Diagrammatic Contraction of Hopf Quadratic Tensors

Computational investigation of efficient tensor contraction over super Hopf algebras with various embeddings

8

Rewrite Rules

1e-14

Pfaffian Precision

0.0

Partial Err (trivial)

~2.0

Full Err (sign)

Pfaffian Validation: max |pf(A)^2 - det(A)|

Scaling: Efficient vs Brute-Force Time

Contraction Relative Error by Embedding

Diagrammatic Rewrite Simplification

Pfaffian Validation Details

n	Max Error	Mean Error	Pass
2	1.4e-17	2.8e-18	Yes
4	6.9e-18	2.1e-18	Yes
6	4.4e-16	2.8e-16	Yes
8	3.6e-15	1.2e-15	Yes
10	1.4e-14	4.3e-15	Yes

Rewrite Rules Summary

Rule	Pattern	Conditional
Antipode cancellation	Delta-S-Mu -> eps-eta	No
Counit-unit collapse	eta-eps -> scalar	No
Embedding through mu	Mu-Emb -> Emb2-Mu	Yes
Embedding through delta	Emb-Delta -> Delta-Emb2	Yes
Quadratic embedding	Q-Emb -> Q_emb	No
Cap-quadratic	Q-Cap -> Q_red-pf	No
Crossing to sign	Cross -> koszul-Id	Yes
SVD factorization	Emb_gen -> UDV	No