ddrg/math_structure_bert
Feature Extraction
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32,460 | 30 = 2220422932^3 + \left(-2218888517\right)^3 + (-283059965) \cdot (-283059965) \cdot (-283059965) |
9,583 | \left(\sqrt{z + d}\right)^2 = \sqrt{G + m} * \sqrt{G + m}\Longrightarrow G + m = z + d |
-6,693 | 80/100 + 3/100 = 8/10 + \dfrac{1}{100}\times 3 |
-14,550 | 1 + 5 \cdot 7 = 1 + 35 = 1 + 35 = 36 |
15,023 | \dfrac{x - y}{x^2 - y \cdot y} = \frac{1}{y + x} |
-5,133 | \dfrac{66.6}{1000} = \frac{66.6}{1000} |
26,406 | \tfrac{6}{35} = 3/5*\frac{2}{7} |
20,175 | \frac{1}{54}\cdot 4 = \frac{\dfrac{1}{2}}{2}\cdot 8\cdot \frac{1}{27} |
17,157 | i^{-1} = i^{1 + 2 \times (-1)} = \dfrac{i}{i^2} = i/(-1) = -i |
6,302 | 0 = k\cdot 3 + (-1) \Rightarrow k = 1/3 |
1,448 | m = 3/2*y rightarrow 2/3*m = y |
2,443 | \left\lfloor{\frac{90000}{35}}\right\rfloor = 2571 |
2,919 | \frac{1}{20} = \frac14 - \frac{1}{5} |
40,555 | \frac{1}{3}*3 = 1 = 3 + 2\left(-1\right) |
10,843 | y\cos(a) = \sin(a) x \Rightarrow -x^2 \sin^2(a)*2 = -y^2 \cos^2(a)*2 |
17,016 | \mathbb{E}[\sum_{l=1}^x X_l] = \sum_{l=1}^x \mathbb{E}[X_l] |
13,601 | 0 = x^3 + b^3 + h \cdot h \cdot h - 3 \cdot x \cdot b \cdot h = (x + b + h) \cdot \left(x^2 + b^2 + h^2 - x \cdot b - b \cdot h - h \cdot x\right) |
7,202 | 2 + 2 + 2 + 2 + \dotsm = -\frac12 |
-7,793 | \frac{1}{-4}\cdot (20\cdot i - 20) = -\frac{20}{-4} + i\cdot 20/\left(-4\right) |
28,915 | z^6 + z^5 + z^4 + z^3 = (z^3 + z) \cdot \left(z^2 + z^3\right) |
7,100 | 90/100 \cdot \left(1 - \frac{75}{100}\right) = \frac{25}{100} \cdot 90 \cdot \frac{1}{100} = 9/40 |
27,794 | m \cdot 0 = m + (-1)^m \cdot 0 = m = 0 + \left(-1\right)^0 \cdot m = 0 \cdot m |
-26,432 | 16 = 24 \times 2/3 |
45,561 | 195 = 3*5*13 |
37,180 | t^2 + 2\cdot y\cdot t + \left(-1\right) = 0 \Rightarrow -y ± \sqrt{1 + y^2} = t |
11,270 | 1 = (1^{1.5})^{\frac{1}{2}} |
46,411 | \sin{4 \cdot x}/\sin{x} = \dfrac{1}{e^{i \cdot x} - e^{-i \cdot x}} \cdot \left(e^{4 \cdot i \cdot x} - e^{-4 \cdot i \cdot x}\right) = e^{3 \cdot i \cdot x} + e^{i \cdot x} + e^{-i \cdot x} + e^{-3 \cdot i \cdot x} = 2 \cdot \cos{x} + 2 \cdot \cos{3 \cdot x} |
-21,055 | 6/8 = \frac34\cdot 2/2 |
3,552 | E(T_1) + \cdots + E(T_x) = E(T_1 + \cdots + T_x) |
6,773 | \cos{6z} = \cos(5z + z) |
-30,916 | 3 \cdot b + 6 = 3 \cdot b + 6 |
21,852 | \alpha \times |Z|^2 + \beta \times |Z^2| = \alpha \times |Z|^2 + \beta \times |Z|^2 = (\alpha + \beta) \times |Z|^2 |
18,533 | \dfrac{D\cdot x}{D} = 1 \Rightarrow x\cdot D = D |
-18,319 | \frac{42 + y^2 - y\cdot 13}{y^2 - 7\cdot y} = \frac{(y + 6\cdot \left(-1\right))\cdot (y + 7\cdot (-1))}{(y + 7\cdot (-1))\cdot y} |
-4,552 | -\frac{5}{x + 2} - \frac{1}{x + (-1)} = \frac{3 - 6*x}{x^2 + x + 2*\left(-1\right)} |
-19,342 | \frac48\tfrac13 = \tfrac{1}{\dfrac143 \cdot 8} |
