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diff --git a/Qwen2.5-Eval/evaluation/latex2sympy/description.txt b/Qwen2.5-Eval/evaluation/latex2sympy/description.txt new file mode 100755 index 0000000..0064c1f --- /dev/null +++ b/Qwen2.5-Eval/evaluation/latex2sympy/description.txt @@ -0,0 +1,152 @@ +latex2sympy2: https://github.com/OrangeX4/latex2sympy + +About + +`latex2sympy2` parses **LaTeX math expressions** and converts it into the equivalent **SymPy form**. The latex2sympy2 is adapted from [augustt198/latex2sympy](https://github.com/augustt198/latex2sympy) and [purdue-tlt / latex2sympy](https://github.com/purdue-tlt/latex2sympy). + +[ANTLR](http://www.antlr.org/) is used to generate the parser. + +Features + +* **Arithmetic:** Add (+), Sub (-), Dot Mul (·), Cross Mul (×), Frac (/), Power (^), Abs (|x|), Sqrt (√), etc... +* **Alphabet:** a - z, A - Z, α - ω, Subscript (x_1), Accent Bar(ā), etc... +* **Common Functions:** gcd, lcm, floor, ceil, max, min, log, ln, exp, sin, cos, tan, csc, sec, cot, arcsin, sinh, arsinh, etc... +* **Calculous:** Limit ($lim_{n\to\infty}$), Derivation ($\frac{d}{dx}(x^2+x)$), Integration ($\int xdx$), etc... +* **Linear Algebra:** Matrix, Determinant, Transpose, Inverse, Elementary Transformation, etc... +* **Other:** Binomial... + +**NOTICE:** It will do some irreversible calculations when converting determinants, transposed matrixes and elementary transformations... + +Installation + +``` +pip install latex2sympy2 +``` + +**Requirements:** `sympy` and `antlr4-python3-runtime` packages. + +Usage + + Basic + +In Python: + +```python +from latex2sympy2 import latex2sympy, latex2latex + +tex = r"\frac{d}{dx}(x^{2}+x)" +# Or you can use '\mathrm{d}' to replace 'd' +latex2sympy(tex) +# => "Derivative(x**2 + x, x)" +latex2latex(tex) +# => "2 x + 1" +``` + + Examples + +|LaTeX|Converted SymPy|Calculated Latex| +|-----|-----|---------------| +|`x^{3}` $x^{3}$| `x**3`|`x^{3}` $x^{3}$| +|`\frac{d}{dx} tx` $\frac{d}{dx}tx$|`Derivative(x*t, x)`|`t` $t$| +|`\sum_{i = 1}^{n} i` $\sum_{i = 1}^{n} i$|`Sum(i, (i, 1, n))`|`\frac{n \left(n + 1\right)}{2}` $\frac{n \left(n + 1\right)}{2}$| +|`\int_{a}^{b} \frac{dt}{t}`|`Integral(1/t, (t, a, b))`|`-\log{(a)} + \log{(b)}` $-\log{(a)} + \log{(b)}$| +|`(2x^3 - x + z)|_{x=3}` $(2x^3 - x + z)\|_{x=3}$|`z + 51`| `z + 51` $z + 51$ | + +If you want to read the math formula, you can click [GitNotes](https://notes.orangex4.cool/?git=github&github=OrangeX4/latex2sympy). + + Matrix + +Determinant + +``` python +from latex2sympy2 import latex2sympy + +tex = r"\begin{vmatrix} x & 0 & 0 \\ 0 & x & 0 \\ 0 & 0 & x \end{vmatrix}" +latex2sympy(tex) +# => "x^{3}" +``` + +Transpose + +``` python +from latex2sympy2 import latex2sympy + +tex = r"\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix}^T" +# Or you can use "\begin{pmatrix}1&2&3\\4&5&6\\7&8&9\end{pmatrix}'" +latex2sympy(tex) +# => "Matrix([[1, 4, 7], [2, 5, 8], [3, 6, 9]])" +``` + +Elementary Transformation + +``` python +from latex2sympy2 import latex2sympy + +matrix = r''' + \begin{pmatrix} + 1 & 2 & 3 \\ + 4 & 5 & 6 \\ + 7 & 8 & 9 \\ + \end{pmatrix} +''' + +# Scale the row with grammar "\xrightarrow{kr_n}" +tex = matrix + r'\xrightarrow{3r_1}' +latex2sympy(tex) +# => "Matrix([[3, 6, 9], [4, 5, 6], [7, 8, 9]])" + +# Swap the cols with grammar "\xrightarrow{c_1<=>c_2}" +# Of course, you can use "\leftrightarrow" to replace "<=>" +tex = matrix + r'\xrightarrow{c_1<=>c_2}' +latex2sympy(tex) +# => "Matrix([[2, 1, 3], [5, 4, 6], [8, 7, 9]])" + +# Scale the second row and add it to the first row +# with grammar "\xrightarrow{r_1+kr_2}" +tex = matrix + r'\xrightarrow{r_1+kr_2}' +latex2sympy(tex) +# => "Matrix([[4*k + 1, 5*k + 2, 6*k + 3], [4, 5, 6], [7, 8, 9]])" + +# You can compose the transform with comma "," +# and grammar "\xrightarrow[4r_3]{2r_1, 3r_2}" +# Remember the priority of "{}" is higher than "[]" +tex = matrix + r'\xrightarrow[4r_3]{2r_1, 3r_2}' +latex2sympy(tex) +# => "Matrix([[2, 4, 6], [12, 15, 18], [28, 32, 36]])" +``` + + Variances + +``` python +from latex2sympy2 import latex2sympy, variances, var, set_variances + +# Assign x a value of 1 +latex2sympy(r"x = 1") + +# Calculate x + y +latex2sympy(r"x + y") +# => "y + 1" + +# Get all variances +print(variances) +# => "{x: 1}" + +# Get variance of "x" +print(var["x"]) +# => "1" + +# Reset all variances +set_variances({}) +latex2sympy(r"x + y") +# => "x + y" +``` + + +Contributing + +If you want to add a new grammar, you can fork the code from [OrangeX4/latex2sympy](https://github.com/OrangeX4/latex2sympy). + +* To modify parser grammar, view the existing structure in `PS.g4`. +* To modify the action associated with each grammar, look into `latex2sympy.py`. + +Contributors are welcome! Feel free to open a pull request or an issue. |
