Alexander--Groebner computation
================================
name: L8n5
invariant: AG_2
coefficient domain: QQ
term order: lex: t1 > t2 > t3

Convention used:
  n = 8 presentation generators
  E_2 = I_{n-2}(A) = I_6(A),
  where A is the abelianized Fox matrix.
  AG_k is the reduced lexicographic Groebner basis of
  the contraction E_k ∩ QQ[t1,t2,t3].

Fox matrix shape: 7 x 8
minor size: 6
candidate minors: 196
nonzero minors: 196
distinct polynomial minor generators: 148

AG_2 (factored for display):
{
  (t1 - 1)*(t2 - 1),
  (t1 - 1)*(t3 - 1),
  (t2 - 1)*(t2 + 1),
  (t2 - 1)*(t3 - 1),
  (t3 - 1)*(t3 + 1)
}
normalized common divisor: 1

Internal consistency checks:
  PASS  fox_fundamental_identity
  PASS  determinantal_generators_in_reported_ideal
  PASS  basis_stable_under_reduced_lex_recomputation
  PASS  independent_reducedness_and_buchberger_check

elapsed time: 0.987674 s
software: Python 3.13.5, SymPy 1.14.0, alexander-grobner 0.4.1
mathematical-input SHA-256: c91092b4fa1751db5d3789f908ff93f1ba00ad36cb44db61ad55cf3526340ef2
normalized-input-record SHA-256: a2c724b3d5a3677dddada44684531e8169b4fa4abd65da6b8dae8c619bcca6cb
canonical-result SHA-256: b9480cbefc541d20fc1b3752f5d158379069cb940abb0e5702226d0f9b5c0bc5