1,050 | 21 \cdot z/20 = \frac{z}{5} \cdot 4 + \dfrac{z}{4} |
23,389 | Y_2\cdot A_1 = A_1\cdot Y_2 |
23,629 | (\tfrac{u}{2} + w/2)*2 = u + w |
-20,651 | \frac{t\cdot (-18)}{3\cdot t + 30\cdot (-1)} = \tfrac33\cdot \frac{(-6)\cdot t}{t + 10\cdot (-1)} |
15,532 | b = \arcsin{h} rightarrow \sin{b} = h |
-15,685 | \frac{1}{s^{12}*x^{15}*(\frac{1}{x^5*s^4})^4} = \frac{\tfrac{1}{x^{15}}*\frac{1}{s^{12}}}{\dfrac{1}{x^{20}}*\frac{1}{s^{16}}} |
-19,488 | \phantom{\dfrac{1}{9} \times \dfrac{8}{5}} = \dfrac{1 \times 8}{9 \times 5} = \dfrac{8}{45} |
24,708 | 1 - \sin^2{z} = \cos^2{z} = (1 + \cos{2*z})/2 |
-12,428 | \frac{1}{2}*116 = 58 |
-12,117 | 1/6 = \frac{x}{6*\pi}*6*\pi = x |
-10,267 | -\tfrac{45 \cdot (-1) + 45 \cdot y}{y \cdot 15 + 60 \cdot (-1)} = 15/15 \cdot \left(-\frac{1}{4 \cdot (-1) + y} \cdot (3 \cdot y + 3 \cdot (-1))\right) |
-154 | \frac{10!}{(3(-1) + 10)!} = 10\cdot 9\cdot 8 |
29,559 | -1/24 = \dfrac{1}{2} + 2/2 + \dots |
23,145 | 1! + 2! + \dots + n! + (n + 1)! \leq 2n! + (n + 1)! = \left(n + 3\right) n! \leq 2(n + 1) n! |
11,212 | \binom{-1}{q} = (\left(-1\right)*\left(-2*\dotsm*(-1 - q + 1)\right))/q! = (-1)^q |
-20,622 | 5/5 \cdot \frac{1}{i \cdot 6} \cdot (-8 \cdot i + 4 \cdot (-1)) = \dfrac{1}{30 \cdot i} \cdot (20 \cdot (-1) - i \cdot 40) |
2,647 | x*x^N = x^{1 + N} |
18,294 | -z^2 \cdot 2 + (z^2 + 1) \cdot (z^2 + 1) = z^4 + 1 |
1,039 | (1/4)^{1/2} = \dfrac{1}{2} |
-19,575 | 7\cdot \frac{1}{3}/9 = 7/(9\cdot 3) = 7/27 |
-20,825 | \frac{1}{\left(-1\right) + n} \cdot ((-4) \cdot n) \cdot 7/7 = \frac{1}{7 \cdot n + 7 \cdot (-1)} \cdot (n \cdot (-28)) |
-11,646 | 22\cdot i - 15 + 8 = -7 + 22\cdot i |
6,332 | n = n + (-1) + 1 = n + 2\cdot (-1) + 2 = \dotsm = (n + 1)/2 + (n + (-1))/2 |
-16,690 | -5\cdot y = -5\cdot y\cdot \left(-5\cdot y\right) + -5\cdot y\cdot \left(-7\right) = 25\cdot y^2 + 35\cdot y = 25\cdot y^2 + 35\cdot y |
-29,144 | 18 = 4\cdot 4 + 1\cdot 2 |
-19,683 | 20/9 = \frac{4}{9} \cdot 5 |
8,496 | 4 \lt z \cdot z \implies 0 \lt (2 + z) \cdot (z + 2 \cdot \left(-1\right)) |
51,751 | 1 = i^0 |
29,559 | 1/2 + \frac{2}{2} + ... = -1/24 |
-12,841 | 3/4 = 18/24 |
28,679 | 2\cdot 5\cdot \dfrac{5!}{2!} = 600 |
-20,286 | \frac13 \cdot 3 \cdot (-10/7) = -30/21 |
7,844 | -\frac{1}{1 + x} + 1/x = \dfrac{1}{x + x \times x} |
-3,338 | 6\times \sqrt{2} = \sqrt{2}\times \left(4 + 3 + (-1)\right) |
-1,423 | -\frac{8}{3}\cdot 3/5 = ((-8)\cdot \frac13)/(5\cdot 1/3) |
-2,886 | 7*\sqrt{2} = (5 + 4 + 2*\left(-1\right))*\sqrt{2} |
808 | \cos(x) = (e^{ix} + e^{-ix})/2 = \overline{\cos(x)} = \frac{1}{2}\left(e^{-ix} + e^{ix}\right) |
20,064 | (a - b)/(b*a) = -1/a + 1/b |
29,492 | 4! \binom{5}{4}*4! = 5!*4! |
-20,665 | \frac33 \frac16(y + 9(-1)) = \frac{1}{18}(y*3 + 27 \left(-1\right)) |
-10,491 | \dfrac{20}{z \cdot z\cdot 16} = 2/2\cdot \dfrac{10}{8\cdot z^2} |
