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Fungrim entry: 0bb73e

xgcd ⁣(a,a)=(a,0,sgn(a))\operatorname{xgcd}\!\left(a, -a\right) = \left(\left|a\right|, 0, -\operatorname{sgn}(a)\right)
Assumptions:aZa \in \mathbb{Z}
TeX:
\operatorname{xgcd}\!\left(a, -a\right) = \left(\left|a\right|, 0, -\operatorname{sgn}(a)\right)

a \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
XGCDxgcd ⁣(a,b)\operatorname{xgcd}\!\left(a, b\right) Extended greatest common divisor
Absz\left|z\right| Absolute value
Signsgn(z)\operatorname{sgn}(z) Sign function
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("0bb73e"),
    Formula(Equal(XGCD(a, Neg(a)), Tuple(Abs(a), 0, Neg(Sign(a))))),
    Variables(a),
    Assumptions(Element(a, ZZ)))

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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