Split (3)

train · 230k rows

latex stringlengths 1 188	sample_id stringlengths 16 16	split_tag stringclasses 1 value	data_type stringclasses 1 value
\tilde{Y}^{n}	be1f5972d5f5d5b5	train	human
0.5\sqrt{2}	a58b29aa8a4f4f31	train	human
\frac{\partial f_{k}}{\partial x_{j}}	554866b1352ca641	train	human
{10^{218}}^{10}-\frac{\frac{4}{\sqrt{375}}}{179}	4d59b397b0f9e669	train	human
\chi=(E_{i}+E_{ea})/2	7f42fa1f682afbb0	train	human
(8\cdot119)/5-319^{97}	28ecab124abb9f5b	train	human
a=\sqrt{2\varphi^{-1}}	07eb112ea61369cf	train	human
\hat{B}	d995ef9e2699ad4f	train	human
y=\sqrt{x^{2}-\|w\|^{2}}>0	81652621ff52a353	train	human
\frac{1}{n}!=\int_{0}^{\infty}e^{-x^{n}}dx	a794cb3748b54914	train	human
\frac{(3-170)}{\frac{7}{8}\cdot169}	18588c0f98998f00	train	human
0=E\{(\hat{x}-x)y\}	dd989331170f4ed9	train	human
(107+393)^{\frac{10}{10}}	5f55e3b4d0b5cbec	train	human
3\cdot10^{{6^{1}}^{1}}	96759dd0136afc20	train	human
\|\|v\|\|=\sqrt{v^{\top}v}	7b94165cf45291de	train	human
\sqrt{re^{i\theta}}=\pm\sqrt{r}e^{i\theta/2}	06f572fe66612448	train	human
\frac{\frac{\frac{\sqrt{449}}{9}}{217}}{(\frac{\sqrt{318}}{313})^{3}}	39f1ae5aa180fe91	train	human
z=i\frac{log3}{4\pi}	72815a520798140f	train	human
v(x_{0})	fd5834356c996180	train	human
(1)y^{\prime}=F(x,y)	a8e8e573167628f0	train	human
[\begin{matrix}1&1\\ 0&1\end{matrix}]	c8a130af45f76b27	train	human
\sum_{i=0}^{4}(\begin{matrix}8\\ 2i\end{matrix})(\begin{matrix}28\\ 16-i\end{matrix})	03bcac8d4ea1dea3	train	human
\int fg=f(x)\int g	8dbd24881a54785b	train	human
\sigma=\sqrt{\frac{B-ND^{2}}{N}}	1fffcc0286cdfd52	train	human
\frac{E_{1}}{E_{2}}=\frac{n_{1}}{n_{2}}	abc84973c454a7e8	train	human
\omega\notin X	57096b3c3e25de85	train	human
\sqrt{-h}h^{ab}\rightarrow\eta^{ab}	7fd44063e9cc0930	train	human
m_{2}=\frac{a^{2}+ab+b^{2}}{3}	d8d32298269dd225	train	human
\frac{2\chi}{\sqrt{\frac{Um_{sen}}{o^{9}}}}	0d8041cb5a09fab5	train	human
y=x^{2}\iff x=\sqrt{y}	c958660677c98097	train	human
\overline{n}	bbe0d36d5a9533f9	train	human
\frac{d\Phi}{dr}=-\frac{1}{\rho}\frac{dP}{dr}	f098dd4f127830ed	train	human
((\frac{442}{\sqrt{389}})^{8})^{395^{1}}	06466a1065289bb5	train	human
(\frac{3^{8}}{209}-3/2)	3dbedacb32fb18b2	train	human
((10\cdot496)-8)^{317\cdot\sqrt{8}+3}	1876794d7755a785	train	human
Z[p^{-1}]	4f5026e7364c078a	train	human
(\begin{matrix}n\\ p\end{matrix})	a44632d92e2b7d3d	train	human
3,\frac{8}{3},\frac{11}{4},\frac{19}{7},\frac{87}{32},...	a3d7b3b345e4f331	train	human
dsin\theta_{n}=n\lambda	e666ef7c09700c13	train	human
(\begin{matrix}N\\ 2\end{matrix})	9e8c89381b09d69b	train	human
p=\frac{m+u}{\sqrt{6-\frac{u^{2}}{c^{2}}}}	906edd61c6be9435	train	human
x^{(3)}=x_{4}	d7508f56a94b00f6	train	human
\frac{4^{4}}{4}=64<70=(\begin{matrix}8\\ 4\end{matrix})	e3ede36163cbcf60	train	human
N\equiv\sqrt{-\frac{g}{\rho}\frac{d\rho}{dz}}	c8db92bbc341612b	train	human
V_{q}=\frac{4\pi e^{2}}{\epsilon q^{2}L^{3}}	5a6711b016d8e32e	train	human
\mu=\beta(1+\frac{\alpha^{2}}{2})	d162376373527d34	train	human
[\begin{matrix}12&12&123&124\\ \end{matrix}]	27943634325d1bd0	train	human
273^{4}+26+403	4441173467e06747	train	human
\frac{D_{P1}}{D_{P2}}=\frac{\rho_{P2}}{\rho_{P1}}	711d84cab90d29a4	train	human
{(H^{f})}^{\xi}	35aa471f328144b0	train	human
