# Fungrim entry: 5636db

$\left(\gamma \eta\right) \circ \tau = \gamma \circ \left(\eta \circ \tau\right)$
Assumptions:$\gamma \in \operatorname{SL}_2(\mathbb{Z}) \,\mathbin{\operatorname{and}}\, \eta \in \operatorname{SL}_2(\mathbb{Z}) \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}$
TeX:
\left(\gamma \eta\right) \circ \tau = \gamma \circ \left(\eta \circ \tau\right)

\gamma \in \operatorname{SL}_2(\mathbb{Z}) \,\mathbin{\operatorname{and}}\, \eta \in \operatorname{SL}_2(\mathbb{Z}) \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
ModularGroupAction$\gamma \circ \tau$ Action of modular group
SL2Z$\operatorname{SL}_2(\mathbb{Z})$ Modular group
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("5636db"),
Formula(Equal(ModularGroupAction(Parentheses(Mul(gamma, eta)), tau), ModularGroupAction(gamma, Parentheses(ModularGroupAction(eta, tau))))),
Variables(gamma, eta, tau),
Assumptions(And(Element(gamma, SL2Z), Element(eta, SL2Z), Element(tau, HH))))

## Topics using this entry

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

2019-10-05 13:11:19.856591 UTC