
Description


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Expression sequences, (or simply sequences), are created using the comma operator (, ). For example s := 1, 2, 3 assigns s the sequence 1, 2, 3. In Maple, sequences form the basis of many data types. In particular, they appear in function calls, lists, sets, and subscripts.


$f\left(s\right)$ applies the function $f$ to the sequence 1, 2, 3


$\left[s\right]$ creates the list containing the elements 1, 2, 3


$\left\{s\right\}$ creates the set containing the elements 1, 2, 3


${a}_{s}$ is the 1, 2, 3 subscript


These are equivalent to $f\left(1\,2\,3\right)$, $\left[1\,2\,3\right]$, $\left\{1\,2\,3\right\}$, and ${a}_{1,2,3}$, respectively.

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When sequences are concatenated with a comma, the result is a single, unnested sequence. Thus t := s, s assigns t the sequence 1, 2, 3, 1, 2, 3. This also means that an expression sequence cannot be passed into a function as a single argument. f(0,s,4) is equivalent to f(0,1,2,3,4). One can create a list or set from the expression sequence to pass it into a function.

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The empty sequence is available as the value of the global variable NULL. It also appears implicitly in the empty list $\left[\right]$, the empty set $\varnothing$, a function call f() with no parameters, and an indexed name $a\left[\right]$ with no subscripts.

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Two key tools for constructing sequences are the seq function and the repetition operator $. For example, the call seq(f(i), i=1..3) will generate the sequence f(1), f(2), f(3). The call x$3 will generate the sequence x, x, x.

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Sequences can also be constructed using the op function. The op function when applied to any Maple expression (except a sequence itself) returns a sequence of the operands of that expression. For example, op([x, y, z]) and op(x+y+z) both return the sequence x, y, z.

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The op and nops functions cannot be applied to a sequence because the elements of the sequence are taken to be individual arguments to the function. However, the ith operand of a sequence s may be accessed using the selection operation s[i]. The length of a sequence may be determined by doing nops([s]), that is, by determining the length of the list containing the expression sequence.

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There is no expression sequence type in Maple. However, the whattype function returns exprseq for objects that are expression sequences.



Examples


>

p := proc() nargs end proc:

>

$p\left(1\,2\,3\right)$

>

$s\u22541\,2\,3$

${s}{\u2254}{1}{,}{2}{,}{3}$
 (2) 
>

$p\left(0\,s\,4\right)$

Passing expression sequences into functions can lead to unexpected results.
>

$\mathrm{map}\left(x\→x\+10\,s\right)$

In this case the expression sequence, $s$, is flattened into the expression sequence of arguments to map. Therefore map sees 4 arguments, the function to be mapped, the argument to map over and two extra arguments that are passed to the mapped function.
Making a list from the expression sequence will work as expected.
>

$\mathrm{map}\left(x\→x\+10\,\left[s\right]\right)$

$\left[{11}{\,}{12}{\,}{13}\right]$
 (6) 


