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<title>Maxima 5.47.0 Manual: Functions and Variables for Properties</title>

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<a name="Functions-and-Variables-for-Properties"></a>
<div class="header">
<p>
Next: <a href="maxima_63.html#Functions-and-Variables-for-Facts" accesskey="n" rel="next">Functions and Variables for Facts</a>, Previous: <a href="maxima_61.html#Introduction-to-Maxima_0027s-Database" accesskey="p" rel="previous">Introduction to Maxima's Database</a>, Up: <a href="maxima_60.html#Maxima_0027s-Database" accesskey="u" rel="up">Maxima's Database</a> &nbsp; [<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="Functions-and-Variables-for-Properties-1"></a>
<h3 class="section">11.2 Functions and Variables for Properties</h3>

<a name="alphabetic"></a><a name="Item_003a-Database_002fdefvr_002falphabetic"></a><dl>
<dt><a name="index-alphabetic"></a>Property: <strong>alphabetic</strong></dt>
<dd>
<p><code>alphabetic</code> is a property type recognized by <code><a href="#declare">declare</a></code>.<!-- /@w -->
The expression <code>declare(<var>s</var>, alphabetic)</code> tells Maxima to recognize
as alphabetic all of the characters in <var>s</var>, which must be a string.
</p>
<p>See also <a href="maxima_31.html#Identifiers">Identifiers</a>.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) xx\~yy\`\@ : 1729;
(%o1)                         1729
(%i2) declare (&quot;~`@&quot;, alphabetic);
(%o2)                         done
(%i3) xx~yy`@ + @yy`xx + `xx@@yy~;
(%o3)               `xx@@yy~ + @yy`xx + 1729
(%i4) listofvars (%);
(%o4)                  [@yy`xx, `xx@@yy~]
</pre></div>

<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
&middot;</div></dd></dl>

<a name="bindtest"></a><a name="Item_003a-Database_002fdefvr_002fbindtest"></a><dl>
<dt><a name="index-bindtest"></a>Property: <strong>bindtest</strong></dt>
<dd>
<p>The command <code>declare(<var>x</var>, bindtest)</code> tells Maxima to trigger an error
when the symbol <var>x</var> is evaluated unbound.
</p>
<div class="example">
<pre class="example">(%i1) aa + bb;
(%o1)                        bb + aa
(%i2) declare (aa, bindtest);
(%o2)                         done
(%i3) aa + bb;
aa unbound variable
 -- an error.  Quitting.  To debug this try debugmode(true);
(%i4) aa : 1234;
(%o4)                         1234
(%i5) aa + bb;
(%o5)                       bb + 1234
</pre></div>
</dd></dl>


<a name="constant"></a><a name="Item_003a-Database_002fdeffn_002fconstant"></a><dl>
<dt><a name="index-constant"></a>Property: <strong>constant</strong></dt>
<dd>
<p><code>declare(<var>a</var>, constant)</code> declares <var>a</var> to be a constant.  The
declaration of a symbol to be constant does not prevent the assignment of a
nonconstant value to the symbol.
</p>
<p>See <code><a href="#constantp">constantp</a></code> and <code><a href="#declare">declare</a></code>.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) declare(c, constant);
(%o1)                         done
(%i2) constantp(c);
(%o2)                         true
(%i3) c : x;
(%o3)                           x
(%i4) constantp(c);
(%o4)                         false
</pre></div>

<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
&middot;<a href="maxima_424.html#Category_003a-Constants">Constants</a>
&middot;</div></dd></dl>

<a name="constantp"></a><a name="Item_003a-Database_002fdeffn_002fconstantp"></a><dl>
<dt><a name="index-constantp"></a>Function: <strong>constantp</strong> <em>(<var>expr</var>)</em></dt>
<dd>
<p>Returns <code>true</code> if <var>expr</var> is a constant expression, otherwise returns
<code>false</code>.
</p>
<p>An expression is considered a constant expression if its arguments are
numbers (including rational numbers, as displayed with <code>/R/</code>),
symbolic constants such as <code><a href="maxima_18.html#g_t_0025pi">%pi</a></code>, <code><a href="maxima_18.html#g_t_0025e">%e</a></code>, and <code><a href="maxima_18.html#g_t_0025i">%i</a></code>,<!-- /@w -->
variables bound to a constant or declared constant by <code><a href="#declare">declare</a></code>,<!-- /@w -->
or functions whose arguments are constant.
</p>
<p><code>constantp</code> evaluates its arguments.
</p>
<p>See the property <code><a href="#constant">constant</a></code> which declares a symbol to be constant.
</p>
<p>Examples:
</p>
<div class="example">
<pre class="example">(%i1) constantp (7 * sin(2));
(%o1)                                true
(%i2) constantp (rat (17/29));
(%o2)                                true
(%i3) constantp (%pi * sin(%e));
(%o3)                                true
(%i4) constantp (exp (x));
(%o4)                                false
(%i5) declare (x, constant);
(%o5)                                done
(%i6) constantp (exp (x));
(%o6)                                true
(%i7) constantp (foo (x) + bar (%e) + baz (2));
(%o7)                                false
(%i8) 
</pre></div>

