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 is verifies one of the claims of the paper.

• verify_e7.m2 — verifies a commutative nonassociative Q-algebra satisfying t₄ = 0 identically for which the 7-Engel identity fails.
• verify_e8.m2 — verifies 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.