README.md

p-adic Norm Calculator

This app is online at https://p-adic-norm.up.railway.app/

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

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.

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 integers a/b, converted by the fractions package

The web app interface returns the valuation and the fractional representation of the norm by default, for pedagogical purposes. The user can choose between float or fraction, and a copy to clipboard button is provided. When abs is an integer (i.e. $val \le 0$), both it and fraction are converted to type int.

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'

Next goals:

• update to a Flask-WTF FlaskForm subclass to include CSRF protection
• light/dark toggle switch
• provide a primality testing method