |
| 1205.5935v1_FO0442 | 40 | 1.000 | \boldsymbol{B}_{\boldsymbol{s}} \boldsymbol{I}^{-1} | | |
| 1205.5935v1_FO0443 | 40 | 0.731 | \boldsymbol{I}^{-1} | | |
| 1205.5935v1_FO0444 | 40 | 0.731 | A^{-\perp} | | |
| 1205.5935v1_FO0445 | 40 | 0.731 | \boldsymbol{I}^{-1}=\boldsymbol{I} / \boldsymbol{I}^{2}, A^{\perp} | | |
| 1205.5935v1_FO0446 | 40 | 1.000 | \boldsymbol{I}^{2} | | |
| 1205.5935v1_FO0447 | 40 | 0.999 | n-1 | | |
| 1205.5935v1_FO0448 | 40 | 0.999 | A_{n-1} | | |
| 1205.5935v1_FO0449 | 41 | 1.000 | C=\boldsymbol{I}^{-1} | | |
| 1205.5935v1_FO0450 | 41 | 1.000 | B^{\perp} | | |
| 1205.5935v1_FO0451 | 41 | 0.993 | \left(a \downharpoonleft \boldsymbol{A}_{\boldsymbol{r}}\right)^{\perp}=a \wedge \boldsymbol{A}_{\boldsymbol{r}}^{\perp} | | |
| 1205.5935v1_FO0452 | 41 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}}^{\perp} | | |
| 1205.5935v1_FO0453 | 41 | 0.996 | a \downharpoonleft \boldsymbol{A}_{\boldsymbol{r}}^{\perp}=0 | | |
| 1205.5935v1_FO0454 | 42 | 1.000 | \frac{1}{2} | | |
| 1205.5935v1_FO0455 | 42 | 1.000 | A \times(B C) | | |
| 1205.5935v1_FO0456 | 42 | 1.000 | A \times(C B) | | |
| 1205.5935v1_FO0457 | 42 | 1.000 | A=\langle A\rangle_{+}+\langle A\rangle_{-} | | |
| 1205.5935v1_FO0458 | 42 | 1.000 | A=\lambda+\mu\langle\boldsymbol{I}\rangle_{-} | | |
| 1205.5935v1_FO0459 | 42 | 1.000 | \lambda+\mu \boldsymbol{I} | | |
| 1205.5935v1_FO0460 | 42 | 1.000 | a \times \boldsymbol{I}=a \wedge \boldsymbol{I} | | |
| 1205.5935v1_FO0461 | 42 | 0.958 | a \downharpoonleft \boldsymbol{I} | | |
| 1205.5935v1_FO0462 | 42 | 0.958 | a \wedge \boldsymbol{I}=0 | | |
| 1205.5935v1_FO0463 | 42 | 0.958 | a \downharpoonleft \boldsymbol{I} \neq 0 | | |
| 1205.5935v1_FO0464 | 42 | 0.614 | 0<r<n | | |
| 1205.5935v1_FO0465 | 42 | 0.614 | \left.a \times \boldsymbol{A}_{\boldsymbol{r}}=a\right\rfloor \boldsymbol{A}_{\boldsymbol{r}} | | |
| 1205.5935v1_FO0466 | 42 | 1.000 | a \times \boldsymbol{A}_{\boldsymbol{r}}=a \wedge \boldsymbol{A}_{\boldsymbol{r}} | | |
| 1205.5935v1_FO0467 | 42 | 1.000 | r<n | | |
| 1205.5935v1_FO0468 | 43 | 0.623 | r \geq 2 | | |
| 1205.5935v1_FO0469 | 43 | 0.623 | r<2 | | |
| 1205.5935v1_FO0470 | 43 | 0.623 | A_{2} \downharpoonleft A_{r}=0 | | |
| 1205.5935v1_FO0471 | 43 | 1.000 | j=1 | | |
| 1205.5935v1_FO0472 | 43 | 1.000 | A=A_{2} | | |
| 1205.5935v1_FO0473 | 43 | 1.000 | \boldsymbol{B}_{\boldsymbol{r}-\mathbf{1}}=a_{1} \wedge a_{2} \wedge \cdots \wedge a_{r-1} | | |
| 1205.5935v1_FO0474 | 44 | 1.000 | \mathbb{R}^{2} | | |
| 1205.5935v1_FO0475 | 44 | 1.000 | \mathbb{E}^{2} | | |
| 1205.5935v1_FO0476 | 44 | 1.000 | \left\{e_{1}, e_{2}\right\} | | |
| 1205.5935v1_FO0477 | 44 | 1.000 | 1, e_{1}, e_{2} | | |
| 1205.5935v1_FO0478 | 44 | 1.000 | e_{1} e_{2} | | |
| 1205.5935v1_FO0479 | 44 | 0.999 | \boldsymbol{I}^{2}=-1 | | |
| 1205.5935v1_FO0480 | 44 | 1.000 | \pi / 2 | | |
| 1205.5935v1_FO0481 | 44 | 0.978 | Z=x+\boldsymbol{I} y | | |
| 1205.5935v1_FO0482 | 44 | 0.978 | y | | |
| 1205.5935v1_FO0483 | 44 | 1.000 | z=r e^{i \theta} | | |
| 1205.5935v1_FO0484 | 44 | 1.000 | z=x e_{1}+y e_{2} | | |
| 1205.5935v1_FO0485 | 44 | 1.000 | z^{\prime}=-e_{2} z e_{2} | | |
| 1205.5935v1_FO0486 | 45 | 1.000 | w | | |
| 1205.5935v1_FO0487 | 45 | 1.000 | W | | |
| 1205.5935v1_FO0488 | 45 | 1.000 | Z | | |
| 1205.5935v1_FO0489 | 45 | 1.000 | r \exp (-\boldsymbol{I} \theta) | | |
| 1205.5935v1_FO0490 | 45 | 0.911 | R=\exp (-\boldsymbol{I} \theta / 2) | | |
| 1205.5935v1_FO0491 | 45 | 1.000 | \exp (\boldsymbol{I} \theta) | | |
| 1205.5935v1_FO0492 | 45 | 1.000 | \mathbb{E}^{3} | | |
| 1205.5935v1_FO0493 | 45 | 1.000 | \left\{e_{1}, e_{2}, e_{3}\right\} | | |
| 1205.5935v1_FO0494 | 45 | 1.000 | 1, e_{1}, e_{2}, e_{3}, e_{1} e_{2}, e_{1} e_{3}, e_{2} e_{3} | | |
| 1205.5935v1_FO0495 | 45 | 1.000 | e_{1} e_{2} e_{3} | | |
| 1205.5935v1_FO0496 | 45 | 0.998 | |\boldsymbol{I}|^{2}=\boldsymbol{I}^{\dagger} \boldsymbol{I}=1 | | |
| 1205.5935v1_FO0497 | 46 | 0.998 | -\boldsymbol{I} | | |
| 1205.5935v1_FO0498 | 46 | 1.000 | W^{\dagger} Z | | |
| 1205.5935v1_FO0499 | 46 | 1.000 | a \cdot b \times c | | |
| 1205.5935v1_FO0500 | 46 | 1.000 | a \times(b \times c) | | |
| 1205.5935v1_FO0501 | 46 | 0.832 | (a \wedge b)^{\perp}=a \downharpoonleft b^{\perp} | | |
| 1205.5935v1_FO0502 | 46 | 0.832 | b^{\perp} | | |
| 1205.5935v1_FO0503 | 46 | 1.000 | a \times b | | |
| 1205.5935v1_FO0504 | 46 | 1.000 | \boldsymbol{v}=\boldsymbol{\omega} \times \boldsymbol{r} | | |
| 1205.5935v1_FO0505 | 46 | 1.000 | v=\Omega\left\lfloor r\right. | | |
| 1205.5935v1_FO0506 | 46 | 1.000 | \Omega=\boldsymbol{\omega}^{\perp} | | |
| 1205.5935v1_FO0507 | 46 | 1.000 | \boldsymbol{F}=q \boldsymbol{v} \times \boldsymbol{B} | | |
| 1205.5935v1_FO0508 | 46 | 1.000 | \boldsymbol{B} | | |
| 1205.5935v1_FO0509 | 46 | 0.777 | F=q v \downharpoonleft B | | |
| 1205.5935v1_FO0510 | 46 | 0.777 | B=B^{\perp} | | |
| 1205.5935v1_FO0511 | 46 | 0.884 | \boldsymbol{A}_{\mathbf{2}} | | |
| 1205.5935v1_FO0512 | 46 | 1.000 | \boldsymbol{B}_{\mathbf{2}} | | |
