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Fungrim entry: 80279d

PSL2(Z)={(abcd):(abcd)SL2(Z)  and  (c>0  or  (c=0  and  d>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)
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, 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))))))))

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2020-04-08 16:14:44.404316 UTC