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<h1 class="chapter"> 37. Lists </h1>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top"><a href="#SEC164">37.1 Introduction to Lists</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#SEC165">37.2 Functions and Variables for Lists</a></td><td> </td><td align="left" valign="top">
</td></tr>
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<p><a name="Item_003a-Introduction-to-Lists"></a>
</p><hr size="6">
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<h2 class="section"> 37.1 Introduction to Lists </h2>
<p>Lists are the basic building block for Maxima and Lisp. All data types
other than arrays, hash tables, numbers are represented as Lisp lists,
These Lisp lists have the form
</p>
<pre class="example">((MPLUS) $A 2)
</pre>
<p>to indicate an expression <code>a+2</code>. At Maxima level one would see
the infix notation <code>a+2</code>. Maxima also has lists which are printed
as
</p>
<pre class="example">[1, 2, 7, x+y]
</pre>
<p>for a list with 4 elements. Internally this corresponds to a Lisp list
of the form
</p>
<pre class="example">((MLIST) 1 2 7 ((MPLUS) $X $Y ))
</pre>
<p>The flag which denotes the type field of the Maxima expression is a list
itself, since after it has been through the simplifier the list would become
</p>
<pre class="example">((MLIST SIMP) 1 2 7 ((MPLUS SIMP) $X $Y))
</pre>
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<h2 class="section"> 37.2 Functions and Variables for Lists </h2>
<p><a name="Item_003a-append"></a>
</p><dl>
<dt><u>Function:</u> <b>append</b><i> (<var>list_1</var>, ..., <var>list_n</var>)</i>
<a name="IDX1301"></a>
</dt>
<dd><p>Returns a single list of the elements of <var>list_1</var> followed
by the elements of <var>list_2</var>, ... <code>append</code> also works on
general expressions, e.g. <code>append (f(a,b), f(c,d,e));</code> yields
<code>f(a,b,c,d,e)</code>.
</p>
<p>Do <code>example(append);</code> for an example.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-assoc"></a>
</p><dl>
<dt><u>Function:</u> <b>assoc</b><i> (<var>key</var>, <var>list</var>, <var>default</var>)</i>
<a name="IDX1302"></a>
</dt>
<dt><u>Function:</u> <b>assoc</b><i> (<var>key</var>, <var>list</var>)</i>
<a name="IDX1303"></a>
</dt>
<dd><p>This function searches for the <var>key</var> in the left hand side of the input <var>list</var>
of the form <code>[x,y,z,...]</code> where each of the <var>list</var> elements is an expression of
a binary operand and 2 elements. For example <code>x=1</code>, <code>2^3</code>, <code>[a,b]</code> etc.
The <var>key</var> is checked againts the first operand. <code>assoc</code> returns the second
operand if the <code>key</code> is found. If the <code>key</code> is not found it
either returns the <var>default</var> value. <var>default</var> is optional
and defaults to <code>false</code>.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-atom"></a>
</p><dl>
<dt><u>Function:</u> <b>atom</b><i> (<var>expr</var>)</i>
<a name="IDX1304"></a>
</dt>
<dd><p>Returns <code>true</code> if <var>expr</var> is atomic (i.e. a number, name or string) else
<code>false</code>. Thus <code>atom(5)</code> is <code>true</code> while <code>atom(a[1])</code> and <code>atom(sin(x))</code> are
<code>false</code> (asuming <code>a[1]</code> and <code>x</code> are unbound).
