Enum AdamsFact 

pub enum AdamsFact {
    Dimension {
        s: usize,
        t: usize,
        dim: usize,
    },
    Product {
        lhs: String,
        rhs: String,
        result: String,
    },
    Vanishing {
        lhs: String,
        rhs: String,
    },
    Relation {
        a: String,
        b: String,
    },
    Doubling {
        from: String,
        to: String,
    },
    StableGroup {
        stem: usize,
        tower_lengths: Vec<usize>,
        truncated: bool,
    },
    Secondary {
        s: usize,
        t: usize,
    },
}

One machine-derived fact about the Adams E₂ chart of the sphere. Every variant is computed from the minimal resolution and its chain-level diagonal — none is asserted.

Variants

Dimension

dim Ext^{s,t}_𝒜(Z/2, Z/2) = dim — a point of the chart.

Fields

s: usize

t: usize

dim: usize

Product

lhs · rhs = result in the cohomology ring of the Steenrod algebra (a named product).

Fields

lhs: String

rhs: String

result: String

Vanishing

lhs · rhs = 0 — an Adem-adjacency / ring vanishing.

Fields

lhs: String

rhs: String

Relation

a = b: two product-paths landed on the same generator. The ring relation, discovered by collision.

Fields

a: String

b: String

Doubling

Sq⁰(from) = to — the algebraic doubling operation on the chart.

Fields

from: String

to: String

StableGroup

π_n^s ⊗ Z₍₂₎ = ⊕ Z/2^Lᵢ — the exact 2-local stable stem, as the h₀-tower-length multiset. When truncated, an h₀-tower runs into the resolution’s filtration ceiling, so the group is only a lower bound (e.g. π_0 = Z₍₂₎, an infinite tower the finite resolution cannot close).

Fields

stem: usize

tower_lengths: Vec<usize>

truncated: bool

Secondary

Ext^{s,t} carries a class that is not a product of the indecomposables h_i — the product-sweep cannot name it. It is the shadow of an Adams differential / a Massey product: the first place the primary (auto-able) structure runs out, and the secondary structure begins.

Fields

s: usize

t: usize

Trait Implementations

impl Clone for AdamsFact

fn clone(&self) -> AdamsFact

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Display for AdamsFact

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

Formats the value using the given formatter.

impl Ord for AdamsFact

fn cmp(&self, other: &AdamsFact) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl PartialEq for AdamsFact

fn eq(&self, other: &AdamsFact) -> 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 PartialOrd for AdamsFact

fn partial_cmp(&self, other: &AdamsFact) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

Tests less than (for self and other) and is used by the < operator.

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

Tests less than or equal to (for self and other) and is used by the <= operator.

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl Eq for AdamsFact

impl StructuralPartialEq for AdamsFact