<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Predicate-functions">Predicate functions</a>
&middot;<a href="maxima_424.html#Category_003a-Constants">Constants</a>
&middot;</div></dd></dl>


<a name="declare"></a><a name="Item_003a-Database_002fdeffn_002fdeclare"></a><dl>
<dt><a name="index-declare"></a>Function: <strong>declare</strong> <em>(<var>a_1</var>, <var>p_1</var>, <var>a_2</var>, <var>p_2</var>, &hellip;)</em></dt>
<dd>
<p>Assigns the atom or list of atoms <var>a_i</var> the property or list of properties
<var>p_i</var>.  When <var>a_i</var> and/or <var>p_i</var> are lists, each of the atoms gets
all of the properties.
</p>
<p><code>declare</code> quotes its arguments.  <code>declare</code> always returns <code>done</code>.
</p>
<p>As noted in the description for each declaration flag, for some flags
<code>featurep(<var>object</var>, <var>feature</var>)</code> returns <code>true</code> if <var>object</var>
has been declared to have <var>feature</var>.
</p>
<p>For more information about the features system, see <code><a href="#features">features</a></code>. To
remove a property from an atom, use <code><a href="#remove">remove</a></code>.
</p>
<p><code>declare</code> recognizes the following properties:
</p>
<dl compact="compact">
<dt><code><code><a href="maxima_46.html#additive">additive</a></code></code></dt>
<dd><p>Tells Maxima to simplify <var>a_i</var> expressions by the substitution
<code><var>a_i</var>(x + y + z + ...)</code> <code>--&gt;</code>
<code><var>a_i</var>(x) + <var>a_i</var>(y) + <var>a_i</var>(z) + ...</code>.
The substitution is carried out on the first argument only.
</p>
</dd>
<dt><code><code><a href="#alphabetic">alphabetic</a></code></code></dt>
<dd><p>Tells Maxima to recognize all characters in <var>a_i</var> (which must be a
string) as alphabetic characters.
</p>
</dd>
<dt><code><code><a href="maxima_46.html#antisymmetric">antisymmetric</a></code>, <code><a href="maxima_46.html#commutative">commutative</a></code>, <code><a href="maxima_46.html#symmetric">symmetric</a></code></code></dt>
<dd><p>Tells Maxima to recognize <var>a_i</var> as a symmetric or antisymmetric
function.  <code>commutative</code> is the same as <code>symmetric</code>.
</p>
</dd>
<dt><code><code><a href="#bindtest">bindtest</a></code></code></dt>
<dd><p>Tells Maxima to trigger an error when <var>a_i</var> is evaluated unbound.
</p>
</dd>
<dt><code><code><a href="#constant">constant</a></code></code></dt>
<dd><p>Tells Maxima to consider <var>a_i</var> a symbolic constant.
</p>
</dd>
<dt><code><code><a href="#even">even</a></code>, <code><a href="#odd">odd</a></code></code></dt>
<dd><p>Tells Maxima to recognize <var>a_i</var> as an even or odd integer variable.
</p>
</dd>
<dt><code><code><a href="maxima_46.html#evenfun">evenfun</a></code>, <code><a href="maxima_46.html#oddfun">oddfun</a></code></code></dt>
<dd><p>Tells Maxima to recognize <var>a_i</var> as an odd or even function.
</p>
</dd>
<dt><code><code><a href="maxima_43.html#evflag">evflag</a></code></code></dt>
<dd><p>Makes <var>a_i</var> known to the <code>ev</code> function so that <var>a_i</var> is bound
to <code>true</code> during the execution of <code>ev</code> when <var>a_i</var> appears as
a flag argument of <code>ev</code>.
</p>
</dd>
<dt><code><code><a href="maxima_43.html#evfun">evfun</a></code></code></dt>
<dd><p>Makes <var>a_i</var> known to <code>ev</code> so that the function named by <var>a_i</var>
is applied when <var>a_i</var> appears as a flag argument of <code>ev</code>.
</p>

