Struct Expansion 

pub struct Expansion<C: Coefficient> { /* private fields */ }

An expansion in the smallest infinitesimal of a value. See the module documentation.

Implementations

impl<C: Coefficient> Expansion<C>

pub fn fraction( num: Vec<C>, den: Vec<C>, q: u32, ) -> Result<Expansion<C>, ExpansionError>

The expansion of num/den, polynomials in s^(1/q) with den nonzero.

pub fn constant(c: C) -> Expansion<C>

A value constant in s: the coefficient itself at order 0.

pub fn source(source: Arc<dyn Source<C>>, floor: i64, q: u32) -> Expansion<C>

The expansion a Source gives, lowest order floor, on the grid q.

pub fn ramification(&self) -> u32

The ramification q: order k is the coefficient of s^(k/q).

pub fn floor(&self) -> i64

The lowest order that may be nonzero.

pub fn refined(&self, m: u32) -> Expansion<C>

The same expansion on a grid m times finer.

pub fn coefficient(&self, k: i64) -> Result<C, ExpansionError>

The coefficient of s^(k/q).

pub fn add(&self, o: &Expansion<C>) -> Expansion<C>

pub fn neg(&self) -> Expansion<C>

pub fn sub(&self, o: &Expansion<C>) -> Expansion<C>

The difference coefficient by coefficient, so a term both sides share cancels in the coefficient’s own arithmetic.

pub fn mul(&self, o: &Expansion<C>) -> Expansion<C>

pub fn leading_through( &self, through: i64, ) -> Result<Option<(i64, C)>, ExpansionError>

The first nonzero term at or below the order through: its order and coefficient; None when every coefficient through it is zero.

pub fn recip(&self, order: i64, lead: C) -> Expansion<C>

1/self for a value whose leading term is lead·s^(order/q).

pub fn exp(&self) -> Expansion<C>

exp(self) for a value with no negative order.

pub fn ln(&self, g0: C) -> Expansion<C>

ln(self) for a value with no infinitesimal order whose coefficient of order 0 is g0.

pub fn root(&self, n: u32, v: i64, c: C) -> Result<Expansion<C>, ExpansionError>

The real n-th root (n ≥ 2) of a value whose leading term is c·s^(v/q), the nonnegative one for an even n; refused for a negative value and an even n. The grid is refined until n divides the leading order.

Trait Implementations

impl<C: Clone + Coefficient> Clone for Expansion<C>

fn clone(&self) -> Expansion<C>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<C: Debug + Coefficient> Debug for Expansion<C>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.