Fungrim entry: b23575

$\mathbb{H} = \left\{ \gamma \circ \tau : \tau \in \mathcal{F}_{\lambda} \;\mathbin{\operatorname{and}}\; \gamma \in \operatorname{SL}_2(\mathbb{Z}) \;\mathbin{\operatorname{and}}\; \gamma \equiv \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \pmod {2} \right\}$
TeX:
\mathbb{H} = \left\{ \gamma \circ \tau : \tau \in \mathcal{F}_{\lambda} \;\mathbin{\operatorname{and}}\; \gamma \in \operatorname{SL}_2(\mathbb{Z}) \;\mathbin{\operatorname{and}}\; \gamma \equiv \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \pmod {2} \right\}
Definitions:
Fungrim symbol Notation Short description
HH$\mathbb{H}$ Upper complex half-plane
ModularGroupAction$\gamma \circ \tau$ Action of modular group
ModularLambdaFundamentalDomain$\mathcal{F}_{\lambda}$ Fundamental domain of the modular lambda function
SL2Z$\operatorname{SL}_2(\mathbb{Z})$ Modular group
Matrix2x2$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ Two by two matrix
Source code for this entry:
Entry(ID("b23575"),
Formula(Equal(HH, Set(ModularGroupAction(gamma, tau), For(Tuple(tau, gamma)), And(Element(tau, ModularLambdaFundamentalDomain), Element(gamma, SL2Z), CongruentMod(gamma, Matrix2x2(1, 0, 0, 1), 2))))))

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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