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<a name="Functions-and-Variables-for-Predicates"></a>
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<p>
Previous: <a href="maxima_63.html#Functions-and-Variables-for-Facts" accesskey="p" rel="previous">Functions and Variables for Facts</a>, Up: <a href="maxima_60.html#Maxima_0027s-Database" accesskey="u" rel="up">Maxima's Database</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="Functions-and-Variables-for-Predicates-1"></a>
<h3 class="section">11.4 Functions and Variables for Predicates</h3>
<a name="charfun"></a><a name="Item_003a-Database_002fdeffn_002fcharfun"></a><dl>
<dt><a name="index-charfun"></a>Function: <strong>charfun</strong> <em>(<var>p</var>)</em></dt>
<dd>
<p>Return 0 when the predicate <var>p</var> evaluates to <code>false</code>; return 1 when
the predicate evaluates to <code>true</code>. When the predicate evaluates to
something other than <code>true</code> or <code>false</code> (unknown), return a noun form.
</p>
<p>Examples:
</p>
<div class="example">
<pre class="example">(%i1) charfun (x < 1);
(%o1) charfun(x < 1)
(%i2) subst (x = -1, %);
(%o2) 1
(%i3) e : charfun ('"and" (-1 < x, x < 1))$
(%i4) [subst (x = -1, e), subst (x = 0, e), subst (x = 1, e)];
(%o4) [0, 1, 0]
</pre></div>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Mathematical-functions">Mathematical functions</a>
·</div></dd></dl>
<a name="compare"></a><a name="Item_003a-Database_002fdeffn_002fcompare"></a><dl>
<dt><a name="index-compare"></a>Function: <strong>compare</strong> <em>(<var>x</var>, <var>y</var>)</em></dt>
<dd>
<p>Return a comparison operator <var>op</var> (<code><</code>, <code><=</code>, <code>></code>, <code>>=</code>,
<code>=</code>, or <code>#</code>) such that <code>is (<var>x</var> <var>op</var> <var>y</var>)</code> evaluates
to <code>true</code>; when either <var>x</var> or <var>y</var> depends on <code>%i</code> and
<code><var>x</var> # <var>y</var></code>, return <code>notcomparable</code>; when there is no such
operator or Maxima isn’t able to determine the operator, return <code>unknown</code>.
</p>
<p>Examples:
</p>
<div class="example">
<pre class="example">(%i1) compare (1, 2);
(%o1) <
(%i2) compare (1, x);
(%o2) unknown
(%i3) compare (%i, %i);
(%o3) =
(%i4) compare (%i, %i + 1);
(%o4) notcomparable
(%i5) compare (1/x, 0);
(%o5) #
(%i6) compare (x, abs(x));
(%o6) <=
</pre></div>
<p>The function <code>compare</code> doesn’t try to determine whether the real domains of
its arguments are nonempty; thus
</p>
<div class="example">
<pre class="example">(%i1) compare (acos (x^2 + 1), acos (x^2 + 1) + 1);
(%o1) <
</pre></div>
<p>The real domain of <code>acos (x^2 + 1)</code> is empty.
</p>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
·</div></dd></dl>
<a name="equal"></a><a name="Item_003a-Database_002fdeffn_002fequal"></a><dl>
<dt><a name="index-equal"></a>Function: <strong>equal</strong> <em>(<var>a</var>, <var>b</var>)</em></dt>
<dd>
<p>Represents equivalence, that is, equal value.
</p>
<p>By itself, <code>equal</code> does not evaluate or simplify.
The function <code><a href="maxima_63.html#is">is</a></code> attempts to evaluate <code>equal</code> to a Boolean value.
<code>is(equal(<var>a</var>, <var>b</var>))</code> returns <code>true</code> (or <code>false</code>) if
and only if <var>a</var> and <var>b</var> are equal (or not equal) for all possible
values of their variables, as determined by evaluating
<code>ratsimp(<var>a</var> - <var>b</var>)</code>; if <code><a href="maxima_80.html#ratsimp">ratsimp</a></code> returns 0, the two
expressions are considered equivalent. Two expressions may be equivalent even
if they are not syntactically equal (i.e., identical).
