exact over QQFox calculusAlexander Fitting idealsreduced lex Gröbner bases
Software and frozen inputs accompanying Gröbner Bases for Alexander Fitting Ideals of Links. The package reproduces the low-crossing calculations displayed in Section 3 and applies the same exact pipeline to new oriented PD codes or finite presentations.
The previously announced version 0.3.0 distribution was not preserved in complete form in the audit environment and therefore could not be re-audited file by file. Version 0.4.0 was rebuilt from the complete version 0.2.0 source tree that remained available for inspection.
While preparing this English release, two provenance-related defects in the 0.4.0 source archive were identified by its own tests and corrected in version 0.4.1. The fixes prevent metadata from overwriting computed PD fields and make the normalized input-record digest independent of JSON whitespace. They do not change the mathematical outputs reported in the paper.
START_HERE_WINDOWS.bat.RUN_DEMO_WINDOWS.bat.VERIFY_PAPER_EXAMPLES_WINDOWS.bat.COMPUTE_INPUT_WINDOWS.bat.The first installation normally requires internet access to obtain SymPy 1.14.0.
oriented PD code / finite presentation
-> abelianized Fox matrix A
-> E_k = I_{n-k}(A)
-> contraction from QQ[t1^±1,...,tell^±1] to QQ[t1,...,tell]
-> reduced lexicographic Gröbner basis AG_k
The coefficient field is QQ, and the final order is t1 > ... > tell. Orientation and component order are part of the input.
The command python -m alexander_grobner verify performs a frozen-input regression comparison. It does not independently certify external link-table labels, decide link equivalence, reproduce unarchived table scans, or replace mathematical proofs.