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<head>
<title>Built-in (core) functions</title>
<link rel="stylesheet" href="yacas.css" TYPE="text/css" MEDIA="screen">
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<a name="c5">
</a>
(directly go to documentation on : <a href="refprogchapter5.html#MathNot" target='Chapters' title="built-in logical "not"">MathNot</a>, <a href="refprogchapter5.html#MathAnd" target='Chapters' title="built-in logical "and"">MathAnd</a>, <a href="refprogchapter5.html#MathOr" target='Chapters' title="built-in logical "or"">MathOr</a>, <a href="refprogchapter5.html#BitAnd" target='Chapters' title="bitwise and operation">BitAnd</a>, <a href="refprogchapter5.html#BitOr" target='Chapters' title="bitwise or operation">BitOr</a>, <a href="refprogchapter5.html#BitXor" target='Chapters' title="bitwise xor operation">BitXor</a>, <a href="refprogchapter5.html#Equals" target='Chapters' title="check equality">Equals</a>, <a href="refprogchapter5.html#GreaterThan" target='Chapters' title="comparison predicate">GreaterThan</a>, <a href="refprogchapter5.html#LessThan" target='Chapters' title="comparison predicate">LessThan</a>, <a href="refprogchapter5.html#Math..." target='Chapters' title="arbitrary-precision math functions">Math...</a>, <a href="refprogchapter5.html#Fast..." target='Chapters' title="double-precision math functions">Fast...</a>, <a href="refprogchapter5.html#ShiftLeft" target='Chapters' title="built-in bitwise shift left operation">ShiftLeft</a>, <a href="refprogchapter5.html#ShiftRight" target='Chapters' title="built-in bitwise shift right operation">ShiftRight</a>, <a href="refprogchapter5.html#IsPromptShown" target='Chapters' title="test for the Yacas prompt option">IsPromptShown</a>, <a href="refprogchapter5.html#GetTime" target='Chapters' title="measure the time taken by an evaluation">GetTime</a>.
)<h1>
5. Built-in (core) functions
</h1>
Yacas comes with a small core of built-in functions and a large library of
user-defined functions. Some of these core functions are documented in this
chapter.
<p> </p>
<center><table>
<tr BGCOLOR=#E0E0E0>
<td><a href="refprogchapter5.html#MathNot" target='Chapters' title="built-in logical "not"">MathNot</a></td>
<td>built-in logical "not"</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refprogchapter5.html#MathAnd" target='Chapters' title="built-in logical "and"">MathAnd</a></td>
<td>built-in logical "and"</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refprogchapter5.html#MathOr" target='Chapters' title="built-in logical "or"">MathOr</a></td>
<td>built-in logical "or"</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refprogchapter5.html#BitAnd" target='Chapters' title="bitwise and operation">BitAnd</a></td>
<td>bitwise and operation</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refprogchapter5.html#BitOr" target='Chapters' title="bitwise or operation">BitOr</a></td>
<td>bitwise or operation</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refprogchapter5.html#BitXor" target='Chapters' title="bitwise xor operation">BitXor</a></td>
<td>bitwise xor operation</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refprogchapter5.html#Equals" target='Chapters' title="check equality">Equals</a></td>
<td>check equality</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refprogchapter5.html#GreaterThan" target='Chapters' title="comparison predicate">GreaterThan</a></td>
<td>comparison predicate</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refprogchapter5.html#LessThan" target='Chapters' title="comparison predicate">LessThan</a></td>
<td>comparison predicate</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refprogchapter5.html#Math..." target='Chapters' title="arbitrary-precision math functions">Math...</a></td>
<td>arbitrary-precision math functions</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refprogchapter5.html#Fast..." target='Chapters' title="double-precision math functions">Fast...</a></td>
<td>double-precision math functions</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refprogchapter5.html#ShiftLeft" target='Chapters' title="built-in bitwise shift left operation">ShiftLeft</a></td>
<td>built-in bitwise shift left operation</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refprogchapter5.html#ShiftRight" target='Chapters' title="built-in bitwise shift right operation">ShiftRight</a></td>
<td>built-in bitwise shift right operation</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refprogchapter5.html#IsPromptShown" target='Chapters' title="test for the Yacas prompt option">IsPromptShown</a></td>
<td>test for the Yacas prompt option</td>
</tr>
<tr BGCOLOR=#E0E0E0>
<td><a href="refprogchapter5.html#GetTime" target='Chapters' title="measure the time taken by an evaluation">GetTime</a></td>
<td>measure the time taken by an evaluation</td>
</tr>
</table></center>
<p>
It is important for a developer to know which functions are built-in and cannot
be redefined or <b><tt>Retract</tt></b>-ed. Also, core functions may be somewhat faster to
execute than functions defined in the script library. All core functions are
listed in the file <b><tt>corefunctions.h</tt></b> in the <b><tt>src/</tt></b> subdirectory of the Yacas
source tree. The declarations typically look like this:
<p>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
SetCommand(LispSubtract, "MathSubtract");
</pre></tr>
</table>
Here <b><tt>LispSubtract</tt></b> is the Yacas internal name for the function and <b><tt>MathSubtract</tt></b> is the name visible to the Yacas language.
