getPadicValuation -- p-adic valuation of a rational number

Usage:

getPadicValuation(a, p)
Inputs:
- a, a rational number, a non-zero rational number in $\mathbb{Q}_p$
- p, an integer, a prime number
Outputs:
- an integer, $n$ where $a=up^n$ and $u$ is a unit in $\mathbb{Z}_p$

Description

This function computes the $p$-adic valuation of a rational number $a$, which is the exponent of the prime $p$ in the factorization of $a$ in $\mathbb{Q}_p$. It returns the integer $n$ such that $a=up^{n}$, where $u$ is a unit in $\mathbb{Z}_p$.

i1 : a = 363/7;

i2 : getPadicValuation(a, 11)

o2 = 2

We have that $363/7 = \frac{3\cdot 11^{2}}{7}$, so the $11$-adic valuation is $2$.

Ways to use getPadicValuation:

getPadicValuation(QQ,ZZ)
getPadicValuation(ZZ,ZZ)

For the programmer

The object getPadicValuation is a method function.

The source of this document is in A1BrouwerDegrees/Documentation/ArithmeticMethodsDoc.m2:27:0.