Fixed bug in A1BrouwerDegrees#4434
Open
wgabrielong wants to merge 1 commit into
Open
Conversation
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
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Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be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.
A bug was identified and fixed by Claude Code in
A1BrouwerDegrees.Consider the quadratic form
beta = makeDiagonalForm(QQ, (-1,-1,-1,-1,-1,1))Since
beta ≅ <-1,-1,-1,-1> + H, its anisotropic part is<-1,-1,-1,-1>, of rank 4.However,
getAnisotropicPart betasilently returns the rank-2 form<-1,1>— thehyperbolic plane, which is isotropic and violates the Witt decomposition identity:
Cause.
reduceAnisotropicPartQQDimension3(Code/Decomposition.m2) must return<alpha>such thatbeta + <-alpha>has anisotropic dimension 2. It choosesalphafrom congruence conditions at the finite primes only, ignoring the real place, where the
anisotropic dimension equals
|signature|. Here the running form<-1,-1,-1,-1,-1,1,1>has signature -3 and an empty relevant-prime list, so the solver returns
alpha = 1;the real anisotropic part is negative definite, so
alphamust be negative. Theanisotropic dimension rises from 3 to 4 instead of dropping to 2, the
== 2/== 1branches of
getAnisotropicPartQQnever fire, and a truncated form is returned with noerror.
Fix (by Claude Code). The congruences determine
alphaonly modulo the productMof the moduli, so the real place is accommodated by shifting to a representative of the
correct sign:
getAnisotropicPart betanow returns<-1,-1,-1,-1>. Tests 48–49 add regressioncoverage (the existing Test 47 never reached the reduction chain); the full package
suite passes under Macaulay2 1.25.11.