Built-in bodied functions and infix operators are declared in the same file.
<p>
<a name="MathNot">
</a>
<a name="mathnot">
</a>
<h3>
<hr>MathNot -- built-in logical "not"
</h3>
<h5 align=right>Internal function</h5><h5>
Calling format:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
MathNot(expression)
</pre></tr>
</table>
<p>
<h5>
Description:
</h5>
Returns "False" if "expression" evaluates
to "True", and vice versa.
<p>
<a name="MathAnd">
</a>
<a name="mathand">
</a>
<h3>
<hr>MathAnd -- built-in logical "and"
</h3>
<h5>
Calling format:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
MathAnd(...)
</pre></tr>
</table>
<p>
<h5>
Description:
</h5>
Lazy logical <b><tt>And</tt></b>: returns <b><tt>True</tt></b> if all args evaluate to
<b><tt>True</tt></b>, and does this by looking at first, and then at the
second argument, until one is <b><tt>False</tt></b>.
If one of the arguments is <b><tt>False</tt></b>, <b><tt>And</tt></b> immediately returns <b><tt>False</tt></b> without
evaluating the rest. This is faster, but also means that none of the
arguments should cause side effects when they are evaluated.
<p>
<a name="MathOr">
</a>
<a name="mathor">
</a>
<h3>
<hr>MathOr -- built-in logical "or"
</h3>
<h5 align=right>Internal function</h5><h5>
Calling format:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
MathOr(...)
</pre></tr>
</table>
<p>
<b><tt>MathOr</tt></b> is the basic logical "or" function. Similarly to <b><tt>And</tt></b>, it is
lazy-evaluated. <b><tt>And(...)</tt></b> and <b><tt>Or(...)</tt></b> do also exist, defined in the script
library. You can redefine them as infix operators yourself, so you have the
choice of precedence. In the standard scripts they are in fact declared as
infix operators, so you can write <b><tt>expr1 And expr</tt></b>.
<p>
<a name="BitAnd">
</a>
<a name="bitand">
</a>
<h3>
<hr>BitAnd -- bitwise and operation
</h3>
<a name="BitOr">
</a>
<a name="bitor">
</a>
<h3>
<hr>BitOr -- bitwise or operation
</h3>
<a name="BitXor">
</a>
<a name="bitxor">
</a>
<h3>
<hr>BitXor -- bitwise xor operation
</h3>
<h5 align=right>Internal function</h5><h5>
Calling format:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
BitAnd(n,m)
BitOr(n,m)
BitXor(n,m)
</pre></tr>
</table>
<p>
<h5>
Description:
</h5>
These functions return bitwise "and", "or" and "xor"
of two numbers.
<p>
<a name="Equals">
</a>
<a name="equals">
</a>
<h3>
<hr>Equals -- check equality
</h3>
<h5 align=right>Internal function</h5><h5>
Calling format:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
Equals(a,b)
</pre></tr>
</table>
<p>
<h5>
Description:
</h5>
Compares evaluated <b><tt>a</tt></b> and <b><tt>b</tt></b> recursively
(stepping into expressions). So "Equals(a,b)" returns
"True" if the expressions would be printed exactly
the same, and "False" otherwise.
<p>
<a name="GreaterThan">
</a>
<a name="greaterthan">
</a>
<h3>
<hr>GreaterThan -- comparison predicate
</h3>
<a name="LessThan">
</a>
<a name="lessthan">
</a>
<h3>
<hr>LessThan -- comparison predicate
</h3>
<h5 align=right>Internal function</h5><h5>
Calling format:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
GreaterThan(a,b)
LessThan(a,b)
</pre></tr>
</table>
<p>
<h5>
Parameters:
</h5>
<b><tt>a</tt></b>, <b><tt>b</tt></b> -- numbers or strings
<h5>
Description:
</h5>
Comparing numbers or strings (lexicographically).
