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

Modular transformations