# Fungrim entry: d530b1

$\Lambda_{(a, b)} = \left\{ a m + b n : m \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z} \right\}$
Assumptions:$a \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, \operatorname{Im}\!\left(\frac{b}{a}\right) > 0$
TeX:
\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
Definitions:
Fungrim symbol Notation Short description
Lattice$\Lambda_{(a, b)}$ Complex lattice with periods a, b
SetBuilder$\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$ Set comprehension
ZZ$\mathbb{Z}$ Integers
CC$\mathbb{C}$ Complex numbers
Im$\operatorname{Im}\!\left(z\right)$ Imaginary part
Source code for this entry:
Entry(ID("d530b1"),
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))))

## Topics using this entry

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