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The operation of binary intermolecular recombination, originating in the theory of DNA computing, permits a natural generalization to n-ary operations which perform simultaneous recombination of n molecules. In the case n = 3, we use computer algebra to determine the polynomial identities of degree ≤ 9 satisfied by this trilinear nonassociative operation. Our approach requires computing a basis for the nullspace of a large integer matrix, and for this we compare two methods: (i) the rowdoi:10.3934/dcdss.2011.4.1387 fatcat:2itmjzgvq5gk7myxfywfu5pzzy