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<a name="Introduction-to-operators"></a>
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<p>
Next: <a href="maxima_36.html#Arithmetic-operators" accesskey="n" rel="next">Arithmetic operators</a>, Previous: <a href="maxima_34.html#Operators" accesskey="p" rel="previous">Operators</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="Introduction-to-operators-1"></a>
<h3 class="section">7.1 Introduction to operators</h3>
<p>It is possible to define new operators with specified precedence, to undefine
existing operators, or to redefine the precedence of existing operators. An
operator may be unary prefix or unary postfix, binary infix, n-ary infix,
matchfix, or nofix. "Matchfix" means a pair of symbols which enclose their
argument or arguments, and "nofix" means an operator which takes no arguments.
As examples of the different types of operators, there are the following.
</p>
<dl compact="compact">
<dt>unary prefix</dt>
<dd><p>negation <code>- a</code>
</p></dd>
<dt>unary postfix</dt>
<dd><p>factorial <code>a!</code>
</p></dd>
<dt>binary infix</dt>
<dd><p>exponentiation <code>a^b</code>
</p></dd>
<dt>n-ary infix</dt>
<dd><p>addition <code>a + b</code>
</p></dd>
<dt>matchfix</dt>
<dd><p>list construction <code>[a, b]</code>
</p></dd>
</dl>
<p>(There are no built-in nofix operators; for an example of such an operator,
see <code>nofix</code>.)
</p>
<p>The mechanism to define a new operator is straightforward. It is only necessary
to declare a function as an operator; the operator function might or might not
be defined.
</p>
<p>An example of user-defined operators is the following. Note that the explicit
function call <code>"dd" (a)</code> is equivalent to <code>dd a</code>, likewise
<code>"<-" (a, b)</code> is equivalent to <code>a <- b</code>. Note also that the functions
<code>"dd"</code> and <code>"<-"</code> are undefined in this example.
</p>
<div class="example">
<pre class="example">(%i1) prefix ("dd");
(%o1) dd
(%i2) dd a;
(%o2) dd a
(%i3) "dd" (a);
(%o3) dd a
(%i4) infix ("<-");
(%o4) <-
(%i5) a <- dd b;
(%o5) a <- dd b
(%i6) "<-" (a, "dd" (b));
(%o6) a <- dd b
</pre></div>
<p>The Maxima functions which define new operators are summarized in this table,
stating the default left and right binding powers (lbp and rbp, respectively).
(Binding power determines operator precedence. However, since left and right
binding powers can differ, binding power is somewhat more complicated than
precedence.) Some of the operation definition functions take additional
arguments; see the function descriptions for details.
</p>
<dl compact="compact">
<dt><code>prefix</code></dt>
<dd><p>rbp=180
</p></dd>
<dt><code>postfix</code></dt>
<dd><p>lbp=180
</p></dd>
<dt><code>infix</code></dt>
<dd><p>lbp=180, rbp=180
</p></dd>
<dt><code>nary</code></dt>
<dd><p>lbp=180, rbp=180
</p></dd>
<dt><code>matchfix</code></dt>
<dd><p>(binding power not applicable)
</p></dd>
<dt><code>nofix</code></dt>
<dd><p>(binding power not applicable)
</p></dd>
</dl>
<p>For comparison, here are some built-in operators and their left and right
binding powers.
</p>
<div class="example">
<pre class="example">Operator lbp rbp
: 180 20
:: 180 20
:= 180 20
::= 180 20
! 160
!! 160
^ 140 139
. 130 129
* 120
/ 120 120
+ 100 100
- 100 134
= 80 80
# 80 80
> 80 80
>= 80 80
< 80 80
<= 80 80
not 70
and 65
or 60
, 10
$ -1
; -1
</pre></div>
<p><code><a href="maxima_62.html#remove">remove</a></code> and <code><a href="maxima_8.html#kill">kill</a></code> remove operator properties from an atom.
<code>remove ("<var>a</var>", op)</code> removes only the operator properties of <var>a</var>.
<code>kill ("<var>a</var>")</code> removes all properties of <var>a</var>, including the
operator properties. Note that the name of the operator must be enclosed in
quotation marks.
</p>
<div class="example">
<pre class="example">(%i1) infix ("##");
(%o1) ##
(%i2) "##" (a, b) := a^b;
b
(%o2) a ## b := a
(%i3) 5 ## 3;
(%o3) 125
(%i4) remove ("##", op);
(%o4) done
(%i5) 5 ## 3;
Incorrect syntax: # is not a prefix operator
5 ##
^
(%i5) "##" (5, 3);
(%o5) 125
(%i6) infix ("##");
(%o6) ##
(%i7) 5 ## 3;
(%o7) 125
(%i8) kill ("##");
(%o8) done
(%i9) 5 ## 3;
Incorrect syntax: # is not a prefix operator
5 ##
^
(%i9) "##" (5, 3);
(%o9) ##(5, 3)
</pre></div>
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Categories:<a href="maxima_424.html#Category_003a-Operators">Operators</a>
·<a href="maxima_424.html#Category_003a-Syntax">Syntax</a>
·</div>
<a name="Item_003a-Operators_002fnode_002fArithmetic-operators"></a><hr>
<div class="header">
<p>
Next: <a href="maxima_36.html#Arithmetic-operators" accesskey="n" rel="next">Arithmetic operators</a>, Previous: <a href="maxima_34.html#Operators" accesskey="p" rel="previous">Operators</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>
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