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
·
<a href="maxima_95.html#Category_003a-Predicate-functions">Predicate functions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-cons"></a>
</p><dl>
<dt><u>Function:</u> <b>cons</b><i> (<var>expr</var>, <var>list</var>)</i>
<a name="IDX1305"></a>
</dt>
<dd><p>Returns a new list constructed of the element <var>expr</var> as
its first element, followed by the elements of <var>list</var>. <code>cons</code> also works
on other expressions, e.g. <code>cons(x, f(a,b,c));</code> -> <code>f(x,a,b,c)</code>.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-copylist"></a>
</p><dl>
<dt><u>Function:</u> <b>copylist</b><i> (<var>list</var>)</i>
<a name="IDX1306"></a>
</dt>
<dd><p>Returns a copy of the list <var>list</var>.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-create_005flist"></a>
</p><dl>
<dt><u>Function:</u> <b>create_list</b><i> (<var>form</var>, <var>x_1</var>, <var>list_1</var>, ..., <var>x_n</var>, <var>list_n</var>)</i>
<a name="IDX1307"></a>
</dt>
<dd><p>Create a list by evaluating <var>form</var> with <var>x_1</var> bound to
each element of <var>list_1</var>, and for each such binding bind <var>x_2</var>
to each element of <var>list_2</var>, ....
The number of elements in the result will be
the product of the number of elements in each list.
Each variable <var>x_i</var> must actually be a symbol - it will not be evaluated.
The list arguments will be evaluated once at the beginning of the
iteration.
</p>
<pre class="example">(%i1) create_list(x^i,i,[1,3,7]);
3 7
(%o1) [x, x , x ]
</pre>
<p>With a double iteration:
</p>
<pre class="example">(%i1) create_list([i,j],i,[a,b],j,[e,f,h]);
(%o1) [[a, e], [a, f], [a, h], [b, e], [b, f], [b, h]]
</pre>
<p>Instead of <var>list_i</var> two args may be supplied each of which should
evaluate to a number. These will be the inclusive lower and
upper bounds for the iteration.
</p>
<pre class="example">(%i1) create_list([i,j],i,[1,2,3],j,1,i);
(%o1) [[1, 1], [2, 1], [2, 2], [3, 1], [3, 2], [3, 3]]
</pre>
<p>Note that the limits or list for the <code>j</code> variable can
depend on the current value of <code>i</code>.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-delete"></a>
</p><dl>
<dt><u>Function:</u> <b>delete</b><i> (<var>expr_1</var>, <var>expr_2</var>)</i>
<a name="IDX1308"></a>
</dt>
<dt><u>Function:</u> <b>delete</b><i> (<var>expr_1</var>, <var>expr_2</var>, <var>n</var>)</i>
<a name="IDX1309"></a>
</dt>
<dd><p><code>delete(<var>expr_1</var>, <var>expr_2</var>)</code>
removes from <var>expr_2</var> any arguments of its top-level operator
which are the same (as determined by "=") as <var>expr_1</var>.
Note that "=" tests for formal equality, not equivalence.
Note also that arguments of subexpressions are not affected.
</p>
<p><var>expr_1</var> may be an atom or a non-atomic expression.
<var>expr_2</var> may be any non-atomic expression.
<code>delete</code> returns a new expression;
it does not modify <var>expr_2</var>.
</p>
<p><code>delete(<var>expr_1</var>, <var>expr_2</var>, <var>n</var>)</code>
removes from <var>expr_2</var> the first <var>n</var> arguments of the top-level operator
which are the same as <var>expr_1</var>.
If there are fewer than <var>n</var> such arguments,
then all such arguments are removed.
</p>
<p>Examples:
</p>
<p>Removing elements from a list.
</p>
<pre class="example">(%i1) delete (y, [w, x, y, z, z, y, x, w]);
(%o1) [w, x, z, z, x, w]
</pre>
<p>Removing terms from a sum.
</p>
<pre class="example">(%i1) delete (sin(x), x + sin(x) + y);
(%o1) y + x
</pre>
<p>Removing factors from a product.
</p>
<pre class="example">(%i1) delete (u - x, (u - w)*(u - x)*(u - y)*(u - z));
(%o1) (u - w) (u - y) (u - z)
</pre>
<p>Removing arguments from an arbitrary expression.
</p>
<pre class="example">(%i1) delete (a, foo (a, b, c, d, a));
(%o1) foo(b, c, d)
</pre>
<p>Limit the number of removed arguments.
</p>
<pre class="example">(%i1) delete (a, foo (a, b, a, c, d, a), 2);
(%o1) foo(b, c, d, a)
</pre>
<p>Whether arguments are the same as <var>expr_1</var> is determined by "=".
