Struct Field 

pub struct Field {
    prime: ValidPrime,
}

$\mathbb{F}_p$, viewed as an Algebra over itself.

As an Algebra, a field is one-dimensional, with basis element 1. It is also trivially a coalgebra via the trivial diagonal comultiplication, and thus a Bialgebra.

Fields

prime: ValidPrime

Implementations

impl Field

pub fn new(p: ValidPrime) -> Self

Returns a new Field over the given prime p.

Trait Implementations

impl Algebra for Field

fn prime(&self) -> ValidPrime

Returns the prime the algebra is over.

fn compute_basis(&self, _degree: i32)

Computes basis elements up to and including degree.

fn dimension(&self, degree: i32) -> usize

Returns the dimension of the algebra in degree degree.

fn multiply_basis_elements( &self, result: FpSliceMut<'_>, coeff: u32, _r_degree: i32, _r_idx: usize, _s_degree: i32, _s_idx: usize, )

Computes the product r * s of two basis elements, and adds the result to result.

fn default_filtration_one_products(&self) -> Vec<(String, i32, usize)>

Returns a list of filtration-one elements in $Ext(k, k)$.

fn basis_element_to_string(&self, degree: i32, _idx: usize) -> String

Converts a basis element into a string for display.

fn element_to_string(&self, degree: i32, element: FpSlice<'_>) -> String

Converts a general element into a string for display.

fn basis_element_from_string(&self, _elt: &str) -> Option<(i32, usize)>

Converts a string to a basis element. This must be a one-sided inverse inverse to both basis_element_to_string and generator_to_string (if GeneratedAlgebra is implemented).

fn prefix(&self) -> &str

A name for the algebra to use in serialization operations. This defaults to “” for algebras that don’t care about this problem.

fn magic(&self) -> u32

A magic constant used to identify the algebra in save files. When working with the Milnor algebra, it is easy to forget to specify the algebra and load Milnor save files with the Adem basis. If we somehow manage to resume computation, this can have disasterous consequences. So we store the magic in the save files.

fn multiply_basis_element_by_element( &self, result: FpSliceMut<'_>, coeff: u32, r_degree: i32, r_idx: usize, s_degree: i32, s: FpSlice<'_>, )

Computes the product r * s of a basis element r and a general element s, and adds the result to result.

fn multiply_element_by_basis_element( &self, result: FpSliceMut<'_>, coeff: u32, r_degree: i32, r: FpSlice<'_>, s_degree: i32, s_idx: usize, )

Computes the product r * s of a general element r and a basis element s, and adds the result to result.

fn multiply_element_by_element( &self, result: FpSliceMut<'_>, coeff: u32, r_degree: i32, r: FpSlice<'_>, s_degree: i32, s: FpSlice<'_>, )

Computes the product r * s of two general elements, and adds the result to result.

impl Bialgebra for Field

fn coproduct( &self, _op_deg: i32, _op_idx: usize, ) -> Vec<(i32, usize, i32, usize)>

Computes a coproduct $\Delta(x)$, expressed as

fn decompose(&self, _op_deg: i32, _op_idx: usize) -> Vec<(i32, usize)>

Decomposes an element of the algebra into a product of elements, each of which we can compute a coproduct on efficiently.

impl Display for Field

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

Formats the value using the given formatter.