PRIMES N_0[x] Irreducibility Code

Type a polynomial and the code will try to decide whether it is reducible or irreducible. It applies the Kaplan-Polo test and the quadrinomial classification test. If those are not applicable, it searches for possible N_0[x] factorizations; within the degree and height range, the fallback gives a correct answer.

Polynomial in N0[x]

Guaranteed answer range: degree <= 20 and height <= 50. Anything bigger is not guaranteed to return a decision.

Test 1: Kaplan-Polo

If the support has a midpoint gap, Kaplan-Polo gives monolithicness; primitive coefficients then certify irreducibility in N0[x].

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Test 2: Quadrinomial

For primitive positive-constant four-term polynomials, support shape and coefficient equations decide reducibility: non-AP rectangles use AD = BC, and AP supports use the cubic parameter equations.

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