Split (3)

train · 230k rows

latex stringlengths 1 188	sample_id stringlengths 16 16	split_tag stringclasses 1 value	data_type stringclasses 1 value
-\sqrt{c}	9436b2b04de8fd42	train	human
f(x)=\int_{a}^{x}g(t)dt	0e2fa51c4248989c	train	human
\int_{\Omega}u_{j}u_{j}=1	c9e14b59dcb1e23c	train	human
g=\prod_{i\in I}(X-\alpha_{i})	5ae1ceb7b1fa1bd0	train	human
\overline{y}=\hat{\alpha}+\hat{\beta}\overline{x}	2f773fe7f27574d4	train	human
[\begin{matrix}\eta_{1}+1\\ -\eta_{2}\end{matrix}]	eeb986ea6ce640db	train	human
G:=-\frac{\partial(U-V)}{\partial A}	1cd11c58df4a0124	train	human
\varphi	493d73c802ca1f2e	train	human
\frac{\partial L}{\partial q}=0	9ac78bd5f0fb3847	train	human
[A]_{0}=[A]+[AB]	4973ec1eb4bd69ea	train	human
\int_{E}f\mu	1149030c04e68a26	train	human
\Delta G_{DF}	43378b881c4d758b	train	human
(b_{1}-d)-(a_{1}-d)	cf279233397384be	train	human
\hat{S}_{n}	2e60b5f029741e85	train	human
(\frac{n}{m})	b16ad330bb9cc987	train	human
(\begin{matrix}p\\ r\end{matrix})	247a4d26295cfa1a	train	human
B_{1}=-\frac{1}{2}	31a5d52324393685	train	human
m_{zal}=\frac{m_{5}}{\sqrt{1-\frac{p^{6}}{c^{6}}}}	6f9ea266265d6bb8	train	human
\frac{dv}{dr}	df437a795957e0bd	train	human
f(x)=\frac{b(x)}{B(x)}	08777eb6737ae774	train	human
\overline{\Phi}(s;\tilde{L})=1	7738a7afa35709ec	train	human
\underline{m}=\{1,2,...,m\}	842359d2617a904f	train	human
-\sqrt{E_{b}}\phi(t)	2636e8c5c320b88d	train	human
r=1/x	d64ea79faeed2f92	train	human
\frac{\Delta k}{t}=\frac{R^{\frac{4k_{e}}{t}}\cdot1}{R^{\frac{4k_{e}}{t}}+1}	2d5d144a5a913ef9	train	human
[\begin{matrix}0&1\\ 0&0\end{matrix}]	de6f33f53cf3c5dc	train	human
\partial_{y}=\frac{\partial}{\partial y}	5850321722bf83c4	train	human
Pr(v\in S)\ge\frac{1}{k}	d1af0c3642fc84aa	train	human
{7^{112}}^{\frac{\sqrt{5}}{\sqrt{10}}}	e2457a3ac2432c93	train	human
\hat{D}=D	57abdd0a7e504268	train	human
(a\pm\sqrt{a^{2}-4})/2	433527618930974b	train	human
\frac{dx}{dt}=x	52ed90ba16818995	train	human
\nu_{M}:M\rightarrow BO(k)	9cdb413d45b26b4e	train	human
f(t)?	ddca600bc4698f14	train	human
\overline{x}=\frac{M_{10}}{M_{00}}	744e56a9f01b763b	train	human
\frac{\sqrt{x+2}}{x^{2}-3}	f20d265a6a89acc2	train	human
\vec{a}=N\vec{V}_{r}\times\vec{\Omega}	ecf17a60d84e65fb	train	human
I=\int Fdt	a93aedc6405f6c14	train	human
[\begin{matrix}a&b\\ c&d\end{matrix}]	995f0fe67645fa5c	train	human
\Delta s=\frac{dP}{dT}\Delta v	ddeb17744c72b409	train	human
(\begin{matrix}n\\ k\end{matrix})+(\begin{matrix}n\\ k-1\end{matrix})=(\begin{matrix}n+1\\ k\end{matrix})	055940b6a1239b49	train	human
m_{rwl}=\frac{m_{0}}{\sqrt{7\cdot\frac{g^{8}}{c^{8}}}}	ee30fba734c38bca	train	human
(\begin{matrix}c_{k}\\ k\end{matrix})	5ab12fe7d56927d9	train	human
V^{2}=\frac{2kb(a+b)}{Ma}	c69def07fd2feb8f	train	human
\sum_{n=1}^{\infty}\frac{1}{n}	ad2e2ea2678b0e5e	train	human
i_{1}^{\prime}=\frac{i_{1}\cdot vt_{1}}{\sqrt{1\cdot\frac{v^{8}}{n^{8}}}}	a2ba59b94788db7b	train	human
\frac{d^{2}x}{dt^{2}}=-sinx	5488bdc00181c788	train	human
\tilde{\eta}	3c31d19e73c7a2d2	train	human
