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<p>
Next: <a href="maxima_41.html#User-defined-operators" accesskey="n" rel="next">User defined operators</a>, Previous: <a href="maxima_39.html#Operators-for-Equations" accesskey="p" rel="previous">Operators for Equations</a>, Up: <a href="maxima_34.html#Operators" accesskey="u" rel="up">Operators</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Assignment-operators-1"></a>
<h3 class="section">7.6 Assignment operators</h3>
<a name="g_t_003a"></a><a name="Item_003a-Operators_002fdeffn_002f_003a"></a><dl>
<dt><a name="index-_003a"></a>Operator: <strong>:</strong></dt>
<dd><a name="index-Assignment-operator"></a>
<p>Assignment operator.
</p>
<p>When the left-hand side is a simple variable (not subscripted), <code>:</code>
evaluates its right-hand side and associates that value with the left-hand side.
</p>
<p>When the left-hand side is a subscripted element of a list, matrix, declared
Maxima array, or Lisp array, the right-hand side is assigned to that element.
The subscript must name an existing element; such objects cannot be extended by
naming nonexistent elements.
</p>
<p>When the left-hand side is a subscripted element of a <code><a href="maxima_23.html#hashed-array">hashed array</a></code>,
the right-hand side is assigned to that element, if it already exists,
or a new element is allocated, if it does not already exist.
</p>
<p>When the left-hand side is a list of simple and/or subscripted variables, the
right-hand side must evaluate to a list, and the elements of the right-hand
side are assigned to the elements of the left-hand side, in parallel.
</p>
<p>See also <code><a href="maxima_8.html#kill">kill</a></code> and <code><a href="maxima_159.html#remvalue">remvalue</a></code>, which undo the association between
the left-hand side and its value.
</p>
<p>Examples:
</p>
<p>Assignment to a simple variable.
</p>
<div class="example">
<pre class="example">(%i1) a;
(%o1) a
(%i2) a : 123;
(%o2) 123
(%i3) a;
(%o3) 123
</pre></div>
<p>Assignment to an element of a list.
</p>
<div class="example">
<pre class="example">(%i1) b : [1, 2, 3];
(%o1) [1, 2, 3]
(%i2) b[3] : 456;
(%o2) 456
(%i3) b;
(%o3) [1, 2, 456]
</pre></div>
<p>Assignment to a variable that neither is the name of a list nor of an array
creates a <code><a href="maxima_23.html#hashed-array">hashed array</a></code>.
</p>
<div class="example">
<pre class="example">(%i1) c[99] : 789;
(%o1) 789
(%i2) c[99];
(%o2) 789
(%i3) c;
(%o3) c
(%i4) arrayinfo (c);
(%o4) [hashed, 1, [99]]
(%i5) listarray (c);
(%o5) [789]
</pre></div>
<p>Multiple assignment.
</p>
<div class="example">
<pre class="example">(%i1) [a, b, c] : [45, 67, 89];
(%o1) [45, 67, 89]
(%i2) a;
(%o2) 45
(%i3) b;
(%o3) 67
(%i4) c;
(%o4) 89
</pre></div>
<p>Multiple assignment is carried out in parallel.
The values of <code>a</code> and <code>b</code> are exchanged in this example.
</p>
<div class="example">
<pre class="example">(%i1) [a, b] : [33, 55];
(%o1) [33, 55]
(%i2) [a, b] : [b, a];
(%o2) [55, 33]
(%i3) a;
(%o3) 55
(%i4) b;
(%o4) 33
</pre></div>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Evaluation">Evaluation</a>
·<a href="maxima_424.html#Category_003a-Operators">Operators</a>
·</div></dd></dl>
<a name="g_t_003a_003a"></a><a name="Item_003a-Operators_002fdeffn_002f_003a_003a"></a><dl>
<dt><a name="index-_003a_003a"></a>Operator: <strong>::</strong></dt>
<dd><a name="index-Assignment-operator-_0028evaluates-left_002dhand-side_0029"></a>
<p>Assignment operator.