</dd>
<dt><code><code><a href="#feature">feature</a></code></code></dt>
<dd><p>Tells Maxima to recognize <var>a_i</var> as the name of a feature.
Other atoms may then be declared to have the <var>a_i</var> property.
</p>
</dd>
<dt><code><code><a href="#increasing">increasing</a></code>, <code><a href="#decreasing">decreasing</a></code></code></dt>
<dd><p>Tells Maxima to recognize <var>a_i</var> as an increasing or decreasing
function.
</p>
</dd>
<dt><code><code><a href="#integer">integer</a></code>, <code><a href="#noninteger">noninteger</a></code></code></dt>
<dd><p>Tells Maxima to recognize <var>a_i</var> as an integer or noninteger variable.
</p>
</dd>
<dt><code><code><a href="#integervalued">integervalued</a></code></code></dt>
<dd><p>Tells Maxima to recognize <var>a_i</var> as an integer-valued function.
</p>
</dd>
<dt><code><code><a href="maxima_46.html#lassociative">lassociative</a></code>, <code><a href="maxima_46.html#rassociative">rassociative</a></code></code></dt>
<dd><p>Tells Maxima to recognize <var>a_i</var> as a right-associative or
left-associative function.
</p>
</dd>
<dt><code><code><a href="maxima_46.html#linear">linear</a></code></code></dt>
<dd><p>Equivalent to declaring <var>a_i</var> both <code>outative</code> and
<code>additive</code>.
</p>
</dd>
<dt><code><code><a href="maxima_33.html#mainvar">mainvar</a></code></code></dt>
<dd><p>Tells Maxima to consider <var>a_i</var> a &quot;main variable&quot;.  A main variable
succeeds all other constants and variables in the canonical ordering of
Maxima expressions, as determined by <code><a href="maxima_33.html#ordergreatp">ordergreatp</a></code>.
</p>
</dd>
<dt><code><code><a href="maxima_46.html#multiplicative">multiplicative</a></code></code></dt>
<dd><p>Tells Maxima to simplify <var>a_i</var> expressions by the substitution
<code><var>a_i</var>(x * y * z * ...)</code> <code>--&gt;</code> 
<code><var>a_i</var>(x) * <var>a_i</var>(y) * <var>a_i</var>(z) * ...</code>.
The substitution is carried out on the first argument only.
</p>
<a name="nary"></a></dd>
<dt><code><code><a href="#nary">nary</a></code></code></dt>
<dd><p>Tells Maxima to recognize <var>a_i</var> as an n-ary function.
</p>
<p>The <code>nary</code> declaration is not the same as calling the <code>nary</code>
function.  The sole effect of <code>declare(foo, nary)</code> is to instruct the
Maxima simplifier to flatten nested expressions, for example, to simplify
<code>foo(x, foo(y, z))</code> to <code>foo(x, y, z)</code>.
</p>
</dd>
<dt><code><code><a href="#nonarray">nonarray</a></code></code></dt>
<dd><p>Tells Maxima to consider <var>a_i</var> not an array.  This declaration
prevents multiple evaluation of a subscripted variable name.
</p>
</dd>
<dt><code><code><a href="#nonscalar">nonscalar</a></code></code></dt>
<dd><p>Tells Maxima to consider <var>a_i</var> a nonscalar variable.  The usual
application is to declare a variable as a symbolic vector or matrix.
</p>
</dd>
<dt><code><code><a href="maxima_33.html#noun">noun</a></code></code></dt>
<dd><p>Tells Maxima to parse <var>a_i</var> as a noun.  The effect of this is to
replace instances of <var>a_i</var> with <code>'<var>a_i</var></code> or
<code>nounify(<var>a_i</var>)</code>, depending on the context.
</p>
</dd>
<dt><code><code><a href="maxima_46.html#outative">outative</a></code></code></dt>
<dd><p>Tells Maxima to simplify <var>a_i</var> expressions by pulling constant factors
out of the first argument.
</p>
<p>When <var>a_i</var> has one argument, a factor is considered constant if it is
a literal or declared constant.
</p>
<p>When <var>a_i</var> has two or more arguments, a factor is considered constant
if the second argument is a symbol and the factor is free of the second
argument.
</p>
</dd>
<dt><code><code><a href="#posfun">posfun</a></code></code></dt>
<dd><p>Tells Maxima to recognize <var>a_i</var> as a positive function.
</p>
</dd>
<dt><code><code><a href="#rational">rational</a></code>, <code><a href="#irrational">irrational</a></code></code></dt>
<dd><p>Tells Maxima to recognize <var>a_i</var> as a rational or irrational real
variable.
</p>
</dd>
<dt><code><code><a href="#real">real</a></code>, <code><a href="#imaginary">imaginary</a></code>, <code><a href="#complex">complex</a></code></code></dt>
<dd><p>Tells Maxima to recognize <var>a_i</var> as a real, pure imaginary, or complex
variable.
</p>
</dd>
<dt><code><code><a href="#scalar">scalar</a></code></code></dt>
<dd><p>Tells Maxima to consider <var>a_i</var> a scalar variable.
</p>
</dd>
</dl>

