The fundamental pair of periods is a pair of complex numbers such that their ratio ω2/ω1 is not real. In other words, considered as vectors in, the two are not collinear. The lattice generated by ω1 and ω2 is
This lattice is also sometimes denoted as Λ(ω1, ω2) to make clear that it depends on ω1 and ω2. It is also sometimes denoted by Ω or Ω(ω1, ω2), or simply by 〈ω1, ω2〉. The two generators ω1 and ω2 are called the lattice basis.
The parallelogram defined by the vertices 0, and is called the fundamental parallelogram.
It is important to note that, while a fundamental pair generates a lattice, a lattice does not have any unique fundamental pair, that is, many (in fact, an infinite number) fundamental pairs correspond to the same lattice.
Read more about Fundamental Pair Of Periods: Topological Properties, Fundamental Region
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