Split (3)

train · 230k rows

latex stringlengths 1 188	sample_id stringlengths 16 16	split_tag stringclasses 1 value	data_type stringclasses 1 value
\frac{1}{4}-\frac{1}{6}\sqrt{3}	a38d80b24435a9f5	train	human
sech(z)=\frac{1}{cosh(z)}	a89e9cc95a7d669e	train	human
M=\frac{\pi abc\rho}{6}	c95d86ba46c372b3	train	human
\frac{\partial\eta}{\partial y}>0	961bff6a2f7e299c	train	human
F=\frac{q_{1}q_{2}}{r^{2}}	a2a50b9bfc5da22e	train	human
\frac{(7\cdot3)^{301}}{{10^{6}}^{3}}	aeb907786e193ac5	train	human
\frac{f^{(k)}(\xi)}{k!}x^{k}	b83dab6bfc3c52a1	train	human
(\begin{matrix}n\\ n\end{matrix})	75f2d5d3277df531	train	human
w(n)\le\lfloor(n-1)/2\rfloor	90f1146c0f0a2bd0	train	human
\int_{0}^{T}PdX=nh	31b73489a4c6b25f	train	human
r(K_{m}+\overline{K_{n}},K_{p}+\overline{K_{q}})	afba50900610ca23	train	human
[\begin{matrix}1&0\\ -G&1\end{matrix}]	fe0fbcb08f9de034	train	human
(\begin{matrix}0&-1\\ 1&0\end{matrix})	8839732b155f17d8	train	human
053^{053^{053^{053^{057}}}}	d659646548752044	train	human
\eta_{th}=1-\frac{1}{r^{\gamma-1}}	f0ab3e93f0d4750e	train	human
x^{13^{13^{13^{122}}}}	3bd1705b92231714	train	human
A,B,E\in2^{X}	c38c1b919dbbbf02	train	human
v(r)=(rd\Phi/dr)^{1/2}	562680bcba49961b	train	human
X_{j}=\frac{\partial g}{\partial\xi_{j}}\|_{\xi_{j}=0}	48cc0b821dd014b2	train	human
c_{k}=0	fe360fcd6e53953c	train	human
2\sqrt{2}	2489a8720c855f15	train	human
T_{b}=\frac{I_{\nu}c^{2}}{2k\nu^{2}}	4a4cb45bbd306585	train	human
(2e^{0i})^{0.5}=\sqrt{2}	c429f115a7c8b8da	train	human
(\begin{matrix}n-1\\ i\end{matrix})	8c582a2a1c708970	train	human
(\begin{matrix}N\\ M\end{matrix})	3df97c2a7cdf48fb	train	human
\rho=\frac{1}{2}r(1-r)	a22d7bf3057af579	train	human
\frac{\partial\delta}{\partial x_{j}}(x)	3c62d4f99f0e0e2b	train	human
{281^{203}}^{52-1}	f387eca3bf67001e	train	human
b_{n}=\sum_{d\|n}\mu(\frac{n}{d})a_{d}	7a93a23f13e42b8d	train	human
lim_{x\rightarrow0}\frac{1-cosx}{x^{2}}=\frac{1}{2}	660c60436117ac56	train	human
(\begin{matrix}0&1\\ 1&0\end{matrix})	d15e7ac49bb56d08	train	human
D_{\mu}=\partial_{\mu}-i\frac{e}{\hbar}A_{\mu}	54e2624734844c67	train	human
\underline{S}_{\lambda}	f65211e5d923b122	train	human
P_{t}=\frac{x_{t}+x_{t-1}}{2}	44fcff412a78862c	train	human
G_{1}\in[0,255]	b4715a0cc9c30219	train	human
\frac{dp_{o}}{p_{o}}	8a424198bda424d3	train	human
\frac{4}{\sqrt{4-\frac{v^{9}}{x^{9}}}}	bbfc517660a54700	train	human
I_{2}=-\frac{Z_{21}}{Z_{22}}I_{1}	68f6c9f5685f4b54	train	human
\psi,\tilde{\psi}	6791cf9d01d8a754	train	human
\frac{\sqrt{3}\cdot\sqrt{168}}{(\frac{413}{3}\cdot326)}	170313490fc019c5	train	human
(i\omega_{1},i\omega_{2})	b8c4f18be1846949	train	human
t=\frac{2L/c}{\sqrt{1-v^{2}/c^{2}}}	9f7c9fef5751e45b	train	human
D^{(r)}X^{n}=(\begin{matrix}n\\ r\end{matrix})X^{n-r}	5550bb54ce1fecbe	train	human
\frac{dW}{dt}	16d83b4e97de58a1	train	human
\tilde{f}_{0}:X\rightarrow E	4595dbf157498a5a	train	human
2\sqrt{n}	7d8dc0458df1ea6b	train	human
\int_{-a}^{a}f(x)dx=0	a73779ad8ee1b1e9	train	human
e^{\cdot\frac{(F\cdot M)^{0}}{0{(s_{F})}^{0}}}	baffe7beb70243b2	train	human
