Are you sure about the first rule? It doesn't seem necessary according to https://oeis.org/A014575.
The problem is really fun.
Since I created the problem series and want the Functions I badge, I thought I'd provide the solution that incorporates vampire_factor and are_fangs. Not a great score, but readable!
Sorry, I mean the Magic Numbers badge.
Return the largest number that is adjacent to a zero
Is my wife right?
Solve the set of simultaneous linear equations
Outer product of multiple vectors
Product of two multivariate polynomials
Multivariate polynomials - overload multiplication
Negation the hard way
Multivariate polynomials - convert monomial form to array
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