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10:55 PM
@Adám It depends on what coefficients you're allowing, but it's morally the same as with integers. You look at each of their (prime/irreducible) factorization, erase any exponents, and multiply all those factors together.
11:16 PM
Hrm, that's not quite right. You want (P∧Q) ≡ (P×Q)÷P∨Q. Finding P∨Q is just a matter of looking at the biggest set of common factors, so P∧Q takes the highest power of each factor.
For example, consider (4+(8×y)+(5×y*2)+y*3) ≡ P←×⌿(y+1)(y+2)(y+2) and (6+(5×y)+y*2) ≡ Q←×⌿(y+2)(y+3). Then (P∧Q) ≡ ×⌿(y+1)(2*y+2)(y+3) and (P∨Q) ≡ y+2.
So with these hypothetical non-scalar and , and representing polynomials as coefficient vectors, I guess we'd write (12 28 23 8 1) ≡ (4 8 5 1)∧6 5 1 and (2 1) ≡ (4 8 5 1)∨6 5 1.
Actually, maybe we don't even need principal ideals, just unique factorization.

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