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Fungrim entry: 80279d

PSL2(Z)={(abcd):(abcd)SL2(Z)and(c>0or(c=0andd>0))}\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
PSL2ZPSL2(Z)\operatorname{PSL}_2(\mathbb{Z}) Modular group (canonical representatives)
SetBuilder{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
Matrix2x2(abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix} Two by two matrix
SL2ZSL2(Z)\operatorname{SL}_2(\mathbb{Z}) Modular group
Source code for this entry:
Entry(ID("80279d"),
    Formula(Equal(PSL2Z, SetBuilder(Matrix2x2(a, b, c, d), Tuple(a, b, c, d), And(Element(Matrix2x2(a, b, c, d), SL2Z), Or(Greater(c, 0), And(Equal(c, 0), Greater(d, 0))))))))

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

2019-08-17 11:32:46.829430 UTC