Struct SchubertClass 

pub struct SchubertClass {
    pub partition: Vec<usize>,
    pub grassmannian_dim: (usize, usize),
}

Schubert class indexed by a Young diagram/partition

Contracts

• Each partition entry must be ≤ n-k
• Partition entries should be weakly decreasing (though we allow flexibility)

Fields

partition: Vec<usize>

The partition indexing this Schubert class

grassmannian_dim: (usize, usize)

Dimension of the underlying Grassmannian

Implementations

impl SchubertClass

pub fn new( partition: Vec<usize>, grassmannian_dim: (usize, usize), ) -> EnumerativeResult<Self>

Create a new Schubert class

Contract

requires: forall i. partition[i] <= n - k
ensures: result.codimension() == partition.iter().sum()

Errors

Returns SchubertError if any partition entry exceeds n-k.

pub fn from_partition( partition: Partition, grassmannian_dim: (usize, usize), ) -> EnumerativeResult<Self>

Create from a Partition type

pub fn to_partition(&self) -> Partition

Convert to a Partition type

pub fn to_chow_class(&self) -> ChowClass

Convert to a Chow class

pub fn dimension(&self) -> usize

Compute the dimension of this Schubert variety

Contract

ensures: result == k * (n - k) - self.codimension()
ensures: result <= k * (n - k)

pub fn codimension(&self) -> usize

Compute the codimension of this Schubert variety

Contract

ensures: result == partition.iter().sum()

pub fn power(&self, exponent: usize) -> SchubertClass

Raise Schubert class to a power (repeated intersection)

pub fn giambelli_determinant( partition: &[usize], grassmannian_dim: (usize, usize), ) -> EnumerativeResult<Self>

Giambelli determinant formula

Trait Implementations

impl Clone for SchubertClass

fn clone(&self) -> SchubertClass

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SchubertClass

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

Formats the value using the given formatter.

impl Hash for SchubertClass

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl PartialEq for SchubertClass

fn eq(&self, other: &SchubertClass) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Eq for SchubertClass

impl StructuralPartialEq for SchubertClass