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<title>Predicates relating to numbers</title>
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(directly go to documentation on : <a href="refchapter3.html#<" target='Chapters' title="test for "less than""><</a>, <a href="refchapter3.html#>" target='Chapters' title="test for "greater than"">></a>, <a href="refchapter3.html#<=" target='Chapters' title="test for "less or equal""><=</a>, <a href="refchapter3.html#>=" target='Chapters' title="test for "greater or equal"">>=</a>, <a href="refchapter3.html#IsZero" target='Chapters' title="test whether argument is zero">IsZero</a>, <a href="refchapter3.html#IsRational" target='Chapters' title="test whether argument is a rational">IsRational</a>.
)<h1>
3. Predicates relating to numbers
</h1>
<p> </p>
<center><table>
<tr BGCOLOR=#E0E0E0>
<td><a href="refchapter3.html#<" target='Chapters' title="test for "less than""><</a></td>
<td>test for "less than"</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refchapter3.html#>" target='Chapters' title="test for "greater than"">></a></td>
<td>test for "greater than"</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refchapter3.html#<=" target='Chapters' title="test for "less or equal""><=</a></td>
<td>test for "less or equal"</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refchapter3.html#>=" target='Chapters' title="test for "greater or equal"">>=</a></td>
<td>test for "greater or equal"</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refchapter3.html#IsZero" target='Chapters' title="test whether argument is zero">IsZero</a></td>
<td>test whether argument is zero</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refchapter3.html#IsRational" target='Chapters' title="test whether argument is a rational">IsRational</a></td>
<td>test whether argument is a rational</td>
</tr>
</table></center>
<a name="<">
</a>
<a name="<">
</a>
<h3>
<hr>< -- test for "less than"
</h3>
<h5 align=right>Standard library</h5><h5>
Calling format:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
e1 < e2
</pre></tr>
</table>
Precedence:
90
<p>
<h5>
Parameters:
</h5>
<b><tt>e1</tt></b>, <b><tt>e2</tt></b> -- expressions to be compared
<p>
<h5>
Description:
</h5>
The two expression are evaluated. If both results are numeric, they
are compared. If the first expression is smaller than the second one,
the result is <b><tt>True</tt></b> and it is <b><tt>False</tt></b> otherwise. If either of the expression is not numeric, after
evaluation, the expression is returned with evaluated arguments.
<p>
The word "numeric" in the previous paragraph has the following
meaning. An expression is numeric if it is either a number (i.e. <b><tt>IsNumber</tt></b> returns <b><tt>True</tt></b>), or the
quotient of two numbers, or an infinity (i.e. <b><tt>IsInfinity</tt></b> returns <b><tt>True</tt></b>). Yacas will try to
coerce the arguments passed to this comparison operator to a real value before making the comparison.
<p>
<h5>
Examples:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
In> 2 < 5;
Out> True;
In> Cos(1) < 5;
Out> True;
</pre></tr>
</table>
<p>
<h5>
See also:
</h5>
<a href="ref.html?IsNumber" target="Chapters">
IsNumber
</a>
, <a href="ref.html?IsInfinity" target="Chapters">
IsInfinity
</a>
, <a href="ref.html?N" target="Chapters">
N
</a>
.<a name=">">
</a>
<a name=">">
</a>
<h3>
<hr>> -- test for "greater than"
</h3>
<h5 align=right>Standard library</h5><h5>
Calling format:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
e1 > e2
</pre></tr>
</table>
Precedence:
90
<p>
<h5>
Parameters:
</h5>
<b><tt>e1</tt></b>, <b><tt>e2</tt></b> -- expressions to be compared
<p>
<h5>
Description:
</h5>
The two expression are evaluated. If both results are numeric, they
are compared. If the first expression is larger than the second one,
the result is <b><tt>True</tt></b> and it is <b><tt>False</tt></b> otherwise. If either of the expression is not numeric, after
evaluation, the expression is returned with evaluated arguments.
<p>
The word "numeric" in the previous paragraph has the following
meaning. An expression is numeric if it is either a number (i.e. <b><tt>IsNumber</tt></b> returns <b><tt>True</tt></b>), or the
quotient of two numbers, or an infinity (i.e. <b><tt>IsInfinity</tt></b> returns <b><tt>True</tt></b>). Yacas will try to
coerce the arguments passed to this comparison operator to a real value before making the comparison.
<p>
<h5>
Examples:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
In> 2 > 5;
Out> False;
In> Cos(1) > 5;
Out> False
</pre></tr>
</table>
<p>
<h5>
See also:
</h5>
<a href="ref.html?IsNumber" target="Chapters">
IsNumber
</a>
, <a href="ref.html?IsInfinity" target="Chapters">
IsInfinity
</a>
, <a href="ref.html?N" target="Chapters">
N
</a>
.<a name="<=">
</a>
<a name="<=">
</a>
<h3>
<hr><= -- test for "less or equal"
</h3>
<h5 align=right>Standard library</h5><h5>
Calling format:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
e1 <= e2
</pre></tr>
</table>
Precedence:
90
<p>
<h5>
Parameters:
</h5>
<b><tt>e1</tt></b>, <b><tt>e2</tt></b> -- expressions to be compared
<p>
<h5>
Description:
</h5>
The two expression are evaluated. If both results are numeric, they
are compared. If the first expression is smaller than or equals the
second one, the result is <b><tt>True</tt></b> and it is <b><tt>False</tt></b> otherwise. If either of the expression is not
numeric, after evaluation, the expression is returned with evaluated
arguments.
