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Fungrim entry: 5daceb

Symbol: XGCD xgcd ⁣(a,b)\operatorname{xgcd}\!\left(a, b\right) Extended greatest common divisor
Domain Codomain
aZandbZa \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} dZ0anduZandvZ   where (d,u,v)=xgcd ⁣(a,b)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: (P,Q)\left(P, Q\right) such that (P)    (Q)\left(P\right) \implies \left(Q\right)
Definitions:
Fungrim symbol Notation Short description
XGCDxgcd ⁣(a,b)\operatorname{xgcd}\!\left(a, b\right) Extended greatest common divisor
ZZZ\mathbb{Z} Integers
ZZGreaterEqualZn\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)))))))

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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