Fungrim home page

Fungrim entry: fd53ab

{γτ:τFandγPSL2(Z)}=H\left\{ \gamma \circ \tau : \tau \in \mathcal{F} \,\mathbin{\operatorname{and}}\, \gamma \in \operatorname{PSL}_2(\mathbb{Z}) \right\} = \mathbb{H}
\left\{ \gamma \circ \tau : \tau \in \mathcal{F} \,\mathbin{\operatorname{and}}\, \gamma \in \operatorname{PSL}_2(\mathbb{Z}) \right\} = \mathbb{H}
Fungrim symbol Notation Short description
SetBuilder{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
ModularGroupActionγτ\gamma \circ \tau Action of modular group
ModularGroupFundamentalDomainF\mathcal{F} Fundamental domain for action of the modular group
PSL2ZPSL2(Z)\operatorname{PSL}_2(\mathbb{Z}) Modular group (canonical representatives)
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
    Formula(Equal(SetBuilder(ModularGroupAction(gamma, tau), Tuple(gamma, tau), And(Element(tau, ModularGroupFundamentalDomain), Element(gamma, PSL2Z))), HH)))

Topics using this entry

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

2019-08-17 11:32:46.829430 UTC