| 1205.5935v1_FO0513 | 46 | 1.000 | \boldsymbol{A}_{\mathbf{2}}=a \wedge b | | |
| 1205.5935v1_FO0514 | 46 | 1.000 | \boldsymbol{B}_{\mathbf{2}}=a \wedge c | | |
| 1205.5935v1_FO0515 | 46 | 1.000 | a=a_{\|}+a_{\perp} | | |
| 1205.5935v1_FO0516 | 46 | 1.000 | a_{\|} | | |
| 1205.5935v1_FO0517 | 46 | 1.000 | a_{\perp} | | |
| 1205.5935v1_FO0518 | 46 | 1.000 | \boldsymbol{B}=a_{\|} b | | |
| 1205.5935v1_FO0519 | 46 | 0.973 | a \downharpoonleft \boldsymbol{B} | | |
| 1205.5935v1_FO0520 | 46 | 1.000 | a \wedge \boldsymbol{B} | | |
| 1205.5935v1_FO0521 | 47 | 1.000 | \boldsymbol{T} | | |
| 1205.5935v1_FO0522 | 47 | 1.000 | \boldsymbol{T}=a b c | | |
| 1205.5935v1_FO0523 | 47 | 0.922 | a \boldsymbol{T} | | |
| 1205.5935v1_FO0524 | 47 | 0.922 | a \downharpoonleft \boldsymbol{T} | | |
| 1205.5935v1_FO0525 | 47 | 0.999 | \boldsymbol{A}_{\mathbf{2}}=b a | | |
| 1205.5935v1_FO0526 | 47 | 0.999 | \boldsymbol{B}_{\mathbf{2}}=a c | | |
| 1205.5935v1_FO0527 | 47 | 0.976 | \left.\boldsymbol{A}_{\mathbf{2}}\right\rfloor \boldsymbol{B}_{\mathbf{2}}=\boldsymbol{A}_{\mathbf{2}}\left\lfloor\boldsymbol{B}_{\mathbf{2}}\right. | | |
| 1205.5935v1_FO0528 | 47 | 0.976 | \boldsymbol{A}_{\mathbf{2}} \times \boldsymbol{B}_{\mathbf{2}} | | |
| 1205.5935v1_FO0529 | 47 | 1.000 | \boldsymbol{B}=a b | | |
| 1205.5935v1_FO0530 | 47 | 1.000 | \boldsymbol{T}=b a c | | |
| 1205.5935v1_FO0531 | 47 | 0.984 | \boldsymbol{B}\rfloor \boldsymbol{T} | | |
| 1205.5935v1_FO0532 | 47 | 1.000 | \hat{\boldsymbol{x}}, \hat{\boldsymbol{y}} | | |
| 1205.5935v1_FO0533 | 47 | 1.000 | \hat{\boldsymbol{z}} | | |
| 1205.5935v1_FO0534 | 47 | 1.000 | \boldsymbol{B}_{\boldsymbol{i}} | | |
| 1205.5935v1_FO0535 | 48 | 1.000 | P_{u}(v) | | |
| 1205.5935v1_FO0536 | 48 | 1.000 | u, R_{u}(v) | | |
| 1205.5935v1_FO0537 | 48 | 1.000 | P_{u}(v)+R_{u}(v)=v | | |
| 1205.5935v1_FO0538 | 48 | 1.000 | S | | |
| 1205.5935v1_FO0539 | 48 | 1.000 | v \in S | | |
| 1205.5935v1_FO0540 | 48 | 1.000 | a=v+(a-v) | | |
| 1205.5935v1_FO0541 | 48 | 1.000 | S_{1} | | |
| 1205.5935v1_FO0542 | 48 | 1.000 | S_{2} | | |
| 1205.5935v1_FO0543 | 48 | 1.000 | S^{\perp} | | |
| 1205.5935v1_FO0544 | 48 | 0.603 | P_{\boldsymbol{A}_{\boldsymbol{r}}}(a)+R_{\boldsymbol{A}_{\boldsymbol{r}}}(a)=a | | |
| 1205.5935v1_FO0545 | 48 | 0.603 | \left.a\right\rfloor \boldsymbol{A}_{\boldsymbol{r}} | | |
| 1205.5935v1_FO0546 | 48 | 1.000 | \left(a \wedge \boldsymbol{A}_{\boldsymbol{r}}\right)^{-1} | | |
| 1205.5935v1_FO0547 | 49 | 0.998 | P_{\boldsymbol{A}_{\boldsymbol{r}}}(a) | | |
| 1205.5935v1_FO0548 | 49 | 1.000 | R_{\boldsymbol{A}_{\boldsymbol{r}}}(a) | | |
| 1205.5935v1_FO0549 | 49 | 1.000 | b_{1}=a_{1} | | |
| 1205.5935v1_FO0550 | 49 | 1.000 | b_{2} | | |
| 1205.5935v1_FO0551 | 49 | 1.000 | b_{3} | | |
| 1205.5935v1_FO0552 | 49 | 1.000 | a_{3} | | |
| 1205.5935v1_FO0553 | 49 | 0.984 | \boldsymbol{B}_{\boldsymbol{j}}=b_{1} \wedge \cdots \wedge b_{j} | | |
| 1205.5935v1_FO0554 | 49 | 0.992 | b_{j+1}=a_{j+1} \wedge \boldsymbol{B}_{\boldsymbol{j}} \boldsymbol{B}_{\boldsymbol{j}}^{-1} | | |
| 1205.5935v1_FO0555 | 49 | 1.000 | \boldsymbol{B}_{\boldsymbol{j}} | | |
| 1205.5935v1_FO0556 | 49 | 0.999 | \boldsymbol{A}_{\boldsymbol{r}} \wedge \boldsymbol{B}_{\boldsymbol{s}}=\boldsymbol{A}_{\boldsymbol{r}} \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0557 | 49 | 0.798 | \left.a\right\rfloor \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0558 | 49 | 0.998 | (-1)^{r(s-1)} | | |
| 1205.5935v1_FO0559 | 49 | 1.000 | (-1)^{r s} | | |
| 1205.5935v1_FO0560 | 50 | 1.000 | \left\{b_{j}\right\}_{j=1, \cdots, s} | | |
| 1205.5935v1_FO0561 | 50 | 0.977 | \left\{b_{j}\right\}_{j=1, \ldots, s} | | |
| 1205.5935v1_FO0562 | 50 | 0.999 | b_{j}=P_{\boldsymbol{A}_{\boldsymbol{r}}}\left(b_{j}\right)+R_{\boldsymbol{A}_{\boldsymbol{r}}}\left(b_{j}\right) | | |
| 1205.5935v1_FO0563 | 50 | 0.830 | P_{\boldsymbol{A}_{r}}\left(b_{1}\right) \wedge \cdots \wedge P_{\boldsymbol{A}_{r}}\left(b_{s}\right) | | |
| 1205.5935v1_FO0564 | 50 | 1.000 | R_{\boldsymbol{A}_{\boldsymbol{r}}}\left(b_{j}\right) | | |
| 1205.5935v1_FO0565 | 50 | 1.000 | P_{\boldsymbol{A}_{\boldsymbol{r}}}\left(b_{1}\right) \wedge \cdots \wedge P_{\boldsymbol{A}_{\boldsymbol{r}}}\left(b_{s}\right) | | |
| 1205.5935v1_FO0566 | 50 | 0.952 | R_{\boldsymbol{A}_{\boldsymbol{r}}}\left(b_{1}\right) \wedge \cdots \wedge R_{\boldsymbol{A}_{\boldsymbol{r}}}\left(b_{s}\right) | | |
| 1205.5935v1_FO0567 | 50 | 0.952 | P_{\boldsymbol{A}_{\boldsymbol{r}}}\left(b_{j}\right) | | |
| 1205.5935v1_FO0568 | 50 | 0.919 | P_{\boldsymbol{A}_{\boldsymbol{r}}}\left(\boldsymbol{B}_{\boldsymbol{s}}\right)=\boldsymbol{B}_{\boldsymbol{s}} \downharpoonleft \boldsymbol{A}_{\boldsymbol{r}} \boldsymbol{A}_{\boldsymbol{r}}^{-1} | | |
| 1205.5935v1_FO0569 | 50 | 0.919 | R_{\boldsymbol{A}_{\boldsymbol{r}}}\left(\boldsymbol{B}_{\boldsymbol{s}}\right)=\boldsymbol{B}_{\boldsymbol{s}} \wedge \boldsymbol{A}_{\boldsymbol{r}} \boldsymbol{A}_{\boldsymbol{r}}^{-1} | | |
