Fungrim entry: fd53ab

\left\{ \gamma \circ \tau : \tau \in \mathcal{F} \,\mathbin{\operatorname{and}}\, \gamma \in \operatorname{PSL}_2(\mathbb{Z}) \right\} = \mathbb{H}

TeX:

\left\{ \gamma \circ \tau : \tau \in \mathcal{F} \,\mathbin{\operatorname{and}}\, \gamma \in \operatorname{PSL}_2(\mathbb{Z}) \right\} = \mathbb{H}

Definitions:

Fungrim symbol	Notation	Short description
`SetBuilder`	$\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$	Set comprehension
`ModularGroupAction`	$\gamma \circ \tau$	Action of modular group
`ModularGroupFundamentalDomain`	$\mathcal{F}$	Fundamental domain for action of the modular group
`PSL2Z`	$\operatorname{PSL}_2(\mathbb{Z})$	Modular group (canonical representatives)
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("fd53ab"),
    Formula(Equal(SetBuilder(ModularGroupAction(gamma, tau), Tuple(gamma, tau), And(Element(tau, ModularGroupFundamentalDomain), Element(gamma, PSL2Z))), HH)))

Topics using this entry

Modular transformations