Fungrim entry: 5daceb

Symbol: XGCD —

\operatorname{xgcd}\!\left(a, b\right)

— Extended greatest common divisor

Domain	Codomain
$a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}$	$d \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; u \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; v \in \mathbb{Z}\; \text{ where } \left(d, u, v\right) = \operatorname{xgcd}\!\left(a, b\right)$

Table data:

\left(P, Q\right)

such that

\left(P\right) \;\implies\; \left(Q\right)

Definitions:

Fungrim symbol	Notation	Short description
`XGCD`	$\operatorname{xgcd}\!\left(a, b\right)$	Extended greatest common divisor
`ZZ`	$\mathbb{Z}$	Integers
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("5daceb"),
    SymbolDefinition(XGCD, XGCD(a, b), "Extended greatest common divisor"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(And(Element(a, ZZ), Element(b, ZZ)), Where(And(Element(d, ZZGreaterEqual(0)), Element(u, ZZ), Element(v, ZZ)), Equal(Tuple(d, u, v), XGCD(a, b)))))))

Topics using this entry

Greatest common divisor