| 1205.5935v1_FO0570 | 51 | 0.529 | A\rfloor \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0571 | 51 | 0.529 | P_{\boldsymbol{B}_{\boldsymbol{s}}}(A) | | |
| 1205.5935v1_FO0572 | 51 | 0.628 | P_{\boldsymbol{A}_{\boldsymbol{r}}}(B)+R_{\boldsymbol{A}_{\boldsymbol{r}}}(B)=B | | |
| 1205.5935v1_FO0573 | 52 | 0.730 | a^{* r} | | |
| 1205.5935v1_FO0574 | 52 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}}=a_{1} a_{2} \cdots a_{r} | | |
| 1205.5935v1_FO0575 | 52 | 1.000 | a B_{s} a | | |
| 1205.5935v1_FO0576 | 52 | 0.993 | (-1)^{s-1}\left(B_{s}\lfloor a)\left\lfloor a=(-1)^{s-1} B_{s}\lfloor(a \wedge a)=0\right.\right. | | |
| 1205.5935v1_FO0577 | 52 | 1.000 | \left(A B A^{-1}\right) \wedge\left(A C A^{-1}\right)=A(B \wedge C) A^{-1} | | |
| 1205.5935v1_FO0578 | 52 | 1.000 | C_{t} | | |
| 1205.5935v1_FO0579 | 52 | 1.000 | |A|^{2} \neq 0 | | |
| 1205.5935v1_FO0580 | 52 | 1.000 | |A|^{4} | | |
| 1205.5935v1_FO0581 | 53 | 1.000 | \boldsymbol{B}_{\boldsymbol{s}}=b_{1} \wedge \cdots \wedge b_{s} | | |
| 1205.5935v1_FO0582 | 53 | 1.000 | \boldsymbol{I}^{*}=(-1)^{n} \boldsymbol{I} | | |
| 1205.5935v1_FO0583 | 54 | 0.999 | \boldsymbol{A}_{\boldsymbol{r}}^{\prime}=a_{1}^{\prime} \wedge \cdots \wedge a_{r}^{\prime} | | |
| 1205.5935v1_FO0584 | 54 | 1.000 | S R S^{-1} | | |
| 1205.5935v1_FO0585 | 54 | 0.993 | S R S^{-1}=R S S^{-1}=R | | |
| 1205.5935v1_FO0586 | 54 | 1.000 | R_{1} | | |
| 1205.5935v1_FO0587 | 54 | 1.000 | R_{2} | | |
| 1205.5935v1_FO0588 | 54 | 1.000 | R=R_{2} R_{1} | | |
| 1205.5935v1_FO0589 | 54 | 1.000 | R=\langle R\rangle+\langle R\rangle_{2} | | |
| 1205.5935v1_FO0590 | 54 | 1.000 | |R|^{2}=1 | | |
| 1205.5935v1_FO0591 | 54 | 1.000 | \langle R\rangle^{2}+\left|\langle R\rangle_{2}\right|^{2}=1 | | |
| 1205.5935v1_FO0592 | 54 | 1.000 | R=\cos (\theta / 2)-B \sin (\theta / 2) | | |
| 1205.5935v1_FO0593 | 54 | 0.910 | R=\exp (-\boldsymbol{B} \theta / 2) | | |
| 1205.5935v1_FO0594 | 54 | 0.977 | R_{2} R_{1} | | |
| 1205.5935v1_FO0595 | 54 | 1.000 | \mathcal{G}^{n} | | |
| 1205.5935v1_FO0596 | 54 | 1.000 | \left\{a_{i}\right\}_{i=1, \ldots, n} | | |
| 1205.5935v1_FO0597 | 54 | 1.000 | a_{i_{1}} a_{i_{2}} \cdots a_{i_{r}} | | |
| 1205.5935v1_FO0598 | 54 | 1.000 | r \leq n | | |
| 1205.5935v1_FO0599 | 54 | 1.000 | \left\{a_{i_{j}}\right\} | | |
| 1205.5935v1_FO0600 | 54 | 1.000 | a_{i_{1}} \wedge a_{i_{2}} \wedge \cdots \wedge a_{i_{r}} | | |
| 1205.5935v1_FO0601 | 55 | 1.000 | \left\{a^{i}\right\}_{i=1, \ldots, n} | | |
| 1205.5935v1_FO0602 | 55 | 1.000 | a^{i} | | |
| 1205.5935v1_FO0603 | 55 | 1.000 | a^{j} | | |
| 1205.5935v1_FO0604 | 55 | 1.000 | a_{N}=a_{1} \wedge a_{2} \wedge \cdots \wedge a_{n} | | |
| 1205.5935v1_FO0605 | 55 | 1.000 | a_{N} | | |
| 1205.5935v1_FO0606 | 55 | 1.000 | \left\{a^{i}\right\} | | |
| 1205.5935v1_FO0607 | 55 | 1.000 | i \neq j | | |
| 1205.5935v1_FO0608 | 55 | 0.997 | i=j | | |
| 1205.5935v1_FO0609 | 55 | 0.997 | i-1 | | |
| 1205.5935v1_FO0610 | 55 | 1.000 | \left\{a_{i}\right\} | | |
| 1205.5935v1_FO0611 | 55 | 1.000 | \left\{a^{j}\right\} | | |
| 1205.5935v1_FO0612 | 55 | 1.000 | v=\sum v^{i} a_{i} | | |
| 1205.5935v1_FO0613 | 55 | 1.000 | v=\sum v_{j} a^{j} | | |
| 1205.5935v1_FO0614 | 55 | 0.424 | \left.v^{i}=v\right\lrcorner a^{i} | | |
| 1205.5935v1_FO0615 | 55 | 0.424 | \left.v_{j}=v\right\lrcorner a_{j} | | |
| 1205.5935v1_FO0616 | 55 | 1.000 | v^{i}=v * a^{i} | | |
| 1205.5935v1_FO0617 | 55 | 1.000 | v_{j}=v * a_{j} | | |
| 1205.5935v1_FO0618 | 55 | 1.000 | b^{i} | | |
| 1205.5935v1_FO0619 | 55 | 1.000 | c_{i} | | |
| 1205.5935v1_FO0620 | 56 | 0.968 | a^{i}=\sum_{j}\left(a^{i} \downharpoonleft a^{j}\right) a_{j} | | |
| 1205.5935v1_FO0621 | 56 | 0.956 | a^{i} \downharpoonleft a^{j} | | |
| 1205.5935v1_FO0622 | 56 | 0.956 | a_{i} \wedge a_{j} | | |
| 1205.5935v1_FO0623 | 56 | 0.956 | \sum_{i} a^{i} a_{i}=n | | |
| 1205.5935v1_FO0624 | 56 | 1.000 | I | | |
| 1205.5935v1_FO0625 | 56 | 1.000 | i_{1}, i_{2}, \ldots, i_{r} | | |
| 1205.5935v1_FO0626 | 56 | 1.000 | a_{I} | | |
| 1205.5935v1_FO0627 | 56 | 1.000 | a^{I} | | |
| 1205.5935v1_FO0628 | 56 | 1.000 | N | | |
| 1205.5935v1_FO0629 | 56 | 1.000 | 1,2, \ldots, n | | |
| 1205.5935v1_FO0630 | 56 | 1.000 | a_{I}=a^{I}=1 | | |
| 1205.5935v1_FO0631 | 56 | 1.000 | a_{I}=a^{I}=0 | | |
| 1205.5935v1_FO0632 | 56 | 1.000 | J | | |
| 1205.5935v1_FO0633 | 56 | 1.000 | a_{I}=(\operatorname{sgn} \sigma) a_{J} | | |
| 1205.5935v1_FO0634 | 56 | 1.000 | a^{I}=(\operatorname{sgn} \sigma) a^{J} | | |
| 1205.5935v1_FO0635 | 56 | 1.000 | \left\{a_{I}\right\} | | |
| 1205.5935v1_FO0636 | 56 | 1.000 | \left\{a^{I}\right\} | | |
| 1205.5935v1_FO0637 | 56 | 1.000 | i_{1}<i_{2}<\cdots<i_{r} | | |
| 1205.5935v1_FO0638 | 56 | 1.000 | \delta_{J}^{I} | | |
| 1205.5935v1_FO0639 | 56 | 1.000 | a_{J} | | |
| 1205.5935v1_FO0640 | 56 | 1.000 | I=i_{1}<i_{2}<\cdots<i_{r} | | |
| 1205.5935v1_FO0641 | 56 | 1.000 | J=j_{1}<j_{2}<\cdots<j_{r} | | |
| 1205.5935v1_FO0642 | 56 | 1.000 | j_{k} | | |