</p>
<p><code>::</code> is the same as <code><a href="#g_t_003a">:</a></code> (which see) except that <code>::</code> evaluates
its left-hand side as well as its right-hand side.
</p>
<p>Examples:
</p>
<div class="example">
<pre class="example">(%i1) x : 'foo;
(%o1) foo
(%i2) x :: 123;
(%o2) 123
(%i3) foo;
(%o3) 123
(%i4) x : '[a, b, c];
(%o4) [a, b, c]
(%i5) x :: [11, 22, 33];
(%o5) [11, 22, 33]
(%i6) a;
(%o6) 11
(%i7) b;
(%o7) 22
(%i8) c;
(%o8) 33
</pre></div>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Evaluation">Evaluation</a>
·<a href="maxima_424.html#Category_003a-Operators">Operators</a>
·</div></dd></dl>
<a name="g_t_003a_003a_003d"></a><a name="Item_003a-Operators_002fdeffn_002f_003a_003a_003d"></a><dl>
<dt><a name="index-_003a_003a_003d"></a>Operator: <strong>::=</strong></dt>
<dd><a name="index-Macro-function-definition-operator"></a>
<p>Macro function definition operator.
<code>::=</code> defines a function (called a "macro" for historical reasons) which
quotes its arguments, and the expression which it returns (called the "macro
expansion") is evaluated in the context from which the macro was called.
A macro function is otherwise the same as an ordinary function.
</p>
<p><code><a href="maxima_169.html#macroexpand">macroexpand</a></code> returns a macro expansion (without evaluating it).
<code>macroexpand (foo (x))</code> followed by <code>''%</code> is equivalent to
<code>foo (x)</code> when <code>foo</code> is a macro function.
</p>
<p><code>::=</code> puts the name of the new macro function onto the global list
<code><a href="maxima_169.html#macros">macros</a></code>. <code><a href="maxima_8.html#kill">kill</a></code>, <code><a href="maxima_62.html#remove">remove</a></code>, and <code><a href="maxima_170.html#remfunction">remfunction</a></code><!-- /@w -->
unbind macro function definitions and remove names from <code>macros</code>.
</p>
<p><code><a href="maxima_170.html#fundef">fundef</a></code> or <code><a href="maxima_170.html#dispfun">dispfun</a></code> return a macro function definition or assign it
to a label, respectively.
</p>
<p>Macro functions commonly contain <code><a href="maxima_169.html#buildq">buildq</a></code> and <code><a href="maxima_169.html#splice">splice</a></code> expressions to
construct an expression, which is then evaluated.
</p>
<p>Examples
</p>
<p>A macro function quotes its arguments, so message (1) shows <code>y - z</code>, not
the value of <code>y - z</code>. The macro expansion (the quoted expression
<code>'(print ("(2) x is equal to", x))</code>) is evaluated in the context from which
the macro was called, printing message (2).
</p>
<div class="example">
<pre class="example">(%i1) x: %pi$
(%i2) y: 1234$
(%i3) z: 1729 * w$
(%i4) printq1 (x) ::= block (print ("(1) x is equal to", x),
'(print ("(2) x is equal to", x)))$
(%i5) printq1 (y - z);
(1) x is equal to y - z
(2) x is equal to %pi
(%o5) %pi
</pre></div>
<p>An ordinary function evaluates its arguments, so message (1) shows the value of
<code>y - z</code>. The return value is not evaluated, so message (2) is not printed
until the explicit evaluation <code>''%</code>.
</p>
<div class="example">
<pre class="example">(%i1) x: %pi$
(%i2) y: 1234$
(%i3) z: 1729 * w$
(%i4) printe1 (x) := block (print ("(1) x is equal to", x),
'(print ("(2) x is equal to", x)))$
(%i5) printe1 (y - z);
(1) x is equal to 1234 - 1729 w
(%o5) print((2) x is equal to, x)
(%i6) ''%;
(2) x is equal to %pi
(%o6) %pi
</pre></div>
<p><code>macroexpand</code> returns a macro expansion.