<p>Examples of the usage of the properties are available in the documentation
for each separate description of a property.
</p>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
&middot;</div></dd></dl>

<a name="decreasing"></a><a name="increasing"></a><a name="Item_003a-Database_002fdefvr_002fdecreasing"></a><dl>
<dt><a name="index-decreasing"></a>Property: <strong>decreasing</strong></dt>
<dd><a name="Item_003a-Database_002fdefvr_002fincreasing"></a></dd><dt><a name="index-increasing"></a>Property: <strong>increasing</strong></dt>
<dd>
<p>The commands <code>declare(<var>f</var>, decreasing)</code> or
<code>declare(<var>f</var>, increasing)</code> tell Maxima to recognize the function
<var>f</var> as an decreasing or increasing function.
</p>
<p>See also <code><a href="#declare">declare</a></code> for more properties.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) assume(a &gt; b);
(%o1)                        [a &gt; b]
(%i2) is(f(a) &gt; f(b));
(%o2)                        unknown
(%i3) declare(f, increasing);
(%o3)                         done
(%i4) is(f(a) &gt; f(b));
(%o4)                         true
</pre></div>

<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
&middot;</div></dd></dl>

<a name="even"></a><a name="odd"></a><a name="Item_003a-Database_002fdefvr_002feven"></a><dl>
<dt><a name="index-even"></a>Property: <strong>even</strong></dt>
<dd><a name="Item_003a-Database_002fdefvr_002fodd"></a></dd><dt><a name="index-odd"></a>Property: <strong>odd</strong></dt>
<dd>
<p><code>declare(<var>a</var>, even)</code> or <code>declare(<var>a</var>, odd)</code> tells Maxima to
recognize the symbol <var>a</var> as an even or odd integer variable.  The
properties <code>even</code> and <code>odd</code> are not recognized by the functions
<code><a href="maxima_13.html#evenp">evenp</a></code>, <code><a href="maxima_13.html#oddp">oddp</a></code>, and <code><a href="maxima_13.html#integerp">integerp</a></code>.
</p>
<p>See also <code><a href="#declare">declare</a></code> and <code><a href="maxima_63.html#askinteger">askinteger</a></code>.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) declare(n, even);
(%o1)                         done
(%i2) askinteger(n, even);
(%o2)                          yes
(%i3) askinteger(n);
(%o3)                          yes
(%i4) evenp(n);
(%o4)                         false
</pre></div>

<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
&middot;</div></dd></dl>


<a name="feature"></a><a name="Item_003a-Database_002fdefvr_002ffeature"></a><dl>
<dt><a name="index-feature"></a>Property: <strong>feature</strong></dt>
<dd>
<p>Maxima understands two distinct types of features, system features and features
which apply to mathematical expressions.  See also <code><a href="maxima_155.html#status">status</a></code> for information
about system features.  See also <code><a href="#features">features</a></code> and <code><a href="#featurep">featurep</a></code> for
information about mathematical features.
</p>
<p><code>feature</code> itself is not the name of a function or variable.
</p></dd></dl>


<a name="featurep"></a><a name="Item_003a-Database_002fdeffn_002ffeaturep"></a><dl>
<dt><a name="index-featurep"></a>Function: <strong>featurep</strong> <em>(<var>a</var>, <var>f</var>)</em></dt>
<dd>
<p>Attempts to determine whether the object <var>a</var> has the feature <var>f</var> on the
basis of the facts in the current database.  If so, it returns <code>true</code>,
else <code>false</code>.
</p>
<p>Note that <code>featurep</code> returns <code>false</code> when neither <var>f</var>
nor the negation of <var>f</var> can be established.
</p>
<p><code>featurep</code> evaluates its argument.
</p>
<p>See also <code><a href="#declare">declare</a></code> and <code><a href="#features">features</a></code>.
</p>
<div class="example">
<pre class="example">(%i1) declare (j, even)$
(%i2) featurep (j, integer);
(%o2)                           true
</pre></div>

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&middot;<a href="maxima_424.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
&middot;</div></dd></dl>

