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We improve on and generalize a 1960 result of Maltsev. For a field F, we denote by
the Heisenberg group with entries in F. Maltsev showed that there is a copy of F defined in
, using existential formulas with an arbitrary non-commuting pair of elements as parameters. We show that F is interpreted in
formulas with no parameters. We give two proofs. The first is an existence proof, relying on a result of Harrison-Trainor, Melnikov, R. Miller, and Montalbán. This proof allows the possibility that the elements of F are represented by tuples in
of no fixed arity. The second proof is direct, giving explicit finitary existential formulas that define the interpretation, with elements of F represented by triples in
. Looking at what was used to arrive at this parameter-free interpretation of F in
, we give general conditions sufficient to eliminate parameters from interpretations.