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Fungrim entry: d530b1

Λ(a,b)={am+bn:mZandnZ}\Lambda_{(a, b)} = \left\{ a m + b n : m \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z} \right\}
Assumptions:aC{0}andbC{0}andIm ⁣(ba)>0a \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, \operatorname{Im}\!\left(\frac{b}{a}\right) > 0
\Lambda_{(a, b)} = \left\{ a m + b n : m \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z} \right\}

a \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, \operatorname{Im}\!\left(\frac{b}{a}\right) > 0
Fungrim symbol Notation Short description
LatticeΛ(a,b)\Lambda_{(a, b)} Complex lattice with periods a, b
SetBuilder{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
ImIm ⁣(z)\operatorname{Im}\!\left(z\right) Imaginary part
Source code for this entry:
    Formula(Equal(Lattice(a, b), SetBuilder(Add(Mul(a, m), Mul(b, n)), Tuple(m, n), And(Element(m, ZZ), Element(n, ZZ))))),
    Variables(a, b),
    Assumptions(And(Element(a, SetMinus(CC, Set(0))), Element(b, SetMinus(CC, Set(0))), Greater(Im(Div(b, a)), 0))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-15 14:14:26.267625 UTC