In an Alg over the PAdicRational(13), the two following vectors

U := [2, 3, 4]
V := [7, 8, 9]

multiply to the multiply to the following product:

2                 2             3
W := U * V = [6 + 13 + 7 13 , 1 + 9 13 + 7 13 , 8 13 + 7 13 ]

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