Struct FixedPoint 

pub struct FixedPoint {
    pub subset: Vec<usize>,
    pub grassmannian: (usize, usize),
}

A torus-fixed point in Gr(k, n): a k-element subset of {0, …, n-1}.

The fixed point e_I corresponds to the coordinate k-plane spanned by {e_i : i ∈ I}.

Fields

subset: Vec<usize>

The k-element subset I ⊂ {0, …, n-1}

grassmannian: (usize, usize)

Grassmannian parameters

Implementations

impl FixedPoint

pub fn new( subset: Vec<usize>, grassmannian: (usize, usize), ) -> EnumerativeResult<Self>

Create a fixed point from a k-element subset.

Contract

requires: subset.len() == k
requires: forall i in subset. i < n

pub fn tangent_euler_class(&self, weights: &TorusWeights) -> Rational64

Compute the equivariant Euler class of the tangent space at this fixed point.

e_T(T_{e_I} Gr) = ∏_{i ∈ I, j ∉ I} (t_j - t_i)

Contract

ensures: result != 0 (when weights are distinct)

pub fn to_partition(&self) -> Vec<usize>

Compute the Schubert partition associated with this fixed point.

For I = {i_0 < … < i_{k-1}}, the partition is λ_a = i_a - a.

Trait Implementations

impl Clone for FixedPoint

fn clone(&self) -> FixedPoint

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for FixedPoint

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

Formats the value using the given formatter.

impl PartialEq for FixedPoint

fn eq(&self, other: &FixedPoint) -> 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 FixedPoint

impl StructuralPartialEq for FixedPoint