<a name="features"></a><a name="Item_003a-Database_002fdefvr_002ffeatures"></a><dl>
<dt><a name="index-features"></a>Declaration: <strong>features</strong></dt>
<dd>
<p>Maxima recognizes certain mathematical properties of functions and variables.
These are called &quot;features&quot;.
</p>
<p><code>declare (<var>x</var>, <var>foo</var>)</code> gives the property <var>foo</var>
to the function or variable <var>x</var>.
</p>
<p><code>declare (<var>foo</var>, feature)</code> declares a new feature <var>foo</var>.
For example,
<code>declare ([red, green, blue], feature)</code>
declares three new features, <code>red</code>, <code>green</code>, and <code>blue</code>.
</p>
<p>The predicate <code>featurep (<var>x</var>, <var>foo</var>)</code>
returns <code>true</code> if <var>x</var> has the <var>foo</var> property,
and <code>false</code> otherwise.
</p>
<p>The infolist <code>features</code> is a list of known features.  These are
</p>
<pre class="verbatim">   integer        noninteger      even
   odd            rational        irrational
   real           imaginary       complex
   analytic       increasing      decreasing
   oddfun         evenfun         posfun
   constant       commutative     lassociative
   rassociative   symmetric       antisymmetric
   integervalued
</pre>
<p>plus any user-defined features.
</p>
<p><code>features</code> is a list of mathematical features.  There is also a list of
non-mathematical, system-dependent features.  See <code><a href="maxima_155.html#status">status</a></code>.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) declare (FOO, feature);
(%o1)                         done
(%i2) declare (x, FOO);
(%o2)                         done
(%i3) featurep (x, FOO);
(%o3)                         true
</pre></div>

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&middot;</div></dd></dl>

<a name="get"></a><a name="Item_003a-Database_002fdeffn_002fget"></a><dl>
<dt><a name="index-get"></a>Function: <strong>get</strong> <em>(<var>a</var>, <var>i</var>)</em></dt>
<dd>
<p>Retrieves the user property indicated by <var>i</var> associated with
atom <var>a</var> or returns <code>false</code> if <var>a</var> doesn&rsquo;t have property <var>i</var>.
</p>
<p><code>get</code> evaluates its arguments.
</p>
<p>See also <code><a href="#put">put</a></code> and <code><a href="#qput">qput</a></code>.
</p>
<div class="example">
<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,&quot;is not numeric.&quot;)) 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>

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Categories:<a href="maxima_424.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
&middot;</div></dd></dl>

<a name="integer"></a><a name="noninteger"></a><a name="Item_003a-Database_002fdefvr_002finteger"></a><dl>
<dt><a name="index-integer"></a>Property: <strong>integer</strong></dt>
<dd><a name="Item_003a-Database_002fdefvr_002fnoninteger"></a></dd><dt><a name="index-noninteger"></a>Property: <strong>noninteger</strong></dt>
<dd>
<p><code>declare(<var>a</var>, integer)</code> or <code>declare(<var>a</var>, noninteger)</code> tells
Maxima to recognize <var>a</var> as an integer or noninteger variable.
</p>
<p>See also <code><a href="#declare">declare</a></code>.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) declare(n, integer, x, noninteger);
(%o1)                         done
(%i2) askinteger(n);
(%o2)                          yes
(%i3) askinteger(x);
(%o3)                          no
</pre></div>

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&middot;</div></dd></dl>

<a name="integervalued"></a><a name="Item_003a-Database_002fdefvr_002fintegervalued"></a><dl>
<dt><a name="index-integervalued"></a>Property: <strong>integervalued</strong></dt>
<dd>
<p><code>declare(<var>f</var>, integervalued)</code> tells Maxima to recognize <var>f</var> as an
integer-valued function.
</p>
<p>See also <code><a href="#declare">declare</a></code>.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) exp(%i)^f(x);
                              %i f(x)
(%o1)                      (%e  )
(%i2) declare(f, integervalued);
(%o2)                         done
(%i3) exp(%i)^f(x);
                              %i f(x)
(%o3)                       %e
</pre></div>

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<a name="nonarray"></a><a name="Item_003a-Database_002fdeffn_002fnonarray"></a><dl>
<dt><a name="index-nonarray"></a>Property: <strong>nonarray</strong></dt>
<dd>
<p>The command <code>declare(a, nonarray)</code> tells Maxima to consider <var>a</var> not
an array.  This declaration prevents multiple evaluation, if <var>a</var> is a
subscripted variable.
</p>
<p>See also <code><a href="#declare">declare</a></code>.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) a:'b$ b:'c$ c:'d$

(%i4) a[x];
(%o4)                          d
                                x
(%i5) declare(a, nonarray);
(%o5)                         done
(%i6) a[x];
(%o6)                          a
                                x
</pre></div>

<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Expressions">Expressions</a>
&middot;</div></dd></dl>


<a name="nonscalar"></a><a name="Item_003a-Database_002fdefvr_002fnonscalar"></a><dl>
<dt><a name="index-nonscalar"></a>Property: <strong>nonscalar</strong></dt>
<dd>
<p>Makes atoms behave as does a list or matrix with respect to the dot operator.
</p>
<p>See also <code><a href="#declare">declare</a></code>.
</p>
<div class=categorybox>
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&middot;<a href="maxima_424.html#Category_003a-Vectors">Vectors</a>
&middot;<a href="maxima_424.html#Category_003a-Matrices">Matrices</a>
&middot;</div></dd></dl>

