Fungrim home page

Fungrim entry: 5636db

(γη)τ=γ(ητ)\left(\gamma \eta\right) \circ \tau = \gamma \circ \left(\eta \circ \tau\right)
Assumptions:γSL2(Z)  and  ηSL2(Z)  and  τH\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
ModularGroupActionγτ\gamma \circ \tau Action of modular group
SL2ZSL2(Z)\operatorname{SL}_2(\mathbb{Z}) Modular group
HHH\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.

2021-03-15 19:12:00.328586 UTC