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# Fungrim entry: 80279d

$\operatorname{PSL}_2(\mathbb{Z}) = \left\{ \begin{pmatrix} a & b \\ c & d \end{pmatrix} : \begin{pmatrix} a & b \\ c & d \end{pmatrix} \in \operatorname{SL}_2(\mathbb{Z}) \;\mathbin{\operatorname{and}}\; \left(c > 0 \;\mathbin{\operatorname{or}}\; \left(c = 0 \;\mathbin{\operatorname{and}}\; d > 0\right)\right) \right\}$
TeX:
\operatorname{PSL}_2(\mathbb{Z}) = \left\{ \begin{pmatrix} a & b \\ c & d \end{pmatrix} : \begin{pmatrix} a & b \\ c & d \end{pmatrix} \in \operatorname{SL}_2(\mathbb{Z}) \;\mathbin{\operatorname{and}}\; \left(c > 0 \;\mathbin{\operatorname{or}}\; \left(c = 0 \;\mathbin{\operatorname{and}}\; d > 0\right)\right) \right\}
Definitions:
Fungrim symbol Notation Short description
PSL2Z$\operatorname{PSL}_2(\mathbb{Z})$ Modular group (canonical representatives)
Matrix2x2$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ Two by two matrix
SL2Z$\operatorname{SL}_2(\mathbb{Z})$ Modular group
Source code for this entry:
Entry(ID("80279d"),
Formula(Equal(PSL2Z, Set(Matrix2x2(a, b, c, d), For(Tuple(a, b, c, d)), And(Element(Matrix2x2(a, b, c, d), SL2Z), Or(Greater(c, 0), And(Equal(c, 0), Greater(d, 0))))))))

## 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