Fungrim entry: 978576

Symbol: ForElement —

\ldots

— Generator for all the elements of a set

ForElement(x, S) declares the variable x just like For(x) and additionally tells the parent operator that

x

is to range over the elements of the set

S

. Examples: Set(Mul(2, n), ForElement(n, ZZ)) becomes

\left\{ 2 n : n \in \mathbb{Z} \right\}

. Sum(Div(1, Pow(n, 2)), ForElement(n, SetMinus(ZZ, Set(0)))) becomes

\sum_{n \in \mathbb{Z} \setminus \left\{0\right\}} \frac{1}{{n}^{2}}

Definitions:

Fungrim symbol	Notation	Short description
`ZZ`	$\mathbb{Z}$	Integers
`Sum`	$\sum_{n} f(n)$	Sum
`Pow`	${a}^{b}$	Power

Source code for this entry:

Entry(ID("978576"),
    SymbolDefinition(ForElement, Ellipsis, "Generator for all the elements of a set"),
    Description(SourceForm(ForElement(x, S)), "declares the variable", SourceForm(x), "just like", SourceForm(For(x)), "and additionally tells the parent operator", "that", x, "is to range over the elements of the set", S, ". ", "Examples: ", SourceForm(Set(Mul(2, n), ForElement(n, ZZ))), "becomes", Set(Mul(2, n), ForElement(n, ZZ)), ". ", SourceForm(Sum(Div(1, Pow(n, 2)), ForElement(n, SetMinus(ZZ, Set(0))))), "becomes", Sum(Div(1, Pow(n, 2)), ForElement(n, SetMinus(ZZ, Set(0)))), ". "))

Topics using this entry

Symbolic expressions