</p>
<p>When <code>is</code> fails to reduce <code>equal</code> to <code>true</code> or <code>false</code>, the
result is governed by the global flag <code><a href="maxima_175.html#prederror">prederror</a></code>. When <code>prederror</code>
is <code>true</code>, <code>is</code> complains with an error message. Otherwise, <code>is</code>
returns <code>unknown</code>.
</p>
<p>In addition to <code>is</code>, some other operators evaluate <code>equal</code> and
<code>notequal</code> to <code>true</code> or <code>false</code>, namely <code><a href="maxima_175.html#if">if</a></code>,<!-- /@w -->
<code><a href="maxima_38.html#and">and</a></code>, <code><a href="maxima_38.html#or">or</a></code>, and <code><a href="maxima_38.html#not">not</a></code>.
</p>
<p>The negation of <code>equal</code> is <code><a href="#notequal">notequal</a></code>.
</p>
<p>Examples:
</p>
<p>By itself, <code>equal</code> does not evaluate or simplify.
</p>
<div class="example">
<pre class="example">(%i1) equal (x^2 - 1, (x + 1) * (x - 1));
2
(%o1) equal(x - 1, (x - 1) (x + 1))
(%i2) equal (x, x + 1);
(%o2) equal(x, x + 1)
(%i3) equal (x, y);
(%o3) equal(x, y)
</pre></div>
<p>The function <code>is</code> attempts to evaluate <code>equal</code> to a Boolean value.
<code>is(equal(<var>a</var>, <var>b</var>))</code> returns <code>true</code> when
<code>ratsimp(<var>a</var> - <var>b</var>)</code> returns 0. Two expressions may be equivalent
even if they are not syntactically equal (i.e., identical).
</p>
<div class="example">
<pre class="example">(%i1) ratsimp (x^2 - 1 - (x + 1) * (x - 1));
(%o1) 0
(%i2) is (equal (x^2 - 1, (x + 1) * (x - 1)));
(%o2) true
(%i3) is (x^2 - 1 = (x + 1) * (x - 1));
(%o3) false
(%i4) ratsimp (x - (x + 1));
(%o4) - 1
(%i5) is (equal (x, x + 1));
(%o5) false
(%i6) is (x = x + 1);
(%o6) false
(%i7) ratsimp (x - y);
(%o7) x - y
(%i8) is (equal (x, y));
(%o8) unknown
(%i9) is (x = y);
(%o9) false
</pre></div>
<p>When <code>is</code> fails to reduce <code>equal</code> to <code>true</code> or <code>false</code>,
the result is governed by the global flag <code>prederror</code>.
</p>
<div class="example">
<pre class="example">(%i1) [aa : x^2 + 2*x + 1, bb : x^2 - 2*x - 1];
2 2
(%o1) [x + 2 x + 1, x - 2 x - 1]
(%i2) ratsimp (aa - bb);
(%o2) 4 x + 2
(%i3) prederror : true;
(%o3) true
(%i4) is (equal (aa, bb));
Maxima was unable to evaluate the predicate:
2 2
equal(x + 2 x + 1, x - 2 x - 1)
-- an error. Quitting. To debug this try debugmode(true);
(%i5) prederror : false;
(%o5) false
(%i6) is (equal (aa, bb));
(%o6) unknown
</pre></div>
<p>Some operators evaluate <code>equal</code> and <code>notequal</code> to <code>true</code> or
<code>false</code>.
</p>
<div class="example">
<pre class="example">(%i1) if equal (y, y - 1) then FOO else BAR;
(%o1) BAR
(%i2) eq_1 : equal (x, x + 1);
(%o2) equal(x, x + 1)
(%i3) eq_2 : equal (y^2 + 2*y + 1, (y + 1)^2);
2 2
(%o3) equal(y + 2 y + 1, (y + 1) )
(%i4) [eq_1 and eq_2, eq_1 or eq_2, not eq_1];
(%o4) [false, true, true]
</pre></div>
<p>Because <code>not <var>expr</var></code> causes evaluation of <var>expr</var>,
<code>not equal(<var>a</var>, <var>b</var>)</code> is equivalent to
<code>is(notequal(<var>a</var>, <var>b</var>))</code>.
