Polynomial identities for ternary intermolecular recombination

Details Polynomial identities for ternary intermolecular recombination Polynomial identities for ternary intermolecular recombination

2010-08-11

arxiv.org/abs/1008.2014v1

Mathematics

Rings and Algebras

14 pages, 11 tables

Scientific paper

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 row canonical form, and (ii) the Hermite normal form with lattice basis reduction. In the conclusion, we formulate some conjectures for the general case of n-ary intermolecular recombination.

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