<code>macroexpand (foo (x))</code> followed by <code>''%</code> is equivalent to
<code>foo (x)</code> when <code>foo</code> is a macro function.
</p>
<div class="example">
<pre class="example">(%i1) x: %pi$
(%i2) y: 1234$
(%i3) z: 1729 * w$
(%i4) g (x) ::= buildq ([x], print ("x is equal to", x))$
(%i5) macroexpand (g (y - z));
(%o5) print(x is equal to, y - z)
(%i6) ''%;
x is equal to 1234 - 1729 w
(%o6) 1234 - 1729 w
(%i7) g (y - z);
x is equal to 1234 - 1729 w
(%o7) 1234 - 1729 w
</pre></div>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Function-definition">Function definition</a>
·<a href="maxima_424.html#Category_003a-Operators">Operators</a>
·</div></dd></dl>
<a name="g_t_003a_003d"></a><a name="Item_003a-Operators_002fdeffn_002f_003a_003d"></a><dl>
<dt><a name="index-_003a_003d"></a>Operator: <strong>:=</strong></dt>
<dd><a name="index-Function-definition-operator"></a>
<p>The function definition operator.
</p>
<p><code><var>f</var>(<var>x_1</var>, ..., <var>x_n</var>) := <var>expr</var></code> defines a function named
<var>f</var> with arguments <var>x_1</var>, …, <var>x_n</var> and function body
<var>expr</var>. <code>:=</code> never evaluates the function body (unless explicitly
evaluated by quote-quote <code>'<!-- /@w -->'</code>).
The function body is evaluated every time the function is called.
</p>
<p><code><var>f</var>[<var>x_1</var>, ..., <var>x_n</var>] := <var>expr</var></code> defines a so-called
<code><a href="maxima_168.html#memoizing-function">memoizing function</a></code>.
Its function body is evaluated just once for each distinct value of its arguments,
and that value is returned, without evaluating the function body,
whenever the arguments have those values again.
(A function of this kind is also known as a “array function”.)
</p>
<p><code><var>f</var>[<var>x_1</var>, ..., <var>x_n</var>](<var>y_1</var>, ..., <var>y_m</var>) := <var>expr</var></code>
is a special case of a <code><a href="maxima_168.html#memoizing-function">memoizing function</a></code>.
<code><var>f</var>[<var>x_1</var>, ..., <var>x_n</var>]</code> is a <code><a href="maxima_168.html#memoizing-function">memoizing function</a></code> which returns a lambda expression
with arguments <code><var>y_1</var>, ..., <var>y_m</var></code>.
The function body is evaluated once for each distinct value of <code><var>x_1</var>, ..., <var>x_n</var></code>,
and the body of the lambda expression is that value.
</p>
<p>When the last or only function argument <var>x_n</var> is a list of one element, the
function defined by <code>:=</code> accepts a variable number of arguments. Actual
arguments are assigned one-to-one to formal arguments <var>x_1</var>, …,
<var>x_(n - 1)</var>, and any further actual arguments, if present, are assigned to
<var>x_n</var> as a list.
</p>
<p>All function definitions appear in the same namespace; defining a function
<code>f</code> within another function <code>g</code> does not automatically limit the scope
of <code>f</code> to <code>g</code>. However, <code>local(f)</code> makes the definition of
function <code>f</code> effective only within the block or other compound expression
in which <code><a href="maxima_170.html#local">local</a></code> appears.
</p>
<p>If some formal argument <var>x_k</var> is a quoted symbol, the function defined by
<code>:=</code> does not evaluate the corresponding actual argument. Otherwise all
actual arguments are evaluated.
</p>
<p>See also <code><a href="maxima_170.html#define">define</a></code> and <code><a href="#g_t_003a_003a_003d">::=</a></code>.
</p>
<p>Examples:
</p>
<p><code>:=</code> never evaluates the function body (unless explicitly evaluated by
quote-quote).
