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Fungrim entry: b43dac

ubd   where (d,u,v)=xgcd ⁣(a,b)\left|u\right| \le \frac{\left|b\right|}{d}\; \text{ where } \left(d, u, v\right) = \operatorname{xgcd}\!\left(a, b\right)
Assumptions:aZ{0}andbZ{0}a \in \mathbb{Z} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \setminus \left\{0\right\}
TeX:
\left|u\right| \le \frac{\left|b\right|}{d}\; \text{ where } \left(d, u, v\right) = \operatorname{xgcd}\!\left(a, b\right)

a \in \mathbb{Z} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
XGCDxgcd ⁣(a,b)\operatorname{xgcd}\!\left(a, b\right) Extended greatest common divisor
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("b43dac"),
    Formula(Where(LessEqual(Abs(u), Div(Abs(b), d)), Equal(Tuple(d, u, v), XGCD(a, b)))),
    Variables(a, b),
    Assumptions(And(Element(a, SetMinus(ZZ, Set(0))), Element(b, SetMinus(ZZ, Set(0))))))

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2019-10-05 13:11:19.856591 UTC