<p>
<h5>
Example:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
In> LessThan(1,1)
Out> False;
In> LessThan("a","b")
Out> True;
</pre></tr>
</table>
<p>
<a name="MathExp@\relax <b><tt>MathExp</tt></b>">
</a>
<a name="MathLog@\relax <b><tt>MathLog</tt></b>">
</a>
<a name="MathPower@\relax <b><tt>MathPower</tt></b>">
</a>
<a name="MathSin@\relax <b><tt>MathSin</tt></b>">
</a>
<a name="MathCos@\relax <b><tt>MathCos</tt></b>">
</a>
<a name="MathTan@\relax <b><tt>MathTan</tt></b>">
</a>
<a name="MathArcSin@\relax <b><tt>MathArcSin</tt></b>">
</a>
<a name="MathArcCos@\relax <b><tt>MathArcCos</tt></b>">
</a>
<a name="MathArcTan@\relax <b><tt>MathArcTan</tt></b>">
</a>
<a name="MathSinh@\relax <b><tt>MathSinh</tt></b>">
</a>
<a name="MathCosh@\relax <b><tt>MathCosh</tt></b>">
</a>
<a name="MathTanh@\relax <b><tt>MathTanh</tt></b>">
</a>
<a name="MathArcSinh@\relax <b><tt>MathArcSinh</tt></b>">
</a>
<a name="MathArcCosh@\relax <b><tt>MathArcCosh</tt></b>">
</a>
<a name="MathArcTanh@\relax <b><tt>MathArcTanh</tt></b>">
</a>
<a name="MathGcd@\relax <b><tt>MathGcd</tt></b>">
</a>
<a name="MathAdd@\relax <b><tt>MathAdd</tt></b>">
</a>
<a name="MathSubtract@\relax <b><tt>MathSubtract</tt></b>">
</a>
<a name="MathMultiply@\relax <b><tt>MathMultiply</tt></b>">
</a>
<a name="MathDivide@\relax <b><tt>MathDivide</tt></b>">
</a>
<a name="MathSqrt@\relax <b><tt>MathSqrt</tt></b>">
</a>
<a name="MathFloor@\relax <b><tt>MathFloor</tt></b>">
</a>
<a name="MathCeil@\relax <b><tt>MathCeil</tt></b>">
</a>
<a name="MathAbs@\relax <b><tt>MathAbs</tt></b>">
</a>
<a name="MathMod@\relax <b><tt>MathMod</tt></b>">
</a>
<a name="MathDiv@\relax <b><tt>MathDiv</tt></b>">
</a>
<a name="Math...">
</a>
<a name="math...">
</a>
<h3>
<hr>Math... -- arbitrary-precision math functions
</h3>
<h5 align=right>Internal function</h5><h5>
Calling format:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
MathGcd(n,m) (Greatest Common Divisor)
MathAdd(x,y) (add two numbers)
MathSubtract(x,y) (subtract two numbers)
MathMultiply(x,y) (multiply two numbers)
MathDivide(x,y) (divide two numbers)
MathSqrt(x) (square root, must be x>=0)
MathFloor(x) (largest integer not larger than x)
MathCeil(x) (smallest integer not smaller than x)
MathAbs(x) (absolute value of x, or |x| )
MathExp(x) (exponential, base 2.718...)
MathLog(x) (natural logarithm, for x>0)
MathPower(x,y) (power, x ^ y)
MathSin(x) (sine)
MathCos(x) (cosine)
MathTan(x) (tangent)
MathSinh(x) (hyperbolic sine)
MathCosh(x) (hyperbolic cosine)
MathTanh(x) (hyperbolic tangent)
MathArcSin(x) (inverse sine)
MathArcCos(x) (inverse cosine)
MathArcTan(x) (inverse tangent)
MathArcSinh(x) (inverse hyperbolic sine)
MathArcCosh(x) (inverse hyperbolic cosine)
MathArcTanh(x) (inverse hyperbolic tangent)
MathDiv(x,y) (integer division, result is an integer)
MathMod(x,y) (remainder of division, or x mod y)
</pre></tr>
</table>
<p>
<h5>
Description:
</h5>
These commands perform the calculation of elementary mathematical functions.
The arguments <i>must</i> be numbers.