</p>
<div class="example">
<pre class="example">(%i1) expr : cos(y) - sin(x);
(%o1) cos(y) - sin(x)
(%i2) F1 (x, y) := expr;
(%o2) F1(x, y) := expr
(%i3) F1 (a, b);
(%o3) cos(y) - sin(x)
(%i4) F2 (x, y) := ''expr;
(%o4) F2(x, y) := cos(y) - sin(x)
(%i5) F2 (a, b);
(%o5) cos(b) - sin(a)
</pre></div>
<p><code>f(<var>x_1</var>, ..., <var>x_n</var>) := ...</code> defines an ordinary function.
</p>
<div class="example">
<pre class="example">(%i1) G1(x, y) := (print ("Evaluating G1 for x=", x, "and y=", y),
x.y - y.x);
(%o1) G1(x, y) := (print("Evaluating G1 for x=", x, "and y=",
y), x . y - y . x)
(%i2) G1([1, a], [2, b]);
Evaluating G1 for x= [1, a] and y= [2, b]
(%o2) 0
(%i3) G1([1, a], [2, b]);
Evaluating G1 for x= [1, a] and y= [2, b]
(%o3) 0
</pre></div>
<p><code>f[<var>x_1</var>, ..., <var>x_n</var>] := ...</code> defines a <code><a href="maxima_168.html#memoizing-function">memoizing function</a></code>.
</p>
<div class="example">
<pre class="example">(%i1) G2[a] := (print ("Evaluating G2 for a=", a), a^2);
2
(%o1) G2 := (print("Evaluating G2 for a=", a), a )
a
(%i2) G2[1234];
Evaluating G2 for a= 1234
(%o2) 1522756
(%i3) G2[1234];
(%o3) 1522756
(%i4) G2[2345];
Evaluating G2 for a= 2345
(%o4) 5499025
(%i5) arrayinfo (G2);
(%o5) [hashed, 1, [1234], [2345]]
(%i6) listarray (G2);
(%o6) [1522756, 5499025]
</pre></div>
<p><code><var>f</var>[<var>x_1</var>, ..., <var>x_n</var>](<var>y_1</var>, ..., <var>y_m</var>) := <var>expr</var></code>
is a special case of a <code><a href="maxima_168.html#memoizing-function">memoizing function</a></code>.
</p>
<div class="example">
<pre class="example">(%i1) G3[n](x) := (print ("Evaluating G3 for n=", n), diff (sin(x)^2,
x, n));
(%o1) G3 (x) := (print("Evaluating G3 for n=", n),
n
2
diff(sin (x), x, n))
(%i2) G3[2];
Evaluating G3 for n= 2
2 2
(%o2) lambda([x], 2 cos (x) - 2 sin (x))
(%i3) G3[2];
2 2
(%o3) lambda([x], 2 cos (x) - 2 sin (x))
(%i4) G3[2](1);
2 2
(%o4) 2 cos (1) - 2 sin (1)
(%i5) arrayinfo (G3);
(%o5) [hashed, 1, [2]]
(%i6) listarray (G3);
2 2
(%o6) [lambda([x], 2 cos (x) - 2 sin (x))]
</pre></div>
<p>When the last or only function argument <var>x_n</var> is a list of one element,
the function defined by <code>:=</code> accepts a variable number of arguments.
</p>
<div class="example">
<pre class="example">(%i1) H ([L]) := apply ("+", L);
(%o1) H([L]) := apply("+", L)
(%i2) H (a, b, c);
(%o2) c + b + a
</pre></div>
<p><code>local</code> makes a local function definition.
</p>
<div class="example">
<pre class="example">(%i1) foo (x) := 1 - x;
(%o1) foo(x) := 1 - x
(%i2) foo (100);
(%o2) - 99
(%i3) block (local (foo), foo (x) := 2 * x, foo (100));
(%o3) 200
(%i4) foo (100);
(%o4) - 99
</pre></div>
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