| 1205.5935v1_FO0643 | 57 | 1.000 | i_{2} | | |
| 1205.5935v1_FO0644 | 57 | 1.000 | j_{l} | | |
| 1205.5935v1_FO0645 | 57 | 0.983 | \left.a^{i_{k}}\right\rfloor a_{j_{l}} | | |
| 1205.5935v1_FO0646 | 57 | 1.000 | \binom{n}{r} | | |
| 1205.5935v1_FO0647 | 57 | 1.000 | B^{I} | | |
| 1205.5935v1_FO0648 | 57 | 1.000 | C_{I} | | |
| 1205.5935v1_FO0649 | 57 | 1.000 | A * B | | |
| 1205.5935v1_FO0650 | 57 | 0.477 | \langle A\rangle | | |
| 1205.5935v1_FO0651 | 57 | 0.477 | a\rfloor A | | |
| 1205.5935v1_FO0652 | 57 | 0.950 | \langle A\rangle=0 | | |
| 1205.5935v1_FO0653 | 57 | 0.950 | a \downharpoonleft A=0 | | |
| 1205.5935v1_FO0654 | 57 | 1.000 | A=0 | | |
| 1205.5935v1_FO0655 | 57 | 1.000 | \left.\left(a^{i_{r}} \wedge \cdots \wedge a^{i_{2}} \wedge a^{i_{1}}\right)\right\rfloor A_{r} | | |
| 1205.5935v1_FO0656 | 57 | 0.998 | a^{i_{1}} \downharpoonleft A_{r}=0 | | |
| 1205.5935v1_FO0657 | 57 | 0.998 | A_{r}=0 | | |
| 1205.5935v1_FO0658 | 58 | 0.930 | \langle A\rangle,\langle A\rangle_{1} | | |
| 1205.5935v1_FO0659 | 58 | 0.930 | A_{2} \downharpoonleft A | | |
| 1205.5935v1_FO0660 | 58 | 1.000 | A_{2} | | |
| 1205.5935v1_FO0661 | 58 | 0.931 | \sum_{i} a^{i} \wedge a_{i}=0 | | |
| 1205.5935v1_FO0662 | 58 | 1.000 | A_{r}=a^{j_{1}} \wedge \cdots \wedge a^{j_{r}} | | |
| 1205.5935v1_FO0663 | 58 | 1.000 | a^{j_{k}} | | |
| 1205.5935v1_FO0664 | 58 | 1.000 | (-1)^{k-1} | | |
| 1205.5935v1_FO0665 | 58 | 1.000 | a^{N} | | |
| 1205.5935v1_FO0666 | 58 | 1.000 | a^{N}=a^{1} \wedge \cdots \wedge a^{n} | | |
| 1205.5935v1_FO0667 | 58 | 0.997 | a_{N} * a^{N}=1 | | |
| 1205.5935v1_FO0668 | 59 | 1.000 | a^{i} \wedge a^{j} | | |
| 1205.5935v1_FO0669 | 59 | 1.000 | a_{1} \wedge \cdots \wedge \check{a}_{i} \wedge \cdots \wedge \check{a}_{j} \wedge \cdots \wedge a_{n} | | |
| 1205.5935v1_FO0670 | 59 | 1.000 | I^{c} | | |
| 1205.5935v1_FO0671 | 59 | 1.000 | a_{I^{c}} | | |
| 1205.5935v1_FO0672 | 59 | 1.000 | a^{I} a_{N} | | |
| 1205.5935v1_FO0673 | 59 | 0.696 | \left.a^{i_{r}}\right\rfloor a_{N} | | |
| 1205.5935v1_FO0674 | 59 | 0.886 | a^{i_{r-1}} \downharpoonleft a_{i_{r}^{c}} | | |
| 1205.5935v1_FO0675 | 59 | 0.886 | a_{i_{r-1}} | | |
| 1205.5935v1_FO0676 | 59 | 0.886 | (-1)^{i_{r-1}-1} | | |
| 1205.5935v1_FO0677 | 59 | 1.000 | a_{i_{r}^{c}} | | |
| 1205.5935v1_FO0678 | 59 | 1.000 | (-1)^{i_{j}-1} | | |
| 1205.5935v1_FO0679 | 59 | 1.000 | I=N | | |
| 1205.5935v1_FO0680 | 59 | 1.000 | a^{I}=a_{N} a_{N}^{-1}=1 | | |
| 1205.5935v1_FO0681 | 59 | 1.000 | I=N, I^{c} | | |
| 1205.5935v1_FO0682 | 59 | 1.000 | a_{I^{c}}=1 | | |
| 1205.5935v1_FO0683 | 60 | 1.000 | \left\{e_{i}\right\} | | |
| 1205.5935v1_FO0684 | 60 | 1.000 | e^{i}=e_{i}^{-1}=e_{i}^{-2} e_{i} | | |
| 1205.5935v1_FO0685 | 60 | 1.000 | e_{i}^{2}= \pm 1 | | |
| 1205.5935v1_FO0686 | 60 | 1.000 | e^{i}= \pm e_{i} | | |
| 1205.5935v1_FO0687 | 60 | 1.000 | I_{m} | | |
| 1205.5935v1_FO0688 | 60 | 1.000 | e_{I} | | |
| 1205.5935v1_FO0689 | 60 | 1.000 | e^{I}=(-1)^{I_{m}} e_{I} | | |
| 1205.5935v1_FO0690 | 60 | 1.000 | I_{m}=0 | | |
| 1205.5935v1_FO0691 | 60 | 1.000 | \left\{a_{j}\right\} | | |
| 1205.5935v1_FO0692 | 60 | 1.000 | \boldsymbol{A}^{\boldsymbol{r}}=a^{1} \wedge \cdots \wedge a^{r} | | |
| 1205.5935v1_FO0693 | 60 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}} /\left|\boldsymbol{A}_{\boldsymbol{r}}\right|^{2} | | |
| 1205.5935v1_FO0694 | 60 | 0.675 | \boldsymbol{A}^{\boldsymbol{r}} | | |
| 1205.5935v1_FO0695 | 61 | 1.000 | U | | |
| 1205.5935v1_FO0696 | 61 | 1.000 | V | | |
| 1205.5935v1_FO0697 | 61 | 1.000 | F: U \rightarrow V | | |
| 1205.5935v1_FO0698 | 61 | 1.000 | F(\alpha u+\beta v)=\alpha F(u)+\beta F(v) | | |
| 1205.5935v1_FO0699 | 61 | 1.000 | F | | |
| 1205.5935v1_FO0700 | 61 | 1.000 | G | | |
| 1205.5935v1_FO0701 | 61 | 0.710 | \operatorname{Ker}(F) | | |
| 1205.5935v1_FO0702 | 61 | 0.883 | \operatorname{range} | | |
| 1205.5935v1_FO0703 | 61 | 0.883 | \operatorname{Range}(F) | | |
| 1205.5935v1_FO0704 | 61 | 0.995 | F^{-1}(0) | | |
| 1205.5935v1_FO0705 | 61 | 0.995 | F(U) . F | | |
| 1205.5935v1_FO0706 | 61 | 0.995 | \operatorname{Ker}(F)=\{0\} | | |
| 1205.5935v1_FO0707 | 61 | 0.999 | \operatorname{Range}(F)=V | | |
| 1205.5935v1_FO0708 | 61 | 0.999 | \operatorname{null}(F) | | |
| 1205.5935v1_FO0709 | 61 | 0.314 | \operatorname{rank} | | |
| 1205.5935v1_FO0710 | 61 | 0.314 | \operatorname{rank}(F) | | |
| 1205.5935v1_FO0711 | 61 | 1.000 | F_{W} | | |
| 1205.5935v1_FO0712 | 61 | 1.000 | F_{\boldsymbol{A}} | | |
| 1205.5935v1_FO0713 | 61 | 0.983 | \operatorname{Id}_{U} | | |
| 1205.5935v1_FO0714 | 61 | 0.742 | u * v | | |
| 1205.5935v1_FO0715 | 61 | 0.742 | u \downharpoonleft v | | |
| 1205.5935v1_FO0716 | 62 | 1.000 | F(u) * v | | |
| 1205.5935v1_FO0717 | 62 | 1.000 | u \in U | | |
| 1205.5935v1_FO0718 | 62 | 1.000 | v \in V | | |
| 1205.5935v1_FO0719 | 62 | 1.000 | F(u)=\sum_{i}\left[a^{i} * F(u)\right] a_{i} | | |
| 1205.5935v1_FO0720 | 62 | 1.000 | \left\{a^{j}\right\}_{j=1, \ldots, n} | | |
| 1205.5935v1_FO0721 | 62 | 1.000 | a^{i} * F(u) | | |
| 1205.5935v1_FO0722 | 62 | 1.000 | F(u) | | |
| 1205.5935v1_FO0723 | 62 | 0.997 | a \downharpoonleft F(b) | | |
| 1205.5935v1_FO0724 | 62 | 0.999 | u \circ v=u \downharpoonleft F(v) | | |
| 1205.5935v1_FO0725 | 62 | 1.000 | F(u)=\sum_{i}\left(a^{i} \circ u\right) a_{i} | | |
| 1205.5935v1_FO0726 | 62 | 0.806 | u \downharpoonleft F(v)=u \circ v | | |
| 1205.5935v1_FO0727 | 62 | 1.000 | \bar{F}: V \rightarrow U | | |
| 1205.5935v1_FO0728 | 62 | 0.845 | \bar{F} | | |
| 1205.5935v1_FO0729 | 62 | 0.845 | * | | |
| 1205.5935v1_FO0730 | 62 | 0.600 | \left\lfloor\right. | | |
| 1205.5935v1_FO0731 | 62 | 0.600 | \overline{\mathrm{Id}_{U}}=\mathrm{Id}_{U} | | |
| 1205.5935v1_FO0732 | 63 | 1.000 | \left\{a_{i}\right\} \subset U | | |
| 1205.5935v1_FO0733 | 63 | 1.000 | G: V \rightarrow W | | |
| 1205.5935v1_FO0734 | 63 | 1.000 | G F: U \rightarrow W | | |
| 1205.5935v1_FO0735 | 63 | 1.000 | F^{n} | | |
| 1205.5935v1_FO0736 | 63 | 1.000 | F^{-1}: V \rightarrow U | | |
| 1205.5935v1_FO0737 | 63 | 1.000 | F^{-1} F=\operatorname{Id}_{U} | | |
| 1205.5935v1_FO0738 | 63 | 1.000 | F F^{-1}=\operatorname{Id}_{V} | | |
| 1205.5935v1_FO0739 | 63 | 0.986 | \bar{F} \overline{F^{-1}}=\overline{F^{-1} F}=\overline{\mathrm{Id}_{U}}=\mathrm{Id}_{U} | | |
| 1205.5935v1_FO0740 | 63 | 0.986 | \overline{F^{-1}} \bar{F}=\mathrm{Id}_{V} | | |
| 1205.5935v1_FO0741 | 63 | 1.000 | \operatorname{Range}(\bar{F}) | | |
| 1205.5935v1_FO0742 | 63 | 1.000 | \operatorname{Range}(\bar{F})^{\perp} | | |
| 1205.5935v1_FO0743 | 64 | 1.000 | F \bar{F}=\bar{F} F | | |
| 1205.5935v1_FO0744 | 64 | 0.957 | F^{n}(\bar{F})^{n} | | |
| 1205.5935v1_FO0745 | 64 | 0.957 | (\bar{F})^{n} F^{n} | | |
| 1205.5935v1_FO0746 | 64 | 0.828 | F(u)\rfloor F(v)=\bar{F}(u)\rfloor \bar{F}(v) | | |
| 1205.5935v1_FO0747 | 64 | 0.841 | 40 F \bar{F}=\bar{F} F | | |
| 1205.5935v1_FO0748 | 64 | 1.000 | F(u)^{2}=\bar{F}(u)^{2} | | |
| 1205.5935v1_FO0749 | 64 | 0.807 | \left.\left.F(u)\right\rfloor F(v)=\bar{F}(u)\right\rfloor \bar{F}(v) | | |
| 1205.5935v1_FO0750 | 64 | 0.808 | F(u)\rfloor F(v)=\bar{F}(u) \downharpoonleft \bar{F}(v) | | |
| 1205.5935v1_FO0751 | 64 | 1.000 | u=v | | |
| 1205.5935v1_FO0752 | 64 | 1.000 | \operatorname{Ker}(F)=\operatorname{Ker}(\bar{F}) | | |
| 1205.5935v1_FO0753 | 64 | 1.000 | \operatorname{Range}(F)=\operatorname{Range}(\bar{F}) | | |
| 1205.5935v1_FO0754 | 64 | 0.999 | \operatorname{Ker}(F)=\operatorname{Range}(\bar{F})^{\perp} | | |
| 1205.5935v1_FO0755 | 64 | 0.999 | \bar{F}(u) \in \operatorname{Range}(\bar{F})^{\perp} | | |
| 1205.5935v1_FO0756 | 64 | 0.999 | \bar{F}(u) \in | | |
| 1205.5935v1_FO0757 | 64 | 0.894 | \bar{F}(u)=0 | | |
| 1205.5935v1_FO0758 | 64 | 0.894 | u \in | | |
| 1205.5935v1_FO0759 | 64 | 1.000 | \operatorname{Ker}(\bar{F}) | | |
| 1205.5935v1_FO0760 | 64 | 1.000 | \operatorname{Ker}(F) \subset \operatorname{Ker}(\bar{F}) | | |
| 1205.5935v1_FO0761 | 64 | 1.000 | \operatorname{Ker}(\bar{F}) \subset \operatorname{Ker}(F) | | |
| 1205.5935v1_FO0762 | 64 | 1.000 | \operatorname{Range}(F)=\operatorname{Ker}(\bar{F})^{\perp} | | |
| 1205.5935v1_FO0763 | 64 | 1.000 | \operatorname{Range}(\bar{F})=\operatorname{Ker}(F)^{\perp} | | |
| 1205.5935v1_FO0764 | 65 | 1.000 | \bar{F}=F | | |
| 1205.5935v1_FO0765 | 65 | 1.000 | \bar{F}=-F | | |
| 1205.5935v1_FO0766 | 65 | 0.952 | a \circ b:=a \downharpoonleft F(b) | | |
| 1205.5935v1_FO0767 | 65 | 0.999 | a \downharpoonleft F(b)=b \downharpoonleft \bar{F}(a) | | |
| 1205.5935v1_FO0768 | 65 | 0.999 | a \circ b=b \circ a | | |
| 1205.5935v1_FO0769 | 65 | 0.999 | a \circ b=-b \circ a | | |
| 1205.5935v1_FO0770 | 65 | 1.000 | \bar{F} F | | |
| 1205.5935v1_FO0771 | 65 | 1.000 | F \bar{F} | | |
| 1205.5935v1_FO0772 | 65 | 1.000 | \overline{F^{n}}=(\bar{F})^{n}, \bar{F}=F | | |
| 1205.5935v1_FO0773 | 65 | 1.000 | \overline{F^{n}}=F^{n} | | |
| 1205.5935v1_FO0774 | 65 | 1.000 | \overline{F^{n}}=(-1)^{n} F^{n} | | |
| 1205.5935v1_FO0775 | 65 | 1.000 | \left\{\lambda_{i}\right\} | | |
| 1205.5935v1_FO0776 | 65 | 1.000 | F(a) | | |
| 1205.5935v1_FO0777 | 65 | 0.998 | a \downharpoonleft F(a)=0 | | |
| 1205.5935v1_FO0778 | 65 | 0.964 | F(a)=a \downharpoonleft A_{2} | | |
| 1205.5935v1_FO0779 | 66 | 0.293 | a \wedge b\rfloor A_{2}=a \downharpoonleft A_{2}\left\lfloor b\right. | | |
| 1205.5935v1_FO0780 | 66 | 0.951 | F(u)\rfloor F(v)=u \downharpoonleft v | | |
| 1205.5935v1_FO0781 | 66 | 0.999 | \bar{F} F=\mathrm{Id} | | |
| 1205.5935v1_FO0782 | 66 | 0.539 | F \bar{F}=\mathrm{Id} | | |
| 1205.5935v1_FO0783 | 66 | 0.539 | \bar{F}=F^{-1} | | |
| 1205.5935v1_FO0784 | 66 | 0.539 | F^{-1} | | |
| 1205.5935v1_FO0785 | 66 | 0.999 | a_{1}, a_{2}, \ldots, a_{r} | | |
| 1205.5935v1_FO0786 | 67 | 1.000 | A_{r}=a_{r} \cdots a_{2} a_{1} | | |
| 1205.5935v1_FO0787 | 67 | 1.000 | A_{r}^{-1} | | |
| 1205.5935v1_FO0788 | 67 | 1.000 | \lambda A_{r} | | |
| 1205.5935v1_FO0789 | 67 | 1.000 | \lambda \neq 0 | | |
| 1205.5935v1_FO0790 | 67 | 1.000 | \lambda a | | |