Arguments which are <code>equal</code> but not "=" are not removed.
</p>
<pre class="example">(%i1) [is (equal (0, 0)), is (equal (0, 0.0)), is (equal (0, 0b0))];
`rat' replaced 0.0 by 0/1 = 0.0
`rat' replaced 0.0B0 by 0/1 = 0.0B0
(%o1) [true, true, true]
(%i2) [is (0 = 0), is (0 = 0.0), is (0 = 0b0)];
(%o2) [true, false, false]
(%i3) delete (0, [0, 0.0, 0b0]);
(%o3) [0.0, 0.0b0]
(%i4) is (equal ((x + y)*(x - y), x^2 - y^2));
(%o4) true
(%i5) is ((x + y)*(x - y) = x^2 - y^2);
(%o5) false
(%i6) delete ((x + y)*(x - y), [(x + y)*(x - y), x^2 - y^2]);
2 2
(%o6) [x - y ]
</pre>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-eighth"></a>
</p><dl>
<dt><u>Function:</u> <b>eighth</b><i> (<var>expr</var>)</i>
<a name="IDX1310"></a>
</dt>
<dd><p>Returns the 8'th item of expression or list <var>expr</var>.
See <code>first</code> for more details.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-endcons"></a>
</p><dl>
<dt><u>Function:</u> <b>endcons</b><i> (<var>expr</var>, <var>list</var>)</i>
<a name="IDX1311"></a>
</dt>
<dd><p>Returns a new list consisting of the elements of
<code>list</code> followed by <var>expr</var>. <code>endcons</code> also works on general expressions, e.g.
<code>endcons(x, f(a,b,c));</code> -> <code>f(a,b,c,x)</code>.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
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<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-fifth"></a>
</p><dl>
<dt><u>Function:</u> <b>fifth</b><i> (<var>expr</var>)</i>
<a name="IDX1312"></a>
</dt>
<dd><p>Returns the 5'th item of expression or list <var>expr</var>.
See <code>first</code> for more details.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-first"></a>
</p><dl>
<dt><u>Function:</u> <b>first</b><i> (<var>expr</var>)</i>
<a name="IDX1313"></a>
</dt>
<dd><p>Returns the first part of <var>expr</var> which may result in the first
element of a list, the first row of a matrix, the first term of a sum,
etc. Note that <code>first</code> and its related functions, <code>rest</code> and <code>last</code>, work
on the form of <var>expr</var> which is displayed not the form which is typed on
input. If the variable <code>inflag</code> is set to <code>true</code> however, these
functions will look at the internal form of <var>expr</var>. Note that the
simplifier re-orders expressions. Thus <code>first(x+y)</code> will be <code>x</code> if <code>inflag</code>
is <code>true</code> and <code>y</code> if <code>inflag</code> is <code>false</code> (<code>first(y+x)</code> gives the same
results). The functions <code>second</code> .. <code>tenth</code> yield the second through the
tenth part of their input argument.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-fourth"></a>
</p><dl>
<dt><u>Function:</u> <b>fourth</b><i> (<var>expr</var>)</i>
<a name="IDX1314"></a>
</dt>
<dd><p>Returns the 4'th item of expression or list <var>expr</var>.
See <code>first</code> for more details.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-get"></a>
</p><dl>
<dt><u>Function:</u> <b>get</b><i> (<var>a</var>, <var>i</var>)</i>
<a name="IDX1315"></a>
</dt>
<dd><p>Retrieves the user property indicated by <var>i</var> associated with
atom <var>a</var> or returns <code>false</code> if a doesn't have property <var>i</var>.
</p>
<p><code>get</code> evaluates its arguments.
