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Fungrim entry: c84f3f

SL2(Z)={(abcd):aZ  and  bZ  and  cZ  and  dZ  and  adbc=1}\operatorname{SL}_2(\mathbb{Z}) = \left\{ \begin{pmatrix} a & b \\ c & d \end{pmatrix} : a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; c \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; d \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; a d - b c = 1 \right\}
TeX:
\operatorname{SL}_2(\mathbb{Z}) = \left\{ \begin{pmatrix} a & b \\ c & d \end{pmatrix} : a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; c \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; d \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; a d - b c = 1 \right\}
Definitions:
Fungrim symbol Notation Short description
SL2ZSL2(Z)\operatorname{SL}_2(\mathbb{Z}) Modular group
Matrix2x2(abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix} Two by two matrix
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("c84f3f"),
    Formula(Equal(SL2Z, Set(Matrix2x2(a, b, c, d), For(Tuple(a, b, c, d)), And(Element(a, ZZ), Element(b, ZZ), Element(c, ZZ), Element(d, ZZ), Equal(Sub(Mul(a, d), Mul(b, c)), 1))))))

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

2020-04-08 16:14:44.404316 UTC