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<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Liste der GEL-Operatoren</title><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot"><link rel="home" href="index.html" title="Genius-Handbuch"><link rel="up" href="ch05.html" title="Chapter 5. GEL-Grundlagen"><link rel="prev" href="ch05s06.html" title="Modulare Auswertung"><link rel="next" href="ch06.html" title="Chapter 6. Programmierung mit GEL"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Liste der GEL-Operatoren</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="ch05s06.html">Prev</a> </td><th width="60%" align="center">Chapter 5. GEL-Grundlagen</th><td width="20%" align="right"> <a accesskey="n" href="ch06.html">Next</a></td></tr></table><hr></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="genius-gel-operator-list"></a>Liste der GEL-Operatoren</h2></div></div></div><p lang="en">
Everything in GEL is really just an expression. Expressions are stringed together with
different operators. As we have seen, even the separator is simply a binary operator
in GEL. Here is a list of the operators in GEL.
</p><div class="variablelist"><dl class="variablelist"><dt><span lang="en" class="term"><strong class="userinput"><code>a;b</code></strong></span></dt><dd><p lang="en">
The separator, just evaluates both
<code class="varname">a</code> and
<code class="varname">b</code>,
but returns only the result of
<code class="varname">b</code>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a=b</code></strong></span></dt><dd><p lang="en">
The assignment operator. This assigns <code class="varname">b</code> to
<code class="varname">a</code> (<code class="varname">a</code> must be a valid <a class="link" href="ch06s09.html" title="Lvalues (linke Werte)">lvalue</a>) (note however that this operator
may be translated to <code class="literal">==</code> if used in a place where boolean
expression is expected)
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a:=b</code></strong></span></dt><dd><p lang="en">
The assignment operator. Assigns <code class="varname">b</code> to
<code class="varname">a</code> (<code class="varname">a</code> must be a valid <a class="link" href="ch06s09.html" title="Lvalues (linke Werte)">lvalue</a>). This is
different from <code class="literal">=</code> because it never gets translated to a
<code class="literal">==</code>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>|a|</code></strong></span></dt><dd><p lang="en">
Absolute value.
In case the expression is a complex number the result will be the modulus
(distance from the origin). For example:
<strong class="userinput"><code>|3 * e^(1i*pi)|</code></strong>
returns 3.
</p><p lang="en">
See
<a class="ulink" href="http://mathworld.wolfram.com/AbsoluteValue.html" target="_top">Mathworld</a> for more information.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a^b</code></strong></span></dt><dd><p lang="en">
Exponentiation, raises <code class="varname">a</code> to the <code class="varname">b</code>th power.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a.^b</code></strong></span></dt><dd><p lang="en">
Element by element exponentiation. Raise each element of a matrix
<code class="varname">a</code> to the <code class="varname">b</code>th power. Or if
<code class="varname">b</code> is a matrix of the same size as
<code class="varname">a</code>, then do the operation element by element.