{(\frac{{w_{z}}^{4}}{{w_{a}}^{4}}-1)}^{4}\ge0	89ffac05e75cdfe8	train	human
\lfloor\frac{37+3}{4}\rfloor=10	a3b491d845aba9e6	train	human
\alpha=\frac{lnC}{T-1}	c3207a4076e6f2a4	train	human
{{417^{103}}^{4}}^{\frac{7}{46}}	c4d268c84416c188	train	human
\overline{x_{i}}	36e0c51d779bc1e5	train	human
\tilde{\gamma}	4a077549da4d749c	train	human
bf(m\tilde{T})	96cd8e0cfbc92a2e	train	human
\frac{(3-\sqrt{2})}{\frac{1^{6}}{7}}	364bf97c6fdd967d	train	human
\underline{P}(Cl_{1}^{\le})=\{x_{1},x_{5}\}	3537d3c8cd31fa86	train	human
W=-\int Fdx	be3365e04f7d6b46	train	human
\|\|f_{\theta}-f_{\theta^{\prime}}\|\|_{L_{1}}\ge\alpha	c8cb375cc1c4678e	train	human
F(r)=\frac{C(r)}{Rr^{3}}	ad30c2589c7c39d6	train	human
\int_{0}^{1}3x^{2}+2x+5dt	05dde2352693762a	train	human
\frac{(b-a)^{3}}{36}f^{(2)}(\xi)	9432e5e59a773a98	train	human
lim_{n\rightarrow\infty}z^{\pm n}	4c87ab92cc5dfbfa	train	human
GZ=GM\cdot sin\phi	28dc474c88ad0dfd	train	human
Af=i\frac{d}{dx}f	3913db154ee42480	train	human
I_{n}=\int sin^{n}x	9b1e5bedd3aad447	train	human
(\begin{matrix}0&i\\ i&0\end{matrix})	a5d201921f51aaa2	train	human
2^{O(\sqrt{k})}n^{O(1)}	5dfbd67654f854ce	train	human
\epsilon_{2}=\lambda^{\lambda^{\lambda^{\cdot^{\cdot^{\cdot}}}}}	df77854b3f98473f	train	human
({\sqrt{56}^{5}}^{1}+10^{\sqrt{5}})	aebf5691c09ed4a3	train	human
P_{max}=P_{m}+H	0afebcff2eab2d0b	train	human
(\begin{matrix}n\\ k\end{matrix})=(\begin{matrix}n-1\\ k-1\end{matrix})+(\begin{matrix}n-1\\ k\end{matrix})	f3181fa678fc5e5a	train	human
\hat{\rho}	8f8f0a10114a79a5	train	human
\pi-\psi=\angle AKP_{2}	b1935edf11cd74c9	train	human
\frac{\partial}{\partial c}P_{c}^{n}(c)	b24910dd4e5a697e	train	human
c_{c}=1	5f5abcf6fd3a473d	train	human
\frac{\sqrt{\frac{(d_{1}n)^{d_{1}}d_{7}^{d_{7}}}{(d_{1}n+d_{7})^{d_{1}+d_{7}}}}}{nU(\frac{d_{1}}{7},\frac{d_{7}}{7})}	7adb6ef7f655dd5d	train	human
(\begin{matrix}n\\ c\end{matrix})	831fbf3ee29135fa	train	human
p=\frac{e^{\theta}}{1+e^{\theta}}=	f6594b46c7ef3083	train	human
x^{p/q}=\sqrt[q]{x^{p}}	27e4ed62587415be	train	human
w^{+\frac{(V+M)^{2}}{2{(s_{V})}^{2}}}	93a68d7d96cec163	train	human
\frac{\frac{2}{3}}{\frac{\frac{7}{300}}{1}}	7e3c2db34885f8ac	train	human
\prod_{j\ne i}(x_{i}-x_{j})	412500632a50c3d8	train	human
(\frac{378}{4}+(\frac{143}{10})^{196})	d1f46a8ca9091110	train	human
RC=\Delta_{T}(\frac{1-\alpha}{\alpha})	e94f2702384c2872	train	human
c_{n}=\prod_{i=1}^{n}p_{i}	e86a0d1a3dbae839	train	human
\tilde{v}_{ij}	2b95997b1dbbc841	train	human
=\frac{(\begin{matrix}K\\ k\end{matrix})(\begin{matrix}N-K\\ n-k\end{matrix})}{(\begin{matrix}N+1\\ n+1\end{matrix})}	f14ca7618d191b18	train	human
\hat{S_{z}}	7a2392e6a2b333b4	train	human
\frac{k-1}{k}	f0cd3b34bf9e9673	train	human
\frac{(5-5)^{7}}{7\cdot7}	452aab155f72bb1f	train	human
F=x^{2}-y^{2}-z^{2}	024a00b093eb3886	train	human
\{\begin{matrix}3\\ 5\end{matrix}\}	9d74b841c1d9ede3	train	human
\tilde{m}=\frac{rhp}{\sqrt{\frac{r_{1}r_{2}}{r_{1}-r_{2}}}}	6da3f05378d2c237	train	human
e^{k}k^{O(logk)}log\|V\|	391e8e07e399429e	train	human
\frac{(210^{9}/4)}{\frac{(\sqrt{9}+317)}{\sqrt{5}}}	7a055c0ae01a06d0	train	human
\sqrt{\frac{\alpha\lambda}{\beta}}(x-\mu)	15dc2648d6f2f527	train	human
{149^{4}}^{\frac{20^{197}}{306}}	72bf2f84fbb1b614	train	human

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