<a name="nonscalarp"></a><a name="Item_003a-Database_002fdeffn_002fnonscalarp"></a><dl>
<dt><a name="index-nonscalarp"></a>Function: <strong>nonscalarp</strong> <em>(<var>expr</var>)</em></dt>
<dd>
<p>Returns <code>true</code> if <var>expr</var> is a non-scalar, i.e., it contains
atoms declared as non-scalars, lists, or matrices.
</p>
<p>See also the predicate function <code><a href="#scalarp">scalarp</a></code> and <code><a href="#declare">declare</a></code>.
</p>
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&middot;<a href="maxima_424.html#Category_003a-Matrices">Matrices</a>
&middot;</div></dd></dl>


<a name="posfun"></a><a name="Item_003a-Database_002fdefvr_002fposfun"></a><dl>
<dt><a name="index-posfun"></a>Property: <strong>posfun</strong></dt>
<dd>
<p><code>declare (f, posfun)</code> declares <code>f</code> to be a positive function.
<code>is (f(x) &gt; 0)</code> yields <code>true</code>.
</p>
<p>See also <code><a href="#declare">declare</a></code>.
</p>
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&middot;<a href="maxima_424.html#Category_003a-Operators">Operators</a>
&middot;</div></dd></dl>


<a name="printprops"></a><a name="Item_003a-Database_002fdeffn_002fprintprops"></a><dl>
<dt><a name="index-printprops"></a>Function: <strong>printprops</strong> <em><br>&nbsp;&nbsp;&nbsp;&nbsp;<tt>printprops</tt> (<var>a</var>, <var>i</var>) <br>&nbsp;&nbsp;&nbsp;&nbsp;<tt>printprops</tt> ([<var>a_1</var>, &hellip;, <var>a_n</var>], <var>i</var>) <br>&nbsp;&nbsp;&nbsp;&nbsp;<tt>printprops</tt> (all, <var>i</var>)</em></dt>
<dd>
<p>Displays the property with the indicator <var>i</var> associated with the atom
<var>a</var>.  <var>a</var> may also be a list of atoms or the atom <code>all</code> in which
case all of the atoms with the given property will be used.  For example,
<code>printprops ([f, g], atvalue)</code>.  <code>printprops</code> is for properties that
cannot otherwise be displayed, i.e.  for <code><a href="maxima_101.html#atvalue">atvalue</a></code>,<!-- /@w -->
<code><a href="maxima_101.html#atomgrad">atomgrad</a></code>, <code><a href="maxima_101.html#gradef">gradef</a></code>, and <code><a href="maxima_162.html#matchdeclare">matchdeclare</a></code>.
</p>
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&middot;<a href="maxima_424.html#Category_003a-Display-functions">Display functions</a>
&middot;</div></dd></dl>


<a name="properties"></a><a name="Item_003a-Database_002fdeffn_002fproperties"></a><dl>
<dt><a name="index-properties"></a>Function: <strong>properties</strong> <em>(<var>a</var>)</em></dt>
<dd>
<p>Returns a list of the names of all the properties associated with the atom
<var>a</var>.
</p>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
&middot;</div></dd></dl>


<a name="props"></a><a name="Item_003a-Database_002fdefvr_002fprops"></a><dl>
<dt><a name="index-props"></a>System variable: <strong>props</strong></dt>
<dd><p>Default value: <code>[]</code>
</p>
<p><code>props</code> are atoms which have any property other than those explicitly
mentioned in <code><a href="maxima_8.html#infolists">infolists</a></code>, such as specified by <code><a href="maxima_101.html#atvalue">atvalue</a></code>,<!-- /@w -->
<code><a href="maxima_162.html#matchdeclare">matchdeclare</a></code>, etc., as well as properties specified in the
<code><a href="#declare">declare</a></code> function.
</p>
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&middot;<a href="maxima_424.html#Category_003a-Global-variables">Global variables</a>
&middot;</div></dd></dl>


<a name="propvars"></a><a name="Item_003a-Database_002fdeffn_002fpropvars"></a><dl>
<dt><a name="index-propvars"></a>Function: <strong>propvars</strong> <em>(<var>prop</var>)</em></dt>
<dd>
<p>Returns a list of those atoms on the <code><a href="#props">props</a></code> list which
have the property indicated by <var>prop</var>.  Thus <code>propvars (atvalue)</code>
returns a list of atoms which have atvalues.
</p>
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&middot;</div></dd></dl>


