Connect quaternion fixture to complex pairs - #92
Draft
isomorphisms wants to merge 1 commit into
Draft
isomorphisms wants to merge 1 commit into
isomorphisms wants to merge 1 commit into
Conversation
isomorphisms
force-pushed
the
examples/quaternion-complex-pair-agreement
branch
from
September 17, 2026 09:12
71a67c0 to
e8214cb
Compare
isomorphisms
changed the base branch from
examples/exact-complex-pair-agreement
to
Idriç
September 17, 2026 09:12
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Purpose
Express the existing exact quaternion acceptance fixture as a pair of existing exact complex values and check that the conjugating pair product matches the repository's current Hamilton multiplication convention on exact fixtures.
Changes
(a,b)(c,d) = (ac - b·conjugate(d), ad + b·conjugate(c))Quaternion↔(ExactComplex, ExactComplex)conversions and prove both round tripsi·j = kquaternion_multiplyon a nontrivial closed four-coordinate fixtureedric009receiptBoundary
This PR does not replace or redefine
Quaternion,ExactComplex, rotation semantics, Hermitian forms, or projective semantics. A universal symbolic proof against the direct Hamilton component formula would require ring identities that this example layer does not yet encode, so this patch keeps that distinction explicit.The branch is now based directly on current
Idriçafter #91. It remains draft pending clean exact-head compiler checks.