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yoneda_product

Function yoneda_product 

Source
pub fn yoneda_product(
    res: &[Vec<ResGen>],
    a_s: usize,
    a_gi: usize,
    b_s: usize,
    b_gi: usize,
) -> Vec<usize>
Expand description

The Yoneda product Ext^{a_s,t_a} ⊗ Ext^{b_s,t_b} → Ext^{a_s+b_s, t_a+t_b} on the cohomology of the Steenrod algebra, computed from the resolution itself. The cocycle dual to generator (a_s, a_gi) is lifted to a comparison chain map φ_•: C_{a_s+•} → C_• (ε·φ_0 = dual, ∂φ_k = φ_{k-1}∂, each step a Z/2 boundary solve), and the product is dual_b ∘ φ_{b_s} — read off as the (b_gi, identity) coefficient. The comparison map is the diagonal X → X×X dualized onto the resolution: the geometric symmetry made algebra. Returns the product’s Z/2 support among the C_{a_s+b_s} generators.