</p>
<pre class="example">(%i1) put (%e, 'transcendental, 'type);
(%o1) transcendental
(%i2) put (%pi, 'transcendental, 'type)$
(%i3) put (%i, 'algebraic, 'type)$
(%i4) typeof (expr) := block ([q],
if numberp (expr)
then return ('algebraic),
if not atom (expr)
then return (maplist ('typeof, expr)),
q: get (expr, 'type),
if q=false
then errcatch (error(expr,"is not numeric.")) else q)$
(%i5) typeof (2*%e + x*%pi);
x is not numeric.
(%o5) [[transcendental, []], [algebraic, transcendental]]
(%i6) typeof (2*%e + %pi);
(%o6) [transcendental, [algebraic, transcendental]]
</pre>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-join"></a>
</p><dl>
<dt><u>Function:</u> <b>join</b><i> (<var>l</var>, <var>m</var>)</i>
<a name="IDX1316"></a>
</dt>
<dd><p>Creates a new list containing the elements of lists <var>l</var> and <var>m</var>, interspersed.
The result has elements <code>[<var>l</var>[1], <var>m</var>[1], <var>l</var>[2], <var>m</var>[2], ...]</code>.
The lists <var>l</var> and <var>m</var> may contain any type of elements.
</p>
<p>If the lists are different lengths, <code>join</code> ignores elements of the longer list.
</p>
<p>Maxima complains if <var>l</var> or <var>m</var> is not a list.
</p>
<p>Examples:
</p>
<pre class="example">(%i1) L1: [a, sin(b), c!, d - 1];
(%o1) [a, sin(b), c!, d - 1]
(%i2) join (L1, [1, 2, 3, 4]);
(%o2) [a, 1, sin(b), 2, c!, 3, d - 1, 4]
(%i3) join (L1, [aa, bb, cc, dd, ee, ff]);
(%o3) [a, aa, sin(b), bb, c!, cc, d - 1, dd]
</pre>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-last"></a>
</p><dl>
<dt><u>Function:</u> <b>last</b><i> (<var>expr</var>)</i>
<a name="IDX1317"></a>
</dt>
<dd><p>Returns the last part (term, row, element, etc.) of the <var>expr</var>.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-length"></a>
</p><dl>
<dt><u>Function:</u> <b>length</b><i> (<var>expr</var>)</i>
<a name="IDX1318"></a>
</dt>
<dd><p>Returns (by default) the number of parts in the external
(displayed) form of <var>expr</var>. For lists this is the number of elements,
for matrices it is the number of rows, and for sums it is the number
of terms (see <code>dispform</code>).
</p>
<p>The <code>length</code> command is affected by the
<code>inflag</code> switch. So, e.g. <code>length(a/(b*c));</code> gives 2 if
<code>inflag</code> is <code>false</code> (Assuming <code>exptdispflag</code> is <code>true</code>), but 3 if <code>inflag</code> is
<code>true</code> (the internal representation is essentially <code>a*b^-1*c^-1</code>).
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
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<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-listarith"></a>
</p><dl>
<dt><u>Option variable:</u> <b>listarith</b>
<a name="IDX1319"></a>
</dt>
<dd><p>default value: <code>true</code> - if <code>false</code> causes any arithmetic operations
with lists to be suppressed; when <code>true</code>, list-matrix operations are
contagious causing lists to be converted to matrices yielding a result
which is always a matrix. However, list-list operations should return
lists.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Global-flags">Global flags</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-listp"></a>
</p><dl>
<dt><u>Function:</u> <b>listp</b><i> (<var>expr</var>)</i>
<a name="IDX1320"></a>
</dt>
<dd><p>Returns <code>true</code> if <var>expr</var> is a list else <code>false</code>.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Predicate-functions">Predicate functions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-makelist"></a>
</p><dl>
<dt><u>Function:</u> <b>makelist</b><i> (<var>expr</var>, <var>i</var>, <var>i_0</var>, <var>i_1</var>)</i>
<a name="IDX1321"></a>
</dt>
<dt><u>Function:</u> <b>makelist</b><i> (<var>expr</var>, <var>x</var>, <var>list</var>)</i>
<a name="IDX1322"></a>
</dt>
<dd><p>Constructs and returns a list,
each element of which is generated from <var>expr</var>.
