Struct LocalField 

pub struct LocalField {
    pub p: u64,
    pub residue_char: u64,
    pub degree: usize,
    pub ramification_index: usize,
    pub inertia_degree: usize,
}

A finite extension L/ℚ_p: a local field of mixed characteristic (0, p).

Fields

p: u64

The residue characteristic.

residue_char: u64

The residue characteristic (same as p for extensions of ℚ_p).

degree: usize

The degree [L : ℚ_p] = e · f.

ramification_index: usize

The ramification index e.

inertia_degree: usize

The inertia degree f (residue field degree).

Implementations

impl LocalField

pub fn new(p: u64, e: usize, f: usize) -> Self

Construct a local field with ramification index e and inertia degree f.

pub fn discriminant_valuation(&self) -> i64

The valuation of the discriminant: v_p(disc(L/ℚ_p)) = e - 1 + v_p(e).

pub fn is_tamely_ramified(&self) -> bool

True if the extension is tamely ramified: e > 1 and p ∤ e.

pub fn is_wildly_ramified(&self) -> bool

True if the extension is wildly ramified: p | e.