</p>
<div class="example">
<pre class="example">(%i1) [notequal (2*z, 2*z - 1), not equal (2*z, 2*z - 1)];
(%o1) [notequal(2 z, 2 z - 1), true]
(%i2) is (notequal (2*z, 2*z - 1));
(%o2) true
</pre></div>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Operators">Operators</a>
·</div></dd></dl>
<a name="notequal"></a><a name="Item_003a-Database_002fdeffn_002fnotequal"></a><dl>
<dt><a name="index-notequal"></a>Function: <strong>notequal</strong> <em>(<var>a</var>, <var>b</var>)</em></dt>
<dd>
<p>Represents the negation of <code>equal(<var>a</var>, <var>b</var>)</code>.
</p>
<p>Examples:
</p>
<div class="example">
<pre class="example">(%i1) equal (a, b);
(%o1) equal(a, b)
(%i2) maybe (equal (a, b));
(%o2) unknown
(%i3) notequal (a, b);
(%o3) notequal(a, b)
(%i4) not equal (a, b);
(%o4) notequal(a, b)
(%i5) maybe (notequal (a, b));
(%o5) unknown
(%i6) assume (a > b);
(%o6) [a > b]
(%i7) equal (a, b);
(%o7) equal(a, b)
(%i8) maybe (equal (a, b));
(%o8) false
(%i9) notequal (a, b);
(%o9) notequal(a, b)
(%i10) maybe (notequal (a, b));
(%o10) true
</pre></div>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Operators">Operators</a>
·</div></dd></dl>
<a name="unknown"></a><a name="Item_003a-Database_002fdeffn_002funknown"></a><dl>
<dt><a name="index-unknown"></a>Function: <strong>unknown</strong> <em>(<var>expr</var>)</em></dt>
<dd>
<p>Returns <code>true</code> if and only if <var>expr</var> contains an operator or function
not recognized by the Maxima simplifier.
</p>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Predicate-functions">Predicate functions</a>
·<a href="maxima_424.html#Category_003a-Simplification-functions">Simplification functions</a>
·</div></dd></dl>
<a name="zeroequiv"></a><a name="Item_003a-Database_002fdeffn_002fzeroequiv"></a><dl>
<dt><a name="index-zeroequiv"></a>Function: <strong>zeroequiv</strong> <em>(<var>expr</var>, <var>v</var>)</em></dt>
<dd>
<p>Tests whether the expression <var>expr</var> in the variable <var>v</var> is equivalent
to zero, returning <code>true</code>, <code>false</code>, or <code>dontknow</code>.
</p>
<p><code>zeroequiv</code> has these restrictions:
</p>
<ol>
<li> Do not use functions that Maxima does not know how to
differentiate and evaluate.
</li><li> If the expression has poles on the real line, there may be errors
in the result (but this is unlikely to occur).
</li><li> If the expression contains functions which are not solutions to first order
differential equations (e.g. Bessel functions) there may be incorrect results.
</li><li> The algorithm uses evaluation at randomly chosen points for carefully selected
subexpressions. This is always a somewhat hazardous business, although the
algorithm tries to minimize the potential for error.
</li></ol>
<p>For example <code>zeroequiv (sin(2 * x) - 2 * sin(x) * cos(x), x)</code> returns
<code>true</code> and <code>zeroequiv (%e^x + x, x)</code> returns <code>false</code>.
On the other hand <code>zeroequiv (log(a * b) - log(a) - log(b), a)</code> returns
<code>dontknow</code> because of the presence of an extra parameter <code>b</code>.
</p>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Predicate-functions">Predicate functions</a>
·</div></dd></dl>
<hr>
<div class="header">
<p>
Previous: <a href="maxima_63.html#Functions-and-Variables-for-Facts" accesskey="p" rel="previous">Functions and Variables for Facts</a>, Up: <a href="maxima_60.html#Maxima_0027s-Database" accesskey="u" rel="up">Maxima's Database</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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