The reason for the prefix <b><tt>Math</tt></b> is that
the library needs to define equivalent
non-numerical functions for symbolic computations, such as <b><tt>Exp</tt></b>, <b><tt>Sin</tt></b> and so on.
<p>
Note that all functions, such as the <b><tt>MathPower</tt></b>, <b><tt>MathSqrt</tt></b>, <b><tt>MathAdd</tt></b> etc., accept integers as well as floating-point numbers.
The resulting values may be integers or floats.
If the mathematical result is an exact integer, then the integer is returned.
For example, <b><tt>MathSqrt(25)</tt></b> returns the integer <b><tt>5</tt></b>, and <b><tt>MathPower(2,3)</tt></b> returns the integer <b><tt>8</tt></b>.
In such cases, the integer result is returned even if the calculation requires more digits than set by <b><tt>Builtin'Precision'Set</tt></b>.
However, when the result is mathematically not an integer, the functions return a floating-point result which is correct only to the current precision.
<p>
<h5>
Example:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
In> Builtin'Precision'Set(10)
Out> True
In> Sqrt(10)
Out> Sqrt(10)
In> MathSqrt(10)
Out> 3.16227766
In> MathSqrt(490000*2^150)
Out> 26445252304070013196697600
In> MathSqrt(490000*2^150+1)
Out> 0.264452523e26
In> MathPower(2,3)
Out> 8
In> MathPower(2,-3)
Out> 0.125
</pre></tr>
</table>
<p>
<a name="FastLog@\relax <b><tt>FastLog</tt></b>">
</a>
<a name="FastPower@\relax <b><tt>FastPower</tt></b>">
</a>
<a name="FastArcSin@\relax <b><tt>FastArcSin</tt></b>">
</a>
<a name="Fast...">
</a>
<a name="fast...">
</a>
<h3>
<hr>Fast... -- double-precision math functions
</h3>
<h5 align=right>Internal function</h5><h5>
Calling format:
</h5>
<p>
FastLog(x) (natural logarithm),
FastPower(x,y),
FastArcSin(x)
<p>
<h5>
Description:
</h5>
Versions of these functions using the C++ library. These
should then at least be faster than the arbitrary precision versions.
<p>
<a name="ShiftLeft">
</a>
<a name="shiftleft">
</a>
<h3>
<hr>ShiftLeft -- built-in bitwise shift left operation
</h3>
<a name="ShiftRight">
</a>
<a name="shiftright">
</a>
<h3>
<hr>ShiftRight -- built-in bitwise shift right operation
</h3>
<h5 align=right>Internal function</h5><h5>
Calling format:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
ShiftLeft(expr,bits)
ShiftRight(expr,bits)
</pre></tr>
</table>
<p>
<h5>
Description:
</h5>
Shift bits to the left or to the right.
<p>
<a name="IsPromptShown">
</a>
<a name="ispromptshown">
</a>
<h3>
<hr>IsPromptShown -- test for the Yacas prompt option
</h3>
<h5 align=right>Internal function</h5><h5>
Calling format:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
IsPromptShown()
</pre></tr>
</table>
<h5>
Description:
</h5>
Returns <b><tt>False</tt></b> if Yacas has been started with the option to suppress the prompt, and <b><tt>True</tt></b> otherwise.
<p>
<a name="GetTime">
</a>
<a name="gettime">
</a>
<h3>
<hr>GetTime -- measure the time taken by an evaluation
</h3>
<h5 align=right>Internal function</h5><h5>
Calling format:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
GetTime(expr)
</pre></tr>
</table>
<h5>
Parameters:
</h5>
<b><tt>expr</tt></b> -- any expression
<h5>
Description:
</h5>
The function <b><tt>GetTime(expr)</tt></b> evaluates the expression <b><tt>expr</tt></b> and returns the time needed for the evaluation.
The result is returned as a floating-point number of seconds.
The value of the expression <b><tt>expr</tt></b> is lost.
<p>
The result is the "user time" as reported by the OS, not the real ("wall clock") time.
Therefore, any CPU-intensive processes running alongside Yacas will not significantly affect the result of <b><tt>GetTime</tt></b>.
<p>
<h5>
Example:
</h5>
<table cellpadding="0" width="100%">
<tr><td width=100% bgcolor="#DDDDEE"><pre>
In> GetTime(Simplify((a*b)/(b*a)))
Out> 0.09;
</pre></tr>
</table>
<p>
<h5>
See also:
</h5>
<a href="ref.html?Time" target="Chapters">
Time
</a>
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