<p>
The word "numeric" in the previous paragraph has the following
meaning. An expression is numeric if it is either a number (i.e. <b><tt>IsNumber</tt></b> returns <b><tt>True</tt></b>), or the
quotient of two numbers, or an infinity (i.e. <b><tt>IsInfinity</tt></b> returns <b><tt>True</tt></b>). Yacas will try to
coerce the arguments passed to this comparison operator to a real value before making the comparison.
<p>
<h5>
Examples:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
In> 2 <= 5;
Out> True;
In> Cos(1) <= 5;
Out> True
</pre></tr>
</table>
<p>
<h5>
See also:
</h5>
<a href="ref.html?IsNumber" target="Chapters">
IsNumber
</a>
, <a href="ref.html?IsInfinity" target="Chapters">
IsInfinity
</a>
, <a href="ref.html?N" target="Chapters">
N
</a>
.<a name=">=">
</a>
<a name=">=">
</a>
<h3>
<hr>>= -- test for "greater or equal"
</h3>
<h5 align=right>Standard library</h5><h5>
Calling format:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
e1 >= e2
</pre></tr>
</table>
Precedence:
90
<p>
<h5>
Parameters:
</h5>
<b><tt>e1</tt></b>, <b><tt>e2</tt></b> -- expressions to be compared
<p>
<h5>
Description:
</h5>
The two expression are evaluated. If both results are numeric, they
are compared. If the first expression is larger than or equals the
second one, the result is <b><tt>True</tt></b> and it is <b><tt>False</tt></b> otherwise. If either of the expression is not
numeric, after evaluation, the expression is returned with evaluated
arguments.
<p>
The word "numeric" in the previous paragraph has the following
meaning. An expression is numeric if it is either a number (i.e. <b><tt>IsNumber</tt></b> returns <b><tt>True</tt></b>), or the
quotient of two numbers, or an infinity (i.e. <b><tt>IsInfinity</tt></b> returns <b><tt>True</tt></b>). Yacas will try to
coerce the arguments passed to this comparison operator to a real value before making the comparison.
<p>
<h5>
Examples:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
In> 2 >= 5;
Out> False;
In> Cos(1) >= 5;
Out> False
</pre></tr>
</table>
<p>
<h5>
See also:
</h5>
<a href="ref.html?IsNumber" target="Chapters">
IsNumber
</a>
, <a href="ref.html?IsInfinity" target="Chapters">
IsInfinity
</a>
, <a href="ref.html?N" target="Chapters">
N
</a>
.<a name="IsZero">
</a>
<a name="iszero">
</a>
<h3>
<hr>IsZero -- test whether argument is zero
</h3>
<h5 align=right>Standard library</h5><h5>
Calling format:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
IsZero(n)
</pre></tr>
</table>
<p>
<h5>
Parameters:
</h5>
<b><tt>n</tt></b> -- number to test
<p>
<h5>
Description:
</h5>
<b><tt>IsZero(n)</tt></b> evaluates to <b><tt>True</tt></b> if
"n" is zero. In case "n" is not a number, the function returns
<b><tt>False</tt></b>.
<p>
<h5>
Examples:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
In> IsZero(3.25)
Out> False;
In> IsZero(0)
Out> True;
In> IsZero(x)
Out> False;
</pre></tr>
</table>
<p>
<h5>
See also:
</h5>
<a href="ref.html?IsNumber" target="Chapters">
IsNumber
</a>
, <a href="ref.html?IsNotZero" target="Chapters">
IsNotZero
</a>
.<a name="IsRational">
</a>
<a name="isrational">
</a>
<h3>
<hr>IsRational -- test whether argument is a rational
</h3>
<h5 align=right>Standard library</h5><h5>
Calling format:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
IsRational(expr)
</pre></tr>
</table>
<p>
<h5>
Parameters:
</h5>
<b><tt>expr</tt></b> -- expression to test
<p>
<h5>
Description:
</h5>
This commands tests whether the expression "expr" is a rational
number, i.e. an integer or a fraction of integers.
<p>
<h5>
Examples:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
In> IsRational(5)
Out> False;
In> IsRational(2/7)
Out> True;
In> IsRational(0.5)
Out> False;
In> IsRational(a/b)
Out> False;
In> IsRational(x + 1/x)
Out> False;
</pre></tr>
</table>
<p>
<h5>
See also:
</h5>
<a href="ref.html?Numer" target="Chapters">
Numer
</a>
, <a href="ref.html?Denom" target="Chapters">
Denom
</a>
.
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