How do LaTeX formulas be converted into computable code logic?

Convert LaTeX formulas to executable code

In scientific computing and programming, converting LaTeX mathematical formulas into code in programming languages ​​such as Python and JavaScript is a common requirement. However, existing tools are often out of their mind when dealing with complex LaTeX formulas. This article discusses how to implement this transformation more efficiently.

Problem description

Given a LaTeX formula string, the goal is to convert it into Python or JavaScript code that can be used for calculations. For example, the following formula:

 {p}_{pv}={p}_{n}\frac {g} {{g}_{n}}\left [ {} \right ]\left [ {1\, \, \partial p\left ( {{t}_{c}-{t}_{stc}} \right )} \right ]

When converting with libraries such as latex2sympy2 , it may not be possible to parse and convert correctly.

Solution

Although latex2sympy2 has shortcomings in dealing with complex formulas, we can try the following:

1. SymPy library: SymPy itself provides powerful symbol computing functions. We can try to parse LaTeX formulas directly using SymPy's sympify function.

    from sympy import symbols, symify, latex
   
    formula = r"{p}_{pv}={p}_{n}\frac {g} {{g}_{n}}\left [ {} \right ]\left [ {1\, \, \partial p\left ( {{t}_{c}-{t}_{stc}} \right )} \right ]"
    try:
        expr = sympify(formula)
        print(expr)
    except Exception as e:
        print(f"SymPy conversion failed: {e}")

   Note that r"" is used to create the original string to avoid backslashes being escaped. Even if SymPy parses successfully, further processing is required to convert it into executable numerical calculation code.

2. Mathpix API: Mathpix is ​​a powerful online tool that converts handwritten or LaTeX formulas into code in multiple programming languages. Through its API, we can implement automated transformations.

    import requests
   
    formula = r"{p}_{pv}={p}_{n}\frac {g} {{g}_{n}}\left [ {} \right ]\left [ {1\, \, \partial p\left ( {{t}_{c}-{t}_{stc}} \right )} \right ]"
    api_url = "https://api.mathpix.com/v3/latex"
    headers = {
        "app_id": "YOUR_APP_ID", # Replace with your App ID
        "app_key": "YOUR_APP_KEY" # Replace with your App Key
    }
    data = {
        "latex": formula,
        "format": "python" # or "javascript"
    }
   
    try:
        response = requests.post(api_url, headers=headers, json=data)
        converted_code = response.json()['code']
        print(converted_code)
    except Exception as e:
        print(f"Mathpix API conversion failed: {e}")
   

   You need to register a Mathpix account and get the API key.

3. Manual Conversion: For very complex formulas, manual conversion is probably the most reliable method, albeit taking longer. This requires a deep understanding of formulas and target programming languages. For example, manually converting the above formula to Python code might be as follows:

    import numpy as np
   
    def calculate_ppv(p_n, g, g_n, partial_p, t_c, t_stc):
        ppv = p_n * (g / g_n) * (1 partial_p * (t_c - t_stc))
        return ppv
   
    # Example numerical calculation p_n = 10
    g = 20
    g_n = 5
    partial_p = 0.1
    t_c = 100
    t_stc = 50
    result = calculate_ppv(p_n, g, g_n, partial_p, t_c, t_stc)
    print(result)

Which method to choose depends on the complexity of the formula and your needs. For simple formulas, SymPy may suffice; for complex formulas, Mathpix API or manual conversion may be more reliable. Regardless of the method chosen, adequate testing is required to ensure the accuracy of the conversion.

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