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We consider the n-dimension Euclidean space Rn. If {v1, ..., vn} is a basis for Rn, then the set L = { ∑1≤i≤n ai vi : ai are integers } is called a lattice in Rn. L is in fact an abelian group, using the ordinary vector addition as operation. One and the same lattice L may be generated by different bases, but the determinant of the vectors vi is uniquely determined by L, and is denoted by d(L). If one thinks of a lattice as dividing the whole of Rn into equal polyhedra, then d(L) is equal to the volume of this polyhedron. |
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We consider the n-dimension Euclidean space Rn. If {v1, ..., vn} is a basis for Rn, then the set L = { ∑1≤i≤n ai vi : ai are integers } is called a lattice in Rn. L is in fact an abelian group, using the ordinary vector addition as operation. One and the same lattice L may be generated by different bases, but the absolute value of the determinant of the vectors vi is uniquely determined by L, and is denoted by d(L). If one thinks of a lattice as dividing the whole of Rn into equal polyhedra, then d(L) is equal to the volume of this polyhedron. |
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