operator for forming an expression sequence
expr $ i = m .. n
expr $ m .. n
expr $ n
$ i = m .. n
$ m .. n
`$`( expr, i = m .. n )
`$`( expr, m .. n )
`$`( expr, n )
`$`( i = m .. n )
`$`( m .. n )
`$`( n )
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.
The $ operator is thread-safe as of Maple 15.
For more information on thread safety, see index/threadsafe.
i^2 $ i = 2/3 .. 8/3;
a[i] $ i = 1..3;
x $ 4;
The $ operator was updated in Maple 2021.
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