Macaulay2 code

These are the Macaulay2 scripts accompanying the paper On a conjecture of Dotsenko on weak nilpotence and the Engel identity (pdf). Each one verifies one of the claims of the paper. This code was produced by Anthropic's Opus 4.8 model via the tool Claude Code.

• verify_e7.m2 — checks that the example is a commutative nonassociative Q-algebra satisfying t₄ = 0 identically for which the 7-Engel identity fails.
• verify_e8.m2 this checks that the example is a commutative nonassociative Q-algebra satisfying t₄ = 0 identically for which the 8-Engel identity fails.
• verify_e9.m2 — checks that e₉(x,y) is a combination of 482 substitution instances of t₄, so that t₄ = 0 implies the 9-Engel identity.