<a name="put"></a><a name="Item_003a-Database_002fdeffn_002fput"></a><dl>
<dt><a name="index-put"></a>Function: <strong>put</strong> <em>(<var>atom</var>, <var>value</var>, <var>indicator</var>)</em></dt>
<dd>
<p>Assigns <var>value</var> to the property (specified by <var>indicator</var>) of
<var>atom</var>.  <var>indicator</var> may be the name of any property, not just a
system-defined property.
</p>
<p><code><a href="#rem">rem</a></code> reverses the effect of <code>put</code>.
</p>
<p><code>put</code> evaluates its arguments.
<code>put</code> returns <var>value</var>.
</p>
<p>See also <code><a href="#qput">qput</a></code> and <code><a href="#get">get</a></code>.
</p>
<p>Examples:
</p>
<div class="example">
<pre class="example">(%i1) put (foo, (a+b)^5, expr);
                                   5
(%o1)                       (b + a)
(%i2) put (foo, &quot;Hello&quot;, str);
(%o2)                         Hello
(%i3) properties (foo);
(%o3)            [[user properties, str, expr]]
(%i4) get (foo, expr);
                                   5
(%o4)                       (b + a)
(%i5) get (foo, str);
(%o5)                         Hello
</pre></div>

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&middot;</div></dd></dl>

<a name="qput"></a><a name="Item_003a-Database_002fdeffn_002fqput"></a><dl>
<dt><a name="index-qput"></a>Function: <strong>qput</strong> <em>(<var>atom</var>, <var>value</var>, <var>indicator</var>)</em></dt>
<dd>
<p>Assigns <var>value</var> to the property (specified by <var>indicator</var>) of
<var>atom</var>.  This is the same as <code><a href="#put">put</a></code>, except that the arguments are
quoted.
</p>
<p>See also <code><a href="#get">get</a></code>.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) foo: aa$ 
(%i2) bar: bb$
(%i3) baz: cc$
(%i4) put (foo, bar, baz);
(%o4)                          bb
(%i5) properties (aa);
(%o5)                [[user properties, cc]]
(%i6) get (aa, cc);
(%o6)                          bb
(%i7) qput (foo, bar, baz);
(%o7)                          bar
(%i8) properties (foo);
(%o8)            [value, [user properties, baz]]
(%i9) get ('foo, 'baz);
(%o9)                          bar
</pre></div>

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Categories:<a href="maxima_424.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
&middot;</div></dd></dl>

<a name="rational"></a><a name="irrational"></a><a name="Item_003a-Database_002fdefvr_002frational"></a><dl>
<dt><a name="index-rational-1"></a>Property: <strong>rational</strong></dt>
<dd><a name="Item_003a-Database_002fdefvr_002firrational"></a></dd><dt><a name="index-irrational"></a>Property: <strong>irrational</strong></dt>
<dd>
<p><code>declare(<var>a</var>, rational)</code> or <code>declare(<var>a</var>, irrational)</code> tells
Maxima to recognize <var>a</var> as a rational or irrational real variable.
</p>
<p>See also <code><a href="#declare">declare</a></code>.
</p>
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&middot;</div></dd></dl>

<a name="real"></a><a name="imaginary"></a><a name="complex"></a><a name="Item_003a-Database_002fdefvr_002freal"></a><dl>
<dt><a name="index-real"></a>Property: <strong>real</strong></dt>
<dd><a name="Item_003a-Database_002fdefvr_002fimaginary"></a></dd><dt><a name="index-imaginary"></a>Property: <strong>imaginary</strong></dt>
<dd><a name="Item_003a-Database_002fdefvr_002fcomplex"></a></dd><dt><a name="index-complex"></a>Property: <strong>complex</strong></dt>
<dd>
<p><code>declare(<var>a</var>, real)</code>, <code>declare(<var>a</var>, imaginary)</code>, or
<code>declare(<var>a</var>, complex)</code> tells Maxima to recognize <var>a</var> as a real,
pure imaginary, or complex variable.
</p>
<p>See also <code><a href="#declare">declare</a></code>.
</p>
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Categories:<a href="maxima_424.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
&middot;</div></dd></dl>


<a name="rem"></a><a name="Item_003a-Database_002fdeffn_002frem"></a><dl>
<dt><a name="index-rem"></a>Function: <strong>rem</strong> <em>(<var>atom</var>, <var>indicator</var>)</em></dt>
<dd>
<p>Removes the property indicated by <var>indicator</var> from <var>atom</var>.
<code>rem</code> reverses the effect of <code><a href="#put">put</a></code>.
</p>
<p><code>rem</code> returns <code>done</code> if <var>atom</var> had an <var>indicator</var> property
when <code>rem</code> was called, or <code>false</code> if it had no such property.
</p>
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&middot;</div></dd></dl>


