# Fungrim entry: 287e28

Symbol: GCD $\gcd\!\left(a, b\right)$ Greatest common divisor
The greatest common divisor function can be called either with with an arbitrary number of integer arguments or with a single finite set of integers as the argument. The current entries only deal with the case of two arguments.
Domain Codomain
$a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}$ $\gcd\!\left(a, b\right) \in \mathbb{Z}_{\ge 0}$
$S \in \mathscr{P}(\mathbb{Z}) \;\mathbin{\operatorname{and}}\; \# S < \# \mathbb{Z}$ $\gcd(S) \in \mathbb{Z}_{\ge 0}$
Table data: $\left(P, Q\right)$ such that $\left(P\right) \;\implies\; \left(Q\right)$
Definitions:
Fungrim symbol Notation Short description
GCD$\gcd\!\left(a, b\right)$ Greatest common divisor
ZZ$\mathbb{Z}$ Integers
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
PowerSet$\mathscr{P}(S)$ Power set
Cardinality$\# S$ Set cardinality
Source code for this entry:
Entry(ID("287e28"),
SymbolDefinition(GCD, GCD(a, b), "Greatest common divisor"),
Description("The greatest common divisor function can be called either with with an arbitrary number of integer arguments or with a single finite set of integers as the argument. The current entries only deal with the case of two arguments."),
Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(And(Element(a, ZZ), Element(b, ZZ)), Element(GCD(a, b), ZZGreaterEqual(0))), Tuple(And(Element(S, PowerSet(ZZ)), Less(Cardinality(S), Cardinality(ZZ))), Element(GCD(S), ZZGreaterEqual(0))))))

## Topics using this entry

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

2021-03-15 19:12:00.328586 UTC