If $M$ has generators $m_1, $m_2, \dots, $m_r$, and $N$ has generators $n_1, n_2, \dots, n_s$, then $M \otimes N$ has generators $m_i\otimes n_j$ for $0<i\leq r$ and $0<j\leq s$.
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Use trim or minimalPresentation if a more compact presentation is desired.
Use flip to produce the isomorphism $M \otimes N \to N \otimes M$.
To recover the factors from the tensor product, use the function formation.