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Fungrim entry: 21b67f

e2πi/3=1+3i2F{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
Expez{e}^{z} Exponential function
ConstPiπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
Sqrtz\sqrt{z} Principal square root
ModularGroupFundamentalDomainF\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, ConstPi), ConstI), 3)), Div(Add(-1, Mul(Sqrt(3), ConstI)), 2), ModularGroupFundamentalDomain)),
    Description("Corner of the fundamental domain."))

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

2019-10-05 13:11:19.856591 UTC