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

Modular transformations