Fungrim home page

Fungrim entry: 127a52

(abcd)τ=aτ+bcτ+d\begin{pmatrix} a & b \\ c & d \end{pmatrix} \circ \tau = \frac{a \tau + b}{c \tau + d}
Assumptions:(abcd)SL2(Z)andτH\begin{pmatrix} a & b \\ c & d \end{pmatrix} \in \operatorname{SL}_2(\mathbb{Z}) \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
TeX:
\begin{pmatrix} a & b \\ c & d \end{pmatrix} \circ \tau = \frac{a \tau + b}{c \tau + d}

\begin{pmatrix} a & b \\ c & d \end{pmatrix} \in \operatorname{SL}_2(\mathbb{Z}) \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
ModularGroupActionγτ\gamma \circ \tau Action of modular group
Matrix2x2(abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix} Two by two matrix
SL2ZSL2(Z)\operatorname{SL}_2(\mathbb{Z}) Modular group
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("127a52"),
    Formula(Equal(ModularGroupAction(Matrix2x2(a, b, c, d), tau), Div(Add(Mul(a, tau), b), Add(Mul(c, tau), d)))),
    Assumptions(And(Element(Matrix2x2(a, b, c, d), SL2Z), Element(tau, HH))))

Topics using this entry

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

2019-10-05 13:11:19.856591 UTC