</p>
<p><code>makelist (<var>expr</var>, <var>i</var>, <var>i_0</var>, <var>i_1</var>)</code> returns a list,
the <code>j</code>'th element of which is equal to <code>ev (<var>expr</var>, <var>i</var>=j)</code>
for <code>j</code> equal to <var>i_0</var> through <var>i_1</var>.
</p>
<p><code>makelist (<var>expr</var>, <var>x</var>, <var>list</var>)</code> returns a list,
the <code>j</code>'th element of which is equal to <code>ev (<var>expr</var>, <var>x</var>=<var>list</var>[j])</code>
for <code>j</code> equal to 1 through <code>length (<var>list</var>)</code>.
</p>
<p>Examples:
</p>
<pre class="example">(%i1) makelist(concat(x,i),i,1,6);
(%o1) [x1, x2, x3, x4, x5, x6]
(%i2) makelist(x=y,y,[a,b,c]);
(%o2) [x = a, x = b, x = c]
</pre>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-member"></a>
</p><dl>
<dt><u>Function:</u> <b>member</b><i> (<var>expr_1</var>, <var>expr_2</var>)</i>
<a name="IDX1323"></a>
</dt>
<dd><p>Returns <code>true</code> if <code>is(<var>expr_1</var> = <var>a</var>)</code>
for some element <var>a</var> in <code>args(<var>expr_2</var>)</code>,
otherwise returns <code>false</code>.
</p>
<p><code>expr_2</code> is typically a list,
in which case <code>args(<var>expr_2</var>) = <var>expr_2</var></code>
and <code>is(<var>expr_1</var> = <var>a</var>)</code> for some element <var>a</var> in <code>expr_2</code> is the test.
</p>
<p><code>member</code> does not inspect parts of the arguments of <code>expr_2</code>,
so it may return <code>false</code> even if <code>expr_1</code> is a part of some argument of <code>expr_2</code>.
</p>
<p>See also <code>elementp</code>.
</p>
<p>Examples:
</p>
<pre class="example">(%i1) member (8, [8, 8.0, 8b0]);
(%o1) true
(%i2) member (8, [8.0, 8b0]);
(%o2) false
(%i3) member (b, [a, b, c]);
(%o3) true
(%i4) member (b, [[a, b], [b, c]]);
(%o4) false
(%i5) member ([b, c], [[a, b], [b, c]]);
(%o5) true
(%i6) F (1, 1/2, 1/4, 1/8);
1 1 1
(%o6) F(1, -, -, -)
2 4 8
(%i7) member (1/8, %);
(%o7) true
(%i8) member ("ab", ["aa", "ab", sin(1), a + b]);
(%o8) true
</pre>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
·
<a href="maxima_95.html#Category_003a-Predicate-functions">Predicate functions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-ninth"></a>
</p><dl>
<dt><u>Function:</u> <b>ninth</b><i> (<var>expr</var>)</i>
<a name="IDX1324"></a>
</dt>
<dd><p>Returns the 9'th item of expression or list <var>expr</var>.
See <code>first</code> for more details.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
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<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-unique"></a>
</p><dl>
<dt><u>Function:</u> <b>unique</b><i> (<var>L</var>)</i>
<a name="IDX1325"></a>
</dt>
<dd><p>Returns the unique elements of the list <var>L</var>.
</p>
<p>When all the elements of <var>L</var> are unique,
<code>unique</code> returns a shallow copy of <var>L</var>,
not <var>L</var> itself.
