Writing L-functions in Python (or any other language)

  • #1
DAntanov
5
1
TL;DR Summary
I am interested in the steps to implement L-functions (of any kind) in python.
Not many code examples exist for how one would go about writing an L-function. Can anyone give me a step-by-step run down of how to do this and/or link me to relevant resources?
 
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  • #2
CORRECTION: This misinterprets what the OP meant by L-function. (See posts #6 and #7)
Here is a simple example in many languages, including Python.
A Python L-function:
def adder(x):
    return lambda y: x + y
add5 = adder(5)
add5(1)
6
 
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  • #3
What kind of L-functions are we talking about? At first I assumed it was automorphic, but after the first reply I am lost.
 
  • #4
martinbn said:
What kind of L-functions are we talking about? At first I assumed it was automorphic, but after the first reply I am lost.
My guess is that the OP is asking about lambda functions. @FactChecker is making the same assumption.
 
  • #5
DAntanov said:
TL;DR Summary: I am interested in the steps to implement L-functions (of any kind) in python.

Not many code examples exist for how one would go about writing an L-function.
Assuming that what you're really asking about are lambda functions, there are tons of examples online. Here are just a few (search string -- python lambda function)
https://www.w3schools.com/python/python_lambda.asp
https://realpython.com/python-lambda/
https://www.programiz.com/python-programming/anonymous-function
https://www.learnbyexample.org/python-lambda-function/

Many other programming languages also provide support for user-defined lambda functions.
 
  • #6
If the OP means Dirichlet L-functions, then chapters 25 and 27 of the NIST Digital Library of Mathematical Functions seem to be a good place to start. However since none of the Methods of Computation, Tables, or Software sections mention Dirichlet L-functions - except § 25.21(ix) which states "No research software has been found for these functions" - I suspect they have not been implemented in any language.
 
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  • #7
pasmith said:
If the OP means Dirichlet L-functions, then chapters 25 and 27 of the NIST Digital Library of Mathematical Functions seem to be a good place to start. However since none of the Methods of Computation, Tables, or Software sections mention Dirichlet L-functions - except § 25.21(ix) which states "No research software has been found for these functions" - I suspect they have not been implemented in any language.
This elaborates my question perfectly. I'm sorry for the vague language in my last post. I am curious about automorphic and Dirichlet L-functions, and became very lost after the first few replies here. I stumbled upon these fairly plain implementations on github: https://github.com/JamesShakarji/L-Function-Types
 
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Related to Writing L-functions in Python (or any other language)

1. How do I write L-functions in Python?

To write L-functions in Python, you can start by defining the function using the def keyword followed by the function name. You can then add the necessary code to calculate the L-function based on your specific requirements.

2. What are some common libraries used for writing L-functions in Python?

Some common libraries used for writing L-functions in Python include SymPy, NumPy, and SciPy. These libraries provide various mathematical functions and tools that can help you in the calculation and manipulation of L-functions.

3. Can L-functions be written in languages other than Python?

Yes, L-functions can be written in languages other than Python. You can write L-functions in languages like C, C++, Java, and more. The choice of language often depends on the specific requirements of your project and your familiarity with the language.

4. Are there any specific considerations when writing L-functions in Python?

When writing L-functions in Python, it is important to consider factors such as efficiency, accuracy, and readability. You may need to optimize your code for performance, handle large numbers or complex calculations, and ensure that your code is well-documented and easy to understand.

5. How can I test and validate my L-functions written in Python?

You can test and validate your L-functions written in Python by using various testing frameworks and methods. You can write unit tests to check the functionality of your L-functions, compare the results with known values or theoretical predictions, and verify the correctness of your implementation.

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