Valuation

Base.abs(a::padic)

Compute the p-adic absolute value of a p-adic number.

For a p-adic number $a$ with valuation $v(a)$, returns $p^{-v(a)}$.

Arguments

• a::padic: A p-adic number

Returns

Float64: The p-adic absolute value $|a|_p = p^{-v(a)}$

Note

This extends Base.abs for padic types, making the codebase generic. To support custom p-adic implementations, define Base.abs for your type.

unit(a::padic)

Extract the unit part of a p-adic number.

For a p-adic number $a = p^v \cdot u$ where $u$ is a p-adic unit, returns the unit $u$.

Arguments

• a::padic: A p-adic number

Returns

The unit part $u$ (accessed via a.u for PadicFieldElem)

Note

This provides a generic interface to the unit part of p-adic numbers. For custom p-adic implementations, define unit(a::YourType) for your type.

valuation(a::padic)

Compute the p-adic valuation of a p-adic number.

For a p-adic number $a = p^v \cdot u$ where $u$ is a p-adic unit, returns the integer $v$.

Arguments

• a::padic: A p-adic number

Returns

The p-adic valuation $v(a)$

Note

This wraps the Nemo/Oscar implementation. To support custom p-adic implementations, define a method valuation(a::YourType) for your type.