| 1205.5935v1_FO0791 | 67 | 1.000 | A_{r}=\lambda B_{s} | | |
| 1205.5935v1_FO0792 | 67 | 1.000 | A_{r} u^{* r} A_{r}^{-1}=B_{s} u^{* s} B_{s}^{-1} | | |
| 1205.5935v1_FO0793 | 67 | 1.000 | A_{r} u A_{r}^{-1}=B_{s} u B_{s}^{-1} | | |
| 1205.5935v1_FO0794 | 67 | 1.000 | B_{s}^{-1} A_{r}=\lambda+\mu\langle\boldsymbol{I}\rangle_{-} | | |
| 1205.5935v1_FO0795 | 67 | 1.000 | B_{s}^{-1} A_{r} | | |
| 1205.5935v1_FO0796 | 67 | 1.000 | B_{s}^{-1} A_{r}=\lambda | | |
| 1205.5935v1_FO0797 | 67 | 1.000 | \lambda=0 | | |
| 1205.5935v1_FO0798 | 68 | 1.000 | a b | | |
| 1205.5935v1_FO0799 | 68 | 0.554 | a\rfloor b+a \wedge b | | |
| 1205.5935v1_FO0800 | 68 | 0.570 | \mu=a \downharpoonleft b | | |
| 1205.5935v1_FO0801 | 68 | 0.997 | a \wedge b=\lambda \boldsymbol{B} | | |
| 1205.5935v1_FO0802 | 68 | 0.997 | (a \wedge b)^{2} \neq 0 | | |
| 1205.5935v1_FO0803 | 68 | 0.984 | a \downharpoonleft b=0,(a \wedge b)^{2}= \pm 1 | | |
| 1205.5935v1_FO0804 | 68 | 0.984 | a b=a \wedge b | | |
| 1205.5935v1_FO0805 | 68 | 1.000 | \boldsymbol{B}^{2} | | |
| 1205.5935v1_FO0806 | 68 | 1.000 | \boldsymbol{B}^{2}=-1 | | |
| 1205.5935v1_FO0807 | 68 | 1.000 | n=2 | | |
| 1205.5935v1_FO0808 | 68 | 1.000 | a^{2} | | |
| 1205.5935v1_FO0809 | 68 | 1.000 | b^{2} | | |
| 1205.5935v1_FO0810 | 68 | 1.000 | a^{2} b^{2}=1 | | |
| 1205.5935v1_FO0811 | 68 | 1.000 | \mu=\cos (\theta / 2) | | |
| 1205.5935v1_FO0812 | 68 | 1.000 | \lambda=-\sin (\theta / 2) | | |
| 1205.5935v1_FO0813 | 68 | 0.902 | \theta=\pi | | |
| 1205.5935v1_FO0814 | 68 | 1.000 | \boldsymbol{B}^{2}=1 | | |
| 1205.5935v1_FO0815 | 68 | 1.000 | \mu= \pm \cosh (\phi / 2) | | |
| 1205.5935v1_FO0816 | 68 | 1.000 | \lambda=\mp \sinh (\phi / 2) | | |
| 1205.5935v1_FO0817 | 68 | 1.000 | c \tanh \phi | | |
| 1205.5935v1_FO0818 | 69 | 0.998 | a^{2}=-b^{2} | | |
| 1205.5935v1_FO0819 | 69 | 1.000 | \mu | | |
| 1205.5935v1_FO0820 | 69 | 1.000 | \mu=\mp \sinh (\phi / 2) | | |
| 1205.5935v1_FO0821 | 69 | 1.000 | \lambda= \pm \cosh (\phi / 2) | | |
| 1205.5935v1_FO0822 | 69 | 1.000 | \boldsymbol{B}^{2}=0 | | |
| 1205.5935v1_FO0823 | 69 | 1.000 | \pm 1=\mu^{2} | | |
| 1205.5935v1_FO0824 | 69 | 1.000 | v^{2} | | |
| 1205.5935v1_FO0825 | 69 | 1.000 | \mu= \pm 1 | | |
| 1205.5935v1_FO0826 | 69 | 1.000 | a \wedge b=\mp \lambda \boldsymbol{B} | | |
| 1205.5935v1_FO0827 | 69 | 1.000 | \pm\left(1+\frac{\lambda}{2} \boldsymbol{B}\right) | | |
| 1205.5935v1_FO0828 | 69 | 0.998 | u^{2} | | |
| 1205.5935v1_FO0829 | 69 | 0.998 | u \downharpoonleft \boldsymbol{B} | | |
| 1205.5935v1_FO0830 | 69 | 0.989 | \boldsymbol{B} u \boldsymbol{B} | | |
| 1205.5935v1_FO0831 | 69 | 0.989 | u \downharpoonleft \boldsymbol{B}, \boldsymbol{B} u \boldsymbol{B} | | |
| 1205.5935v1_FO0832 | 70 | 1.000 | \left\{F\left(a_{i}\right)\right\} | | |
| 1205.5935v1_FO0833 | 70 | 1.000 | F(A \wedge B)=F(A) \wedge F(B) | | |
| 1205.5935v1_FO0834 | 70 | 1.000 | u \rightarrow-u | | |
| 1205.5935v1_FO0835 | 70 | 1.000 | \mathcal{F}=\alpha \mathcal{F}_{1}+\beta \mathcal{F}_{2} | | |
| 1205.5935v1_FO0836 | 70 | 1.000 | \mathcal{F}_{1} | | |
| 1205.5935v1_FO0837 | 70 | 1.000 | \mathcal{F}_{2} | | |
| 1205.5935v1_FO0838 | 70 | 1.000 | \mathcal{F}(A \wedge B) | | |
| 1205.5935v1_FO0839 | 70 | 1.000 | \mathcal{F}(A) \wedge \mathcal{F}(B) | | |
| 1205.5935v1_FO0840 | 70 | 1.000 | \mathcal{F} | | |
| 1205.5935v1_FO0841 | 70 | 1.000 | \mathcal{F}(\lambda)=\mathcal{F}(\lambda 1)=\lambda \mathcal{F}(1) | | |
| 1205.5935v1_FO0842 | 71 | 1.000 | \mathcal{F}(1) | | |
| 1205.5935v1_FO0843 | 71 | 1.000 | 1=1 \wedge 1 | | |
| 1205.5935v1_FO0844 | 71 | 0.988 | \mathcal{F}(1)=\mathcal{F}(1) \wedge \mathcal{F}(1) | | |
| 1205.5935v1_FO0845 | 71 | 0.988 | 1, \mathcal{F}(1) | | |
| 1205.5935v1_FO0846 | 71 | 0.827 | A=A \wedge A | | |
| 1205.5935v1_FO0847 | 71 | 0.995 | A_{0} | | |
| 1205.5935v1_FO0848 | 71 | 0.936 | A_{1}=0 | | |
| 1205.5935v1_FO0849 | 71 | 0.976 | \mathcal{F}(1)=0 | | |
| 1205.5935v1_FO0850 | 71 | 1.000 | \mathcal{F}=0 | | |
| 1205.5935v1_FO0851 | 71 | 1.000 | \mathcal{F}(\lambda)=\lambda | | |
| 1205.5935v1_FO0852 | 71 | 1.000 | \mathcal{F}(1)=1 | | |
| 1205.5935v1_FO0853 | 71 | 1.000 | \mathcal{F}: \mathcal{G}^{1} \rightarrow \mathcal{G}^{2} | | |
| 1205.5935v1_FO0854 | 71 | 1.000 | \overline{\mathcal{F}}: \mathcal{G}^{2} \rightarrow \mathcal{G}^{1} | | |
| 1205.5935v1_FO0855 | 72 | 1.000 | [F] | | |
| 1205.5935v1_FO0856 | 72 | 1.000 | F \neq 0 | | |
| 1205.5935v1_FO0857 | 72 | 1.000 | F=0 | | |
| 1205.5935v1_FO0858 | 72 | 1.000 | [F]=0 | | |
| 1205.5935v1_FO0859 | 72 | 1.000 | [F](A)=\langle A\rangle | | |
| 1205.5935v1_FO0860 | 72 | 1.000 | U, V | | |
| 1205.5935v1_FO0861 | 72 | 1.000 | \mathcal{G}^{1}, \mathcal{G}^{2} | | |
| 1205.5935v1_FO0862 | 72 | 1.000 | \mathcal{G}^{3} | | |
| 1205.5935v1_FO0863 | 72 | 1.000 | [G F]=[G][F] | | |
| 1205.5935v1_FO0864 | 72 | 0.676 | [F]^{-1}=\left[F^{-1}\right] | | |
| 1205.5935v1_FO0865 | 72 | 1.000 | [F]\left[F^{-1}\right]=\operatorname{Id}_{\mathcal{G}^{2}} | | |