</p>
<p>If <var>L</var> is not a list, <code>unique</code> returns <var>L</var>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) unique ([1, %pi, a + b, 2, 1, %e, %pi, a + b, [1]]);
(%o1) [1, 2, %e, %pi, [1], b + a]
</pre></dd></dl>
<p><a name="Item_003a-rest"></a>
</p><dl>
<dt><u>Function:</u> <b>rest</b><i> (<var>expr</var>, <var>n</var>)</i>
<a name="IDX1326"></a>
</dt>
<dt><u>Function:</u> <b>rest</b><i> (<var>expr</var>)</i>
<a name="IDX1327"></a>
</dt>
<dd><p>Returns <var>expr</var> with its first <var>n</var> elements removed if <var>n</var> is
positive and its last <code>- <var>n</var></code> elements removed if <var>n</var> is negative. If <var>n</var> is 1
it may be omitted. <var>expr</var> may be a list, matrix, or other expression.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
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</p>
</div>
</dd></dl>
<p><a name="Item_003a-reverse"></a>
</p><dl>
<dt><u>Function:</u> <b>reverse</b><i> (<var>list</var>)</i>
<a name="IDX1328"></a>
</dt>
<dd><p>Reverses the order of the members of the <var>list</var> (not
the members themselves). <code>reverse</code> also works on general expressions,
e.g. <code>reverse(a=b);</code> gives <code>b=a</code>.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
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<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-second"></a>
</p><dl>
<dt><u>Function:</u> <b>second</b><i> (<var>expr</var>)</i>
<a name="IDX1329"></a>
</dt>
<dd><p>Returns the 2'nd item of expression or list <var>expr</var>.
See <code>first</code> for more details.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-seventh"></a>
</p><dl>
<dt><u>Function:</u> <b>seventh</b><i> (<var>expr</var>)</i>
<a name="IDX1330"></a>
</dt>
<dd><p>Returns the 7'th item of expression or list <var>expr</var>.
See <code>first</code> for more details.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-sixth"></a>
</p><dl>
<dt><u>Function:</u> <b>sixth</b><i> (<var>expr</var>)</i>
<a name="IDX1331"></a>
</dt>
<dd><p>Returns the 6'th item of expression or list <var>expr</var>.
See <code>first</code> for more details.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-sublist_005findices"></a>
</p><dl>
<dt><u>Function:</u> <b>sublist_indices</b><i> (<var>L</var>, <var>P</var>)</i>
<a name="IDX1332"></a>
</dt>
<dd><p>Returns the indices of the elements <code>x</code> of the list <var>L</var> for which
the predicate <code>maybe(<var>P</var>(x))</code> returns <code>true</code>;
this excludes <code>unknown</code> as well as <code>false</code>.
<var>P</var> may be the name of a function or a lambda expression.
<var>L</var> must be a literal list.
</p>
<p>Examples:
</p>
<pre class="example">(%i1) sublist_indices ('[a, b, b, c, 1, 2, b, 3, b],
lambda ([x], x='b));
(%o1) [2, 3, 7, 9]
(%i2) sublist_indices ('[a, b, b, c, 1, 2, b, 3, b], symbolp);
(%o2) [1, 2, 3, 4, 7, 9]
(%i3) sublist_indices ([1 > 0, 1 < 0, 2 < 1, 2 > 1, 2 > 0],
identity);
(%o3) [1, 4, 5]
(%i4) assume (x < -1);
(%o4) [x < - 1]
(%i5) map (maybe, [x > 0, x < 0, x < -2]);
(%o5) [false, true, unknown]
(%i6) sublist_indices ([x > 0, x < 0, x < -2], identity);
(%o6) [2]
</pre>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-tenth"></a>
</p><dl>
<dt><u>Function:</u> <b>tenth</b><i> (<var>expr</var>)</i>
<a name="IDX1333"></a>
</dt>
<dd><p>Returns the 10'th item of expression or list <var>expr</var>.
See <code>first</code> for more details.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-third"></a>
</p><dl>
<dt><u>Function:</u> <b>third</b><i> (<var>expr</var>)</i>
<a name="IDX1334"></a>
</dt>
<dd><p>Returns the 3'rd item of expression or list <var>expr</var>.
See <code>first</code> for more details.
</p>
<div class=categorybox>
<p>Categories: <a href="maxima_95.html#Category_003a-Lists">Lists</a>
·
<a href="maxima_95.html#Category_003a-Expressions">Expressions</a>
</p>
</div>
</dd></dl>
<p><a name="Item_003a-Sets"></a>
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