Fungrim entry: 21b67f

{e}^{2 \pi i / 3} = \frac{-1 + \sqrt{3} i}{2} \in \mathcal{F}

Corner of the fundamental domain.

TeX:

{e}^{2 \pi i / 3} = \frac{-1 + \sqrt{3} i}{2} \in \mathcal{F}

Definitions:

Fungrim symbol	Notation	Short description
`Exp`	${e}^{z}$	Exponential function
`Pi`	$\pi$	The constant pi (3.14...)
`ConstI`	$i$	Imaginary unit
`Sqrt`	$\sqrt{z}$	Principal square root
`ModularGroupFundamentalDomain`	$\mathcal{F}$	Fundamental domain for action of the modular group

Source code for this entry:

Entry(ID("21b67f"),
    Formula(EqualAndElement(Exp(Div(Mul(Mul(2, Pi), ConstI), 3)), Div(Add(-1, Mul(Sqrt(3), ConstI)), 2), ModularGroupFundamentalDomain)),
    Description("Corner of the fundamental domain."))

Topics using this entry

Modular transformations

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

2021-03-15 19:12:00.328586 UTC