| 1205.5935v1_FO0866 | 72 | 1.000 | \left[F^{-1}\right] | | |
| 1205.5935v1_FO0867 | 73 | 1.000 | \overline{[F]}=[\bar{F}] | | |
| 1205.5935v1_FO0868 | 73 | 0.999 | [\bar{F}] | | |
| 1205.5935v1_FO0869 | 73 | 1.000 | \lambda[\bar{F}]\left(B_{s}\right) | | |
| 1205.5935v1_FO0870 | 73 | 1.000 | s \geq 1 | | |
| 1205.5935v1_FO0871 | 73 | 1.000 | s-1 | | |
| 1205.5935v1_FO0872 | 73 | 1.000 | \boldsymbol{B}_{\boldsymbol{s}}=b \wedge \boldsymbol{B}_{\boldsymbol{s}-\mathbf{1}} | | |
| 1205.5935v1_FO0873 | 73 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}}=\boldsymbol{A}_{\boldsymbol{r}-\mathbf{1}} \wedge a | | |
| 1205.5935v1_FO0874 | 74 | 1.000 | \mathcal{F}=[F] | | |
| 1205.5935v1_FO0875 | 74 | 0.977 | A\rfloor F(B)= | | |
| 1205.5935v1_FO0876 | 74 | 0.709 | F(\bar{F}(A)\rfloor B) | | |
| 1205.5935v1_FO0877 | 74 | 1.000 | F_{\boldsymbol{A}_{\boldsymbol{r}}} | | |
| 1205.5935v1_FO0878 | 74 | 1.000 | F\left(\boldsymbol{A}_{\boldsymbol{r}}\right) | | |
| 1205.5935v1_FO0879 | 74 | 1.000 | F\left(\boldsymbol{A}_{\boldsymbol{r}}\right)=0 | | |
| 1205.5935v1_FO0880 | 74 | 1.000 | \operatorname{rank}\left(F_{\boldsymbol{A}_{\boldsymbol{r}}}\right)<r | | |
| 1205.5935v1_FO0881 | 74 | 1.000 | \operatorname{null}\left(F_{\boldsymbol{A}_{\boldsymbol{r}}}\right)>0 | | |
| 1205.5935v1_FO0882 | 74 | 0.992 | \boldsymbol{A}_{\boldsymbol{r}} \in \operatorname{Ker} F | | |
| 1205.5935v1_FO0883 | 74 | 0.992 | \operatorname{Ker}\left(F_{\boldsymbol{A}_{\boldsymbol{r}}}\right) \neq\{0\} | | |
| 1205.5935v1_FO0884 | 74 | 1.000 | F(A B)=F(A) F(B) | | |
| 1205.5935v1_FO0885 | 74 | 0.960 | F(A\rfloor B)=F(A)\rfloor F(B) | | |
| 1205.5935v1_FO0886 | 74 | 0.960 | F(A\lfloor B)=F(A)\lfloor F(B) | | |
| 1205.5935v1_FO0887 | 74 | 0.971 | F(a)\rfloor F(b)=a \downharpoonleft b | | |
| 1205.5935v1_FO0888 | 74 | 0.180 | a \downharpoonleft b | | |
| 1205.5935v1_FO0889 | 74 | 0.180 | F(a \downarrow b)=a\rfloor b | | |
| 1205.5935v1_FO0890 | 74 | 0.180 | F(a\rfloor b)=F(a) \downharpoonleft F(b) | | |
| 1205.5935v1_FO0891 | 74 | 0.180 | F(a \wedge b)=F(a) \wedge F(b) | | |
| 1205.5935v1_FO0892 | 74 | 1.000 | F(a b)=F(a) F(b) | | |
| 1205.5935v1_FO0893 | 74 | 1.000 | F\left(a_{1} a_{2} \cdots a_{r}\right)= | | |
| 1205.5935v1_FO0894 | 74 | 1.000 | F\left(a_{1}\right) F\left(a_{2}\right) \cdots F\left(a_{r}\right) | | |
| 1205.5935v1_FO0895 | 75 | 1.000 | F(A B) | | |
| 1205.5935v1_FO0896 | 75 | 1.000 | F\left(\boldsymbol{A}_{\boldsymbol{r}} \boldsymbol{B}_{\boldsymbol{s}}\right) | | |
| 1205.5935v1_FO0897 | 75 | 0.998 | F\left(\boldsymbol{A}_{\boldsymbol{r}} \boldsymbol{B}_{\boldsymbol{s}}\right)=F\left(\boldsymbol{A}_{\boldsymbol{r}}\right) F\left(\boldsymbol{B}_{\boldsymbol{s}}\right) | | |
| 1205.5935v1_FO0898 | 75 | 1.000 | \boldsymbol{B}_{\boldsymbol{s}}=b_{1} b_{2} \cdots b_{s} | | |
| 1205.5935v1_FO0899 | 75 | 1.000 | a_{r} | | |
| 1205.5935v1_FO0900 | 75 | 0.450 | F(A\rfloor B)=F(A) \downharpoonleft F(B) | | |
| 1205.5935v1_FO0901 | 75 | 0.450 | F(a) \downharpoonleft F(b)=F(a \downarrow b)=a \downharpoonleft b | | |
| 1205.5935v1_FO0902 | 75 | 0.998 | F(a)=\lambda a | | |
| 1205.5935v1_FO0903 | 75 | 0.998 | a \in \operatorname{Ker}(F-\lambda \operatorname{Id}) | | |
| 1205.5935v1_FO0904 | 75 | 1.000 | \lambda_{1} | | |
| 1205.5935v1_FO0905 | 75 | 1.000 | \lambda_{2} | | |
| 1205.5935v1_FO0906 | 75 | 1.000 | \boldsymbol{A}=a_{1} \wedge a_{2} | | |
| 1205.5935v1_FO0907 | 75 | 1.000 | F(\boldsymbol{A})=\lambda \boldsymbol{A} | | |
| 1205.5935v1_FO0908 | 75 | 0.999 | F(A)=\exp (-\boldsymbol{B} \theta / 2) A \exp (\boldsymbol{B} \theta / 2) | | |
| 1205.5935v1_FO0909 | 76 | 0.999 | \boldsymbol{B}^{\perp} | | |
| 1205.5935v1_FO0910 | 76 | 1.000 | F(\boldsymbol{A})=\boldsymbol{A} | | |
| 1205.5935v1_FO0911 | 76 | 1.000 | F(a)=a | | |
| 1205.5935v1_FO0912 | 76 | 1.000 | \operatorname{Range}\left(F_{\boldsymbol{A}}\right) | | |
| 1205.5935v1_FO0913 | 76 | 1.000 | \boldsymbol{A} \wedge a=0 | | |
| 1205.5935v1_FO0914 | 76 | 1.000 | |F(\boldsymbol{A})|^{2}=\lambda^{2}|\boldsymbol{A}|^{2} | | |
| 1205.5935v1_FO0915 | 76 | 1.000 | |\lambda| | | |
| 1205.5935v1_FO0916 | 76 | 1.000 | F(\boldsymbol{I}) | | |
| 1205.5935v1_FO0917 | 76 | 1.000 | \operatorname{det}(\mathrm{Id})=1 | | |
| 1205.5935v1_FO0919 | 77 | 1.000 | \operatorname{det}(F) \neq 0 | | |
| 1205.5935v1_FO0920 | 77 | 1.000 | a_{1} \wedge \cdots \wedge a_{n} | | |
| 1205.5935v1_FO0921 | 77 | 1.000 | F(v)=A_{r} v^{* r} A_{r}^{-1} | | |
| 1205.5935v1_FO0923 | 78 | 1.000 | { }^{\perp} | | |
| 1205.5935v1_FO0924 | 78 | 1.000 | { }^{-\perp} | | |
| 1205.5935v1_FO0925 | 78 | 0.987 | G(A)=\bar{F}\left(A^{-\perp}\right)^{\perp} | | |
| 1205.5935v1_FO0926 | 78 | 0.987 | \left.A\right\rfloor \bar{F}(B)= | | |
| 1205.5935v1_FO0927 | 78 | 0.879 | \bar{F}(F(A)\rfloor B) | | |
| 1205.5935v1_FO0928 | 78 | 1.000 | F G(A)=\operatorname{det}(F) A | | |
| 1205.5935v1_FO0929 | 78 | 1.000 | F^{-1}=G / \operatorname{det}(F) | | |
| 1205.5935v1_FO0930 | 78 | 1.000 | F^{-1}(a) | | |