1,688 | (x + (-1))*\left(x + 2*\left(-1\right)\right)*(x + 3*\left(-1\right)) = x^3 - 6*x^2 + x*11 + 6*(-1) |
1,332 | \tfrac{\tfrac{F'}{F}\cdot \frac{K}{F}}{K \cap F'/F} = K\cdot F'/F |
22,322 | 4\cdot3/2=6 |
13,205 | x + 4x = 1x + 4x = (1+4)x = 5x |
5,313 | 1/2 + \tfrac{1}{3} + 1/3 = 7/6 |
-20,083 | \frac{1}{4(-1) + z*4}\left(-14 z + 10 (-1)\right) = \frac122 \frac{5\left(-1\right) - 7z}{2(-1) + 2z} |
26,714 | |c| \cdot c/|c| = c |
29,605 | (2^d)^3 = 8^d |
17,826 | \sin(x + g + d) = \sin(d + g + x) |
-15,507 | \frac{1}{k^{20} \times (\dfrac{q}{k^4})^2} = \frac{1}{k^{20} \times \dfrac{1}{k^8} \times q^2} |
9,579 | 5/27 = 6/27\cdot 5/6 |
-5,785 | \frac{2}{20 + z \cdot 4} = \frac{1}{(5 + z) \cdot 4} \cdot 2 |
6,255 | \sqrt{7}\cdot 2 = \sqrt{7} + \sqrt{2} + \sqrt{7} - \sqrt{2} |
26,707 | 128 = (1 + 1) \cdot (1 + 1) \cdot (1 + 1) \cdot (3 + 1) \cdot (1 + 3) |
-9,354 | 2*3*11 + x*11 = 11 x + 66 |
23,744 | g\cdot p = g\cdot p\cdot g = p\cdot g |
14,441 | y^{b + c} = y^b*y^c |
-1,560 | \frac{9}{4} = \frac14 \cdot 9 |
-18,264 | \tfrac{1}{(k + 6)\times k}\times (k + 6)\times (9\times \left(-1\right) + k) = \frac{54\times \left(-1\right) + k^2 - 3\times k}{k\times 6 + k^2} |
15,028 | ((x - b)^2 + (-d + b)^2 + (-x + d)^2)/2 = -d*x + x^2 + b^2 + d^2 - b*x - b*d |
8,916 | 14.5 = \cos{z} + 5 \implies 9.5 = \cos{z} |
-13,377 | 2 + \frac{1}{8}72 = 2 + 9 = 2 + 9 = 11 |
274 | \binom{1/2}{m} = \frac{1}{2 \cdot (\frac12 + \left(-1\right)) \cdot (\frac{1}{2} + 2 \cdot (-1)) \cdot \dots \cdot (1/2 - m + 1) \cdot m!} |
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Dataset Card for "math_formulas"
Mathematical dataset containing formulas based on the AMPS Khan dataset and the ARQMath dataset V1.3. Based on the retrieved LaTeX formulas, more equivalent versions have been generated by applying randomized LaTeX printing with this SymPy fork. The formulas are intended to be well applicable for MLM. For instance, a masking for a formula like (a+b)^2 = a^2 + 2ab + b^2 makes sense (e.g., (a+[MASK])^2 = a^2 + [MASK]ab + b[MASK]2 -> masked tokens are deducable by the context), in contrast, formulas such as f(x) = 3x+1 are not (e.g., [MASK](x) = 3x[MASK]1 -> [MASK] tokens are ambigious).
You can find more information in MAMUT: A Novel Framework for Modifying Mathematical Formulas for the Generation of Specialized Datasets for Language Model Training.
Citation
@misc{drechsel2025mamutnovelframeworkmodifying,
title={{MAMUT}: A Novel Framework for Modifying Mathematical Formulas for the Generation of Specialized Datasets for Language Model Training},
author={Jonathan Drechsel and Anja Reusch and Steffen Herbold},
year={2025},
eprint={2502.20855},
archivePrefix={arXiv},
primaryClass={cs.CL},
url={https://arxiv.org/abs/2502.20855},
}
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