\phi(p)=\frac{e^{-\frac{p^{5}}{5}}}{\sqrt{5\epsilon}}	f518a77188bd8084	train	human
\tau=\mu\frac{du}{dx}	c23d35448579aa37	train	human
\frac{dx}{dy}=	2d65f9b34eed9580	train	human
\int_{0}^{x}1dt=x	eefca94a0127dc24	train	human
w_{z}^{\psi}	fe3d2be0acf404c3	train	human
\sum_{i=1}^{n}S_{i}S_{i}^{*}=I	9ed9f42f6e248a44	train	human
\beta(A^{T}\cdot)	0c4583003ac59b9e	train	human
n![z^{n}]g_{m}(z)=[\begin{matrix}n\\ m\end{matrix}]	7075f88f27db3bc7	train	human
F(u,\lambda_{0})=0	036cd16ac020a4be	train	human
\frac{\mu^{2}}{2\sigma^{2}}+ln\sigma	9f96ae787cd685b0	train	human
\sqrt{\frac{\sum{A_{f}}^{2}}{n}}	0613fc23963319f7	train	human
-\frac{1}{b}	4ffe52fbd61c21ee	train	human
g:=f^{\frac{n-1}{n}}	20635f8005a9abb0	train	human
\int_{0}^{a}sinxdx	2d2d61f7edcd90cc	train	human
\sqrt{\frac{\alpha\lambda}{\beta}}(x-\mu)	e773824ffd3f3ec1	train	human
R_{0}=\sqrt{x^{2}+y^{2}+z^{2}}	af79620a4f726be2	train	human
\int_{1}^{\infty}x^{-x}dx	eb9d7eebb240986f	train	human
Pe=\frac{F}{D}=\frac{\rho u}{\Gamma/\delta x}	8f6db2dcc4299455	train	human
\frac{\partial^{2}C_{i}(q_{i})}{\partial q_{i}^{2}}=0	26119abb256939c6	train	human
z(v)\ge deg^{+}(v)	480c0abf25466926	train	human
\hat{a}_{1}	83ce5cbe26e648a6	train	human
r=(1+\frac{i}{n})^{n}-1	581741064ff0ae46	train	human
\frac{v}{c}=\frac{b}{a}	7fc9d5666150eb00	train	human
3^{3^{3^{3^{46}}}}	15ec1f58f140f94b	train	human
\|1-\lambda R(\underline{k},\omega)\|<1	d270ef61ba709003	train	human
\sqrt{64}	fe008cb32d866d79	train	human
j=1,..,n-1	1131fa36c0687e14	train	human
\frac{4\zeta m}{\sqrt{1-\frac{0m}{vu^{0}}}}	b0d5af6f53548c7a	train	human
\frac{317^{\sqrt{385}}}{78}-(454-\sqrt{6})	dc4eaf049f1c392d	train	human
[\begin{matrix}4&6\\ 3&5\end{matrix}]	56c9a040d0f1fb2d	train	human
a^{2}-Nb^{2}=k	3a1340e6c8b8e9a3	train	human
kx^{\prime2}/z	5edc6cd7cf76ffe2	train	human
\frac{\frac{5}{365}}{\frac{448^{119}}{3}}	23bf44a390a6016f	train	human
\int d^{3}r	a2c1da4fa31062c4	train	human
\theta=\frac{\mu_{1}-\mu_{2}}{\sigma}	b29a4252d9d94132	train	human
\overline{m}_{a}	a11234798ae04a24	train	human
\tilde{E}	6f16715368d7df81	train	human
fg=f^{}(-t)*g	7a7cd05fcfc900b7	train	human
\sqrt{x^{7}}+x^{2}	25e728163e2b4fa6	train	human
\frac{ds}{dt}=0	33bcb812d824eb01	train	human
s=\int ds	83f591a1ec76f0af	train	human
\frac{\frac{9}{60}}{(303\cdot246)/10}	e9c36346393cf12b	train	human
G_{\mu\nu}=8\pi\frac{G}{c^{4}}T_{\mu\nu}	634984b2030fd100	train	human
\mathbb{C}[x_{1}^{\pm1},...,x_{n}^{\pm1}]	13d8debef11195e0	train	human
H=-\gamma\hbar B\sigma_{3}	6a2ce93c6f1b7d0b	train	human
T^{t}=e^{t\frac{d}{dx}}	e5982288ce1b3fca	train	human
\frac{(x-X)(y-Y)}{(x-Y)(y-X)}	848e56a03944e949	train	human
(\begin{matrix}p\\ r\end{matrix})	e32d2f52eb0a156b	train	human
\frac{F}{EI}=\frac{\pi^{2}}{L^{2}}	a555bbe3eff4a099	train	human
sup_{\|\|u\|\|=1}\|B(u,v)\|>0	21904ec7f3e4e929	train	human
C_{i}=\frac{N_{i}}{V}	c71774ac8c2fdd6e	train	human
p_{y,0}=\frac{eE_{0}}{\omega}	c178cedc5195d897	train	human

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