| 1205.5935v1_FO0931 | 78 | 1.000 | \bar{F}\left(a^{-\perp}\right) | | |
| 1205.5935v1_FO0932 | 78 | 1.000 | a^{-\perp} | | |
| 1205.5935v1_FO0933 | 78 | 1.000 | \boldsymbol{a}, \boldsymbol{b} | | |
| 1205.5935v1_FO0934 | 78 | 1.000 | \boldsymbol{a} | | |
| 1205.5935v1_FO0935 | 78 | 0.849 | { }^{\text {^ }} | | |
| 1205.5935v1_FO0936 | 78 | 1.000 | \boldsymbol{r} | | |
| 1205.5935v1_FO0937 | 78 | 1.000 | \boldsymbol{v}=\dot{\boldsymbol{r}} | | |
| 1205.5935v1_FO0938 | 78 | 0.997 | \boldsymbol{L}=\boldsymbol{r} \times \boldsymbol{p} | | |
| 1205.5935v1_FO0939 | 78 | 0.997 | \boldsymbol{p} | | |
| 1205.5935v1_FO0940 | 79 | 0.880 | L | | |
| 1205.5935v1_FO0941 | 79 | 0.880 | \boldsymbol{F} | | |
| 1205.5935v1_FO0942 | 79 | 0.880 | \dot{A}=0, \mathrm{I} | | |
| 1205.5935v1_FO0943 | 79 | 0.999 | \boldsymbol{r}=r \hat{\boldsymbol{r}} | | |
| 1205.5935v1_FO0944 | 79 | 0.936 | \boldsymbol{v}=\dot{r} \hat{\boldsymbol{r}}+r \dot{\hat{\boldsymbol{r}}} | | |
| 1205.5935v1_FO0945 | 79 | 1.000 | \hat{\boldsymbol{r}} \wedge \hat{\boldsymbol{r}}=0 | | |
| 1205.5935v1_FO0946 | 79 | 1.000 | \hat{\boldsymbol{r}} | | |
| 1205.5935v1_FO0947 | 79 | 1.000 | \hat{\boldsymbol{r}}\rfloor \hat{\boldsymbol{r}}=1 | | |
| 1205.5935v1_FO0948 | 79 | 1.000 | \hat{\boldsymbol{r}}\rfloor \dot{\hat{\boldsymbol{r}}}=0 | | |
| 1205.5935v1_FO0949 | 79 | 0.782 | \boldsymbol{v}=\dot{r} \hat{\boldsymbol{r}}+r \dot{\boldsymbol{r}} | | |
| 1205.5935v1_FO0950 | 79 | 0.906 | \hat{\boldsymbol{r}} \wedge \dot{\hat{\boldsymbol{r}}}=\hat{\boldsymbol{r}} \dot{\hat{\boldsymbol{r}}} | | |
| 1205.5935v1_FO0951 | 79 | 1.000 | l | | |
| 1205.5935v1_FO0953 | 79 | 1.000 | V=-k / r | | |
| 1205.5935v1_FO0954 | 79 | 1.000 | r^{2} | | |
| 1205.5935v1_FO0955 | 79 | 1.000 | k \hat{\boldsymbol{r}} | | |
| 1205.5935v1_FO0957 | 80 | 0.934 | \boldsymbol{v} | | |
| 1205.5935v1_FO0958 | 80 | 0.934 | L \boldsymbol{v}=L\lfloor\boldsymbol{v} | | |
| 1205.5935v1_FO0959 | 80 | 1.000 | \boldsymbol{e} | | |
| 1205.5935v1_FO0960 | 80 | 1.000 | \hat{\boldsymbol{r}} \boldsymbol{r}=r | | |
| 1205.5935v1_FO0961 | 80 | 1.000 | k \boldsymbol{r} | | |
| 1205.5935v1_FO0962 | 80 | 0.965 | \boldsymbol{e r}=e r \cos \theta+\boldsymbol{e} \wedge \boldsymbol{r} | | |
| 1205.5935v1_FO0963 | 80 | 0.999 | e | | |
| 1205.5935v1_FO0964 | 80 | 1.000 | k>0 | | |
| 1205.5935v1_FO0965 | 80 | 1.000 | \theta=0 | | |
| 1205.5935v1_FO0966 | 80 | 1.000 | k<0 | | |
| 1205.5935v1_FO0967 | 80 | 1.000 | 1+e \cos \theta \leq 0 | | |
| 1205.5935v1_FO0968 | 80 | 1.000 | e>1 | | |
| 1205.5935v1_FO0969 | 81 | 1.000 | -2 k | | |
| 1205.5935v1_FO0975 | 87 | 1.000 | A^{-1} | | |
| 1205.5935v1_FO0990 | 83 | 1.000 | a_{1} \wedge \cdots \wedge a_{r} | | |
| 1205.5935v1_FO0991 | 83 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}}=0 | | |
| 1205.5935v1_FO0992 | 83 | 0.999 | \left(\boldsymbol{A}_{\boldsymbol{s}}=\boldsymbol{A}_{\boldsymbol{s}-\boldsymbol{r}} \wedge \boldsymbol{A}_{\boldsymbol{r}}\right) | | |
| 1205.5935v1_FO0993 | 83 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}} B^{* r} \boldsymbol{A}_{\boldsymbol{r}}^{-1} | | |
| 1205.5935v1_FO0994 | 83 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}}, \boldsymbol{A}_{\boldsymbol{r}}^{*}, \boldsymbol{A}_{\boldsymbol{r}}^{\dagger}, \boldsymbol{A}_{\boldsymbol{r}}^{\ddagger} | | |
| 1205.5935v1_FO0995 | 84 | 1.000 | A=a_{1} a_{2} \cdots a_{r} | | |
| 1205.5935v1_FO0996 | 85 | 0.832 | \boldsymbol{A}_{\boldsymbol{r}} \boldsymbol{B}_{\boldsymbol{s}}=\boldsymbol{A}_{\boldsymbol{r}} \downharpoonleft \boldsymbol{B}_{\boldsymbol{s}} | | |
| 1205.5935v1_FO0997 | 87 | 0.906 | a\lrcorner A | | |
| 1205.5935v1_FO0998 | 87 | 1.000 | |A|^{2}=A^{\dagger} A=a_{1}^{2} a_{2}^{2} \cdots a_{r}^{2} | | |
| 1205.5935v1_FO0999 | 87 | 1.000 | A^{-1}=A^{\dagger} /|A|^{2} | | |
| 1205.5935v1_FO1000 | 87 | 1.000 | \left|A^{-1}\right|^{2}=|A|^{-2} | | |
| 1205.5935v1_FO1001 | 87 | 1.000 | (A B) *(A C)=(B A) *(C A)=|A|^{2} B * C | | |
| 1205.5935v1_FO1002 | 87 | 1.000 | \left|\boldsymbol{A}_{\boldsymbol{r}}\right|^{2}=0 | | |
| 1205.5935v1_FO1003 | 87 | 1.000 | \left|\boldsymbol{A}_{\boldsymbol{r}}\right|^{2} \neq 0 | | |
| 1205.5935v1_FO1004 | 87 | 1.000 | \boldsymbol{A}_{\boldsymbol{r}}^{-1}=(-1)^{r(r-1) / 2} \boldsymbol{A}_{\boldsymbol{r}} /\left|\boldsymbol{A}_{\boldsymbol{r}}\right|^{2}=\boldsymbol{A}_{\boldsymbol{r}} / \boldsymbol{A}_{\boldsymbol{r}}^{2} | | |
| 1205.5935v1_FO1005 | 88 | 1.000 | \boldsymbol{A}^{\perp} | | |
| 1205.5935v1_FO1006 | 89 | 1.000 | a_{N}=a_{1} \wedge \cdots \wedge a_{n} | | |
| 1205.5935v1_FO1007 | 90 | 0.808 | F(a)=\sum_{i} \lambda_{i}\left(a * a^{i}\right) a_{i} | | |
| 1205.5935v1_FO1008 | 90 | 1.000 | \operatorname{iff} \bar{F} F=\mathrm{Id} | | |
| 1205.5935v1_FO1009 | 90 | 1.000 | F(a)=A_{r} a^{* r} A_{r}^{-1} | | |
| 1205.5935v1_FO1010 | 90 | 1.000 | F(B)=A_{r} B^{* r} A_{r}^{-1} | | |
| 1205.5935v1_FO1011 | 91 | 1.000 | \boldsymbol{A} \neq 0 | | |
| 1205.5935v1_FO1012 | 91 | 0.997 | \operatorname{det}\left(F_{\boldsymbol{A}}\right) | |