2^{2^{2^{2^{74}}}}	bb688f22742e99b6	train	human
Q_{4}	e9c15afd4d4c0046	train	human
E=\frac{mg^{2}}{\sqrt{5\cdot\frac{w^{2}}{g^{2}}}}	b4ceb27e5e94d9bf	train	human
(\begin{matrix}n\\ p\end{matrix})	cd2e982cb0f7d65a	train	human
b(m)=e^{m/T}	13291c72394e9fcf	train	human
\prod_{i}S_{i}	4ddf5b38b19fa210	train	human
\int(p(x))^{n}f(x)dx	de21a16122121304	train	human
\underline{v_{row}}=2	24cf5532e3ac76e1	train	human
\|f^{\prime}(0)\|=1	7e113da49b5bba7d	train	human
\{R_{t}\}_{t\in D}	927bd8f4bfa893b0	train	human
(S^{3})=	0412f13ec9bf1cb7	train	human
\beta_{T}=\beta_{S}+\frac{TV\alpha^{2}}{Nc_{P}}	064da36670efeb8f	train	human
\prod_{i=1}^{n}	0efb07e3b2c94ea4	train	human
d_{1}=[\begin{matrix}x&y\\ \end{matrix}]	aaaa548e13d78cd8	train	human
F_{m}\approx-\frac{\mu_{0}I_{1}I_{2}}{2\pi r}	0745dc1e393efa87	train	human
T_{0}\approx2\sqrt{l}	b584509d8fc32e45	train	human
\tilde{O}(\theta dlog\frac{1}{d})	c79c7c99af5c649a	train	human
\underline{V}	2cac26fb519729ae	train	human
\int dx=0	b9d356d7eb47c35c	train	human
\Rightarrow v=\sqrt{2gz}	5153a20b92ef77c0	train	human
j\notin T	6aeebd8a4137e779	train	human
M=K[\begin{matrix}R&t\end{matrix}]	557fd1f762cbbded	train	human
\forall X,Y\in L^{0}(F_{T})	fc9d0a3b44e50668	train	human
(\frac{10}{164}+7)^{\frac{10}{451}-\sqrt{21}}	0b3423cf1f05f32d	train	human
[\begin{matrix}4&6\end{matrix}]	7767eab105eb8735	train	human
M=\int_{V}\rho dV	20449b7b725d2113	train	human
(\frac{3/345}{130})^{2^{3}/4}	5d24932c6ebf5b7b	train	human
a_{n}=e^{i\frac{2\pi}{q}x_{n}}	7aa4be8ad29d5f9e	train	human
n_{0}=\frac{p_{0}N_{A}}{RT_{0}}	4a7b83c9a7d3c70c	train	human
\overline{abc}	91a773c4242b390e	train	human
tan\gamma=\frac{d}{R}	637b6b275680ffd4	train	human
(\begin{matrix}6\\ 4\end{matrix})	7927b0b546602095	train	human
p\notin F(t)(\partial\Omega)	290b51283c5f8ec4	train	human
\frac{\partial g}{\partial x}	cb56a626f4ef1fb7	train	human
\Delta s^{\prime}=\frac{\Delta s}{\sqrt{1+\frac{v^{5}}{u^{5}}}}	c6da24b83abf477b	train	human
\tilde{A}_{7}	4628c6115b00544f	train	human
V=\frac{\sqrt{2}}{6}a^{3}	a737824b73d67423	train	human
\frac{p}{q}=\frac{a+c}{b+d}	ba9ca81ae7732191	train	human
9\cdot5^{\frac{\frac{7}{399}}{324}}	ec67f861c0b9bc29	train	human
T(3,1)_{-\frac{1}{3}}	2af42881870fca41	train	human
cosx=\frac{e^{ix}+e^{-ix}}{2}	a496cc813b710e1c	train	human
a^{s^{n^{\cdot^{\cdot^{\cdot}}}}}	4ad9dd3587887062	train	human
Q^{(ab...n)}	6ca41256db3ce39b	train	human
f(z)=\sum_{k=0}^{\infty}(\begin{matrix}1/2\\ k\end{matrix})z^{k}	be5c6f7aa296abb6	train	human
\int x^{s}\phi(x)dx	c9f34b6f82fce077	train	human
2\sqrt{n}	2e4985970b125e17	train	human
\hat{s}=S(S+N)^{-1}d	7d7c39f55a4b2b96	train	human
\frac{\Gamma_{s}A_{s}}{{\delta x}_{SP}}	a1abfc39d924adb7	train	human
[\begin{matrix}p&t\\ q&u\end{matrix}]	b4b9ac8f63079774	train	human
(\begin{matrix}n\\ b\end{matrix})	f0eff8d2bd111762	train	human
\hat{v}_{k}	3e2f23ef854ee620	train	human
n=\frac{m_{9}v}{\sqrt{1+\frac{v^{3}}{c^{3}}}}	a1b5bc906b2034f4	train	human

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