Fungrim symbol: GCD

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 symbol

The symbol GCD appears in 10 topics:

Greatest common divisor (in 52 entries)
Totient function (in 12 entries)
Dirichlet characters (in 10 entries)
Fibonacci numbers (in 3 entries)
Eisenstein series (in 2 entries)
Partition function (in 1 entries)
Modular j-invariant (in 1 entries)
Hurwitz zeta function (in 1 entries)
Dirichlet L-functions (in 1 entries)
Dedekind eta function (in 1 entries)

Entries using this symbol

The symbol GCD appears in 82 entries: