README.md

p-adic Absolute Value

This is a tiny Flask application to calculate the p-adic norm of a rational number.

1. Install the Flask, WTForms, and flask_wtf packages (see requirements.txt).
2. python p_adic_controller.py runs the application in a browser at http://127.0.0.1:5000/test.

p_adic_controller.py contains the app logic.

p_adic_view.html is the Jinja view template.

p_adic_model.py is a WTForms Form subclass. This will be updated to a Flask-WTF FlaskForm subclass to include CSRF protection.

p_adic_compute contains the computation functions. p_adic_abs is the old version.

The function p_adic_abs takes a prime $p$ and a rational number $x$ as its arguments, and returns a dictionary:

{ 
    'valuation': val,
    'float': abs,
    'fraction: to_fraction(abs)
}

where:

• val is the p-adic valuation $val_p(x)$
• abs is the p-adic norm $|x|_p$ as a float
• to_fraction(abs) is a string expressed as a ratio of integer a/b

When abs is an integer, it has type int. Floats are converted to an integer ratio (with the fractions package). This is for pedagogical rather than computational purposes.

The web app interface returns the valuation and the fractional representation of the norm. The user can then choose between float or fraction. A copy to the clipboard button is also provided.

Example in terminal:

import p_adic_compute as p

p.p_adic_abs(5, 1/200)
25

p.p_adic_abs(5, 200)
'1/25'