LaTex OCR

• Website: https://lukas-blecher.github.io/LaTeX-OCR/

• Github Repo: lukas-blecher/LaTeX-OCR

!pip install "pix2tex[gui]"

from PIL import Image
from pix2tex.cli import LatexOCR

img = Image.open('LaTex_OCR_Input_Image.png')
model = LatexOCR()
print(model(img))

S=\int_{x}\left\{\frac{1}{2}\sum_{a}\partial^{\mu}\chi_{a}\partial_{\mu}\chi_{a}+V(\rho)\right\},\right\}

from IPython.display import Image
Image(filename='LaTex_OCR_Input_Image.png') 

!pip install latex2sympy2

Requirement already satisfied: latex2sympy2 in c:\users\richa\anaconda3\lib\site-packages (1.9.1)
Requirement already satisfied: sympy>=1.4 in c:\users\richa\anaconda3\lib\site-packages (from latex2sympy2) (1.11.1)
Requirement already satisfied: antlr4-python3-runtime==4.7.2 in c:\users\richa\anaconda3\lib\site-packages (from latex2sympy2) (4.7.2)
Requirement already satisfied: mpmath>=0.19 in c:\users\richa\anaconda3\lib\site-packages (from sympy>=1.4->latex2sympy2) (1.3.0)

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"

'2 x + 1'

Use ChatGPT to convert Latex to C# source code with prompt: convert the following latex expression to C# function: S=\int_{x}\left{\frac{1}{2}\sum_{a}\partial^{\mu}\chi_{a}\partial_{\mu}\chi_{a}+V(\rho)\right},\right}

To convert the given LaTeX expression into a C# function, we first need to understand what the LaTeX expression represents. This expression describes an action ( S ) in terms of an integral over a function of ( \chi_a ) and ( V(\rho) ), where ( \chi_a ) seems to be a field that depends on space or spacetime coordinates, and ( V(\rho) ) is some potential that also depends on another variable ( \rho ).

The LaTeX expression: [ S=\int_{x}\left{\frac{1}{2}\sum_{a}\partial^{\mu}\chi_{a}\partial_{\mu}\chi_{a}+V(\rho)\right} ]

This expression involves:

• An integral over space or spacetime coordinates ( x ).

• A sum over ( a ), which might index different components or fields ( \chi_a ).

• A derivative ( \partial^\mu ) indicating a partial derivative with respect to the spacetime coordinates, suggesting this might be a field theory expression from physics.

• A potential ( V(\rho) ), the form of which is unspecified.

To convert this into a C# function, we have to make several assumptions due to the abstract nature of the expression:

• We assume ( \chi_a ) and ( V(\rho) ) can be represented by functions or methods in C#.

• We assume discrete spacetime or spatial coordinates since we cannot directly translate continuous mathematical integrals and derivatives into code without numerical methods.

• We need to define the domain of integration and the method of numerical integration.

Given these considerations, a C# implementation might focus on the numerical computation of the integral, possibly using a simple method like the trapezoidal rule, and finite differences for derivatives. Without specific forms for ( \chi_a ) and ( V(\rho) ), the function might look something like this in a very generalized form:

double ComputeAction(double[] x, Func<double, double>[] chi, Func<double, double> V, double[] rho)
{
    double sum = 0.0;
    int N = x.Length;
    
    // Assuming x is discretized spacetime coordinates
    // and chi is an array of functions representing different chi_a
    // Assuming a simple numerical derivative and midpoint rule for integration
    
    for (int i = 1; i < N; i++) // Simple numerical integration loop
    {
        double dx = x[i] - x[i - 1];
        double midPoint = (x[i] + x[i - 1]) / 2;
        double sumChi = 0.0;
        
        foreach (var chiFunc in chi)
        {
            // Simple finite difference for derivative, assuming uniform spacing
            double derivative = (chiFunc(x[i]) - chiFunc(x[i - 1])) / dx;
            sumChi += 0.5 * derivative * derivative;
        }
        
        sum += (sumChi + V(rho[i])) * dx; // Assuming rho is somehow related to x or chi, needs specification
    }
    
    return sum;
}

This function is highly speculative and assumes:

• x is an array representing discretized spacetime or spatial coordinates.

• chi is an array of functions, each corresponding to ( \chi_a(x) ).

• V is a function representing the potential ( V(\rho) ).

• rho is an array with values that V depends on, which must be related to x or the fields ( \chi_a ) somehow.

Actual implementation would require more specific details about the physical system being modeled, the form of ( \chi_a ) and ( V(\rho) ), and how ( \rho ) is related to the other quantities.