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operator for forming an expression sequence

 Calling Sequence expr $i = m .. n expr$ m .. n expr $n$ i = m .. n $m .. n$ n $( expr, i = m .. n ) $( expr, m .. n ) $( expr, n ) $( i = m .. n ) $( m .. n ) $( n )

Parameters

 expr - expression i - unevaluated name m, n - expressions

Description

 • In its most general form, expr $i = m..n, the$ operator returns the expression sequence produced by substituting for i in expr the values m, m+1, ..., n (or up to the last value not exceeding n if n-m is not an integer)
 • If m > n then the NULL (empty) expression sequence is returned.
 • If expr does not refer to i, the right operand of the $operator can be written as just m..n.  Furthermore, if expr does not refer to i and if m is 1, m..n can be specified as just n. Thus, expr$ n produces a sequence of n occurrences of expr.
 • The left operand of $may be omitted when generating simple sequences of numbers:  – The forms$ i = m..n and $m..n are equivalent to i$ i = m..n, and produce the sequence m, m+1, ..., n (or up to the last value not exceeding n).
 – The form $n is equivalent to i$ i = 1..n when n is of type algebraic.
 – The form $n when n is a string is equivalent to n[i]$ i = 1..length(n), returning a sequence of the individual characters within the string.
 • The $operator can also be invoked in function call form, using the name $.
 Note:  Some of these calling sequences are not currently supported in 2-D input in the Standard interface.  However, equivalent forms work.  You can always use the forms expr $i = m .. n, expr$ n, and $m .. n.  Note: It is recommended (and often necessary) that both expr and i be enclosed in single quotes to prevent premature evaluation. For example, if i had been assigned a value, the i in the expression would be evaluated to its value, and so could not be used as a counting variable. The most common usage is 'expr'$ 'i' = m..n.
 The seq function, which has many of the same capabilities as the $operator, has special evaluation rules that make this quoting unnecessary.  • In a procedure parameter declaration section,$ is used as the end-of-parameters marker. For more information on this use of $, see Parameter Declarations. Thread Safety  • The$ operator is thread-safe as of Maple 15.

Examples

 > i^2 $i = 2/3 .. 8/3;  $\frac{{4}}{{9}}{,}\frac{{25}}{{9}}{,}\frac{{64}}{{9}}$ (1)  > a[i]$ i = 1..3;
 ${{a}}_{{1}}{,}{{a}}_{{2}}{,}{{a}}_{{3}}$ (2)
 > $2..5;  ${2}{,}{3}{,}{4}{,}{5}$ (3)  >$ 3;
 ${1}{,}{2}{,}{3}$ (4)
 > x $4;  ${x}{,}{x}{,}{x}{,}{x}$ (5)  >$ "Maple";
 ${"M"}{,}{"a"}{,}{"p"}{,}{"l"}{,}{"e"}$ (6)

Compatibility

 • The \$ operator was updated in Maple 2021.