1. Sequence

>	X := x$10;

>	whattype(X);

We can create sequences with the command "seq":

>	Y := seq(y[i],i=1..10);

To get access to the elements in a sequence, we use the square brackets:

>

Y[6];

>	op(6,[Y]);

In this alternative selection of an element in a sequence, we converted the sequence Y into the list [Y], because the "op" command only works on lists, not on sequences.

>	Z := Y||(1..10);

The difference between the sequence Y and Z is that we have the more natural indexing.

>

Z[6];

The 6-th element of the sequence Z is Y6 which is not like Y[6] = y[6]: the Y6 is a concatenation of two symbols: the letter Y with the number 6.

>

Y[6];

>	op(Y[6])= op(y[6]);

>

op(Z[6]);

The little y is an indexed variable, with the op command we recover its index.

2. Set

A set is created from a sequence by placing curly braces around it:

>

S := {Y};

The reason for this conversion from a sequence to a set is that we have special operations on the set.

>	T := S union {Z};

>	sZ := T intersect {Z};

Any idea how to convert a set into a sequence?

A good reason for doing this conversion is to impose an order on the elements, because Maple may order the elements in a set in any way.

>

op(sZ);

>	whattype(%); whattype(sZ);

3. List

We create a list from a sequence by placing square brackets around the sequence:

>

L := [Y];

We can convert to a set by removing the square brackets via the op command again, and then placing curly braces round the result of op:

>	S := {op(L)};

We can zip two lists:

>	i := [seq(k,k=1..10)];

>	d := [stats[random,uniform[-1,1]](10)];

Suppose we want to create points [i,d[i]]:

>	zip((x,y) -> [x,y],i,d);

We just created another list of x and y coordinates.  But suppose that we want to create a list of powers of the data in d.  The i-th element is d[i]^i:

>	zip((x,y) -> y^x,i,d);

The reason for converting a sequence or a set into a list is because of the anonymous functions which may be applied by map, select, or zip.