<a name="remove"></a><a name="Item_003a-Database_002fdeffn_002fremove"></a><dl>
<dt><a name="index-remove"></a>Function: <strong>remove</strong> <em><br>&nbsp;&nbsp;&nbsp;&nbsp;<tt>remove</tt> (<var>a_1</var>, <var>p_1</var>, &hellip;, <var>a_n</var>, <var>p_n</var>) <br>&nbsp;&nbsp;&nbsp;&nbsp;<tt>remove</tt> ([<var>a_1</var>, &hellip;, <var>a_m</var>], [<var>p_1</var>, &hellip;, <var>p_n</var>], &hellip;) <br>&nbsp;&nbsp;&nbsp;&nbsp;<tt>remove</tt> (&quot;<var>a</var>&quot;, operator) <br>&nbsp;&nbsp;&nbsp;&nbsp;<tt>remove</tt> (<var>a</var>, transfun) <br>&nbsp;&nbsp;&nbsp;&nbsp;<tt>remove</tt> (all, <var>p</var>)</em></dt>
<dd>
<p>Removes properties associated with atoms.
</p>
<p><code>remove (<var>a_1</var>, <var>p_1</var>, ..., <var>a_n</var>, <var>p_n</var>)</code>
removes property <code>p_k</code> from atom <code>a_k</code>.
</p>
<p><code>remove ([<var>a_1</var>, ..., <var>a_m</var>], [<var>p_1</var>, ..., <var>p_n</var>], ...)</code>
removes properties <code><var>p_1</var>, ..., <var>p_n</var></code>
from atoms <var>a_1</var>, &hellip;, <var>a_m</var>.
There may be more than one pair of lists.
</p>
<p><code>remove (all, <var>p</var>)</code> removes the property <var>p</var> from all atoms which
have it.
</p>
<p>The removed properties may be system-defined properties such as
<code>function</code>, <code>macro</code>, or <code><a href="maxima_170.html#mode_005fdeclare">mode_declare</a></code>.
<code>remove</code> does not remove properties defined by <code><a href="#put">put</a></code>.
</p>
<p>A property may be <code>transfun</code> to remove
the translated Lisp version of a function.
After executing this, the Maxima version of the function is executed
rather than the translated version.
</p>
<p><code>remove (&quot;<var>a</var>&quot;, operator)</code> or, equivalently,
<code>remove (&quot;<var>a</var>&quot;, op)</code> removes from <var>a</var> the operator properties
declared by <code><a href="maxima_41.html#prefix">prefix</a></code>, <code><a href="maxima_41.html#infix">infix</a></code>,<!-- /@w -->
<code><a href="maxima_41.html#function_005fnary">nary</a></code>, <code><a href="maxima_41.html#postfix">postfix</a></code>, <code><a href="maxima_41.html#matchfix">matchfix</a></code>, or
<code><a href="maxima_41.html#nofix">nofix</a></code>.  Note that the name of the operator must be written as a quoted
string.
</p>
<p><code>remove</code> always returns <code>done</code> whether or not an atom has a specified
property.  This behavior is unlike the more specific remove functions
<code><a href="maxima_159.html#remvalue">remvalue</a></code>, <code><a href="maxima_24.html#remarray">remarray</a></code>, <code><a href="maxima_170.html#remfunction">remfunction</a></code>, and
<code><a href="maxima_162.html#remrule">remrule</a></code>.
</p>
<p><code>remove</code> quotes its arguments.
</p>
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&middot;</div></dd></dl>

<a name="scalar"></a><a name="Item_003a-Database_002fdefvr_002fscalar"></a><dl>
<dt><a name="index-scalar"></a>Property: <strong>scalar</strong></dt>
<dd>
<p><code>declare(<var>a</var>, scalar)</code> tells Maxima to consider <var>a</var> a scalar
variable.
</p>
<p>See also <code><a href="#declare">declare</a></code>.
</p>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
&middot;</div></dd></dl>


<a name="scalarp"></a><a name="Item_003a-Database_002fdeffn_002fscalarp"></a><dl>
<dt><a name="index-scalarp"></a>Function: <strong>scalarp</strong> <em>(<var>expr</var>)</em></dt>
<dd>
<p>Returns <code>true</code> if <var>expr</var> is a number, constant, or variable declared
<code><a href="#scalar">scalar</a></code> with <code><a href="#declare">declare</a></code>, or composed entirely of numbers,
constants, and such variables, but not containing matrices or lists.
</p>
<p>See also the predicate function <code><a href="#nonscalarp">nonscalarp</a></code>.
</p>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Predicate-functions">Predicate functions</a>
&middot;<a href="maxima_424.html#Category_003a-Vectors">Vectors</a>
&middot;<a href="maxima_424.html#Category_003a-Matrices">Matrices</a>
&middot;</div></dd></dl>

<a name="Item_003a-Database_002fnode_002fFunctions-and-Variables-for-Facts"></a><hr>
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