Basis of a toric lattice
= Basis of a toric lattice
= Lattice basis
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= Lattice bases
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A lattice basis $v_1,\ldots,v_n$ expresses each vector of the <toric lattice> uniquely as $\sum_i a_iv_i$ with $a_i\in\mathbb Z$. Relative to any fixed integral basis, vectors form another lattice basis exactly when their determinant is $\pm1$. A primitive vector is one whose integer span is saturated; it can be completed to such a basis by the Euclidean algorithm.