If <code class="varname">a</code> is a number and <code class="varname">b</code> is a
matrix then it creates matrix of the same size as
<code class="varname">b</code> with <code class="varname">a</code> raised to all the
different powers in <code class="varname">b</code>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a+b</code></strong></span></dt><dd><p lang="en">
Addition. Adds two numbers, matrices, functions or strings. If
you add a string to anything the result will just be a string. If one is
a square matrix and the other a number, then the number is multiplied by
the identity matrix.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a-b</code></strong></span></dt><dd><p lang="en">
Subtraction. Subtract two numbers, matrices or functions.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a*b</code></strong></span></dt><dd><p lang="en">
Multiplication. This is the normal matrix multiplication.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a.*b</code></strong></span></dt><dd><p lang="en">
Element by element multiplication if <code class="varname">a</code> and
<code class="varname">b</code> are matrices.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a/b</code></strong></span></dt><dd><p lang="en">
Division. When <code class="varname">a</code> and <code class="varname">b</code> are just numbers
this is the normal division. When they are matrices, then this is
equivalent to <strong class="userinput"><code>a*b^-1</code></strong>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a./b</code></strong></span></dt><dd><p lang="en">
Element by element division. Same as <strong class="userinput"><code>a/b</code></strong> for
numbers, but operates element by element on matrices.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a\b</code></strong></span></dt><dd><p lang="en">
Back division. That is this is the same as <strong class="userinput"><code>b/a</code></strong>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a.\b</code></strong></span></dt><dd><p lang="en">
Element by element back division.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a%b</code></strong></span></dt><dd><p lang="en">
The mod operator. This does not turn on the <a class="link" href="ch05s06.html" title="Modulare Auswertung">modular mode</a>, but
just returns the remainder of integer division
<strong class="userinput"><code>a/b</code></strong>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a.%b</code></strong></span></dt><dd><p lang="en">
Element by element mod operator. Returns the remainder
after element by element integer division
<strong class="userinput"><code>a./b</code></strong>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a mod b</code></strong></span></dt><dd><p lang="en">
Modular evaluation operator. The expression <code class="varname">a</code>
is evaluated modulo <code class="varname">b</code>. See <a class="xref" href="ch05s06.html" title="Modulare Auswertung">the section called “Modulare Auswertung”</a>.
Some functions and operators behave differently modulo an integer.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a!</code></strong></span></dt><dd><p lang="en">
Factorial operator. This is like
<strong class="userinput"><code>1*...*(n-2)*(n-1)*n</code></strong>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a!!</code></strong></span></dt><dd><p lang="en">
Double factorial operator. This is like
<strong class="userinput"><code>1*...*(n-4)*(n-2)*n</code></strong>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a==b</code></strong></span></dt><dd><p lang="en">
Equality operator.
Returns <code class="constant">true</code> or <code class="constant">false</code>
depending on <code class="varname">a</code> and <code class="varname">b</code> being equal or not.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a!=b</code></strong></span></dt><dd><p lang="en">
Inequality operator,
returns <code class="constant">true</code> if <code class="varname">a</code> does not
equal <code class="varname">b</code> else returns <code class="constant">false</code>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a<>b</code></strong></span></dt><dd><p lang="en">
Alternative inequality operator,
returns <code class="constant">true</code> if <code class="varname">a</code> does not
equal <code class="varname">b</code> else returns <code class="constant">false</code>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a<=b</code></strong></span></dt><dd><p lang="en">
Less than or equal operator,
returns <code class="constant">true</code> if <code class="varname">a</code> is
less than or equal to
<code class="varname">b</code> else returns <code class="constant">false</code>.
These can be chained as in <strong class="userinput"><code>a <= b <= c</code></strong> (can
also be combined with the less than operator).
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a>=b</code></strong></span></dt><dd><p lang="en">
Greater than or equal operator,
returns <code class="constant">true</code> if <code class="varname">a</code> is
greater than or equal to
<code class="varname">b</code> else returns <code class="constant">false</code>.
These can be chained as in <strong class="userinput"><code>a >= b >= c</code></strong>
(and they can also be combined with the greater than operator).
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a<b</code></strong></span></dt><dd><p lang="en">
Less than operator,
returns <code class="constant">true</code> if <code class="varname">a</code> is
less than
<code class="varname">b</code> else returns <code class="constant">false</code>.
These can be chained as in <strong class="userinput"><code>a < b < c</code></strong>
(they can also be combined with the less than or equal to operator).
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a>b</code></strong></span></dt><dd><p lang="en">
Greater than operator,
returns <code class="constant">true</code> if <code class="varname">a</code> is
greater than
<code class="varname">b</code> else returns <code class="constant">false</code>.
These can be chained as in <strong class="userinput"><code>a > b > c</code></strong>
(they can also be combined with the greater than or equal to operator).
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a<=>b</code></strong></span></dt><dd><p lang="en">
Comparison operator. If <code class="varname">a</code> is equal to
<code class="varname">b</code> it returns 0, if <code class="varname">a</code> is less
than <code class="varname">b</code> it returns -1 and if
<code class="varname">a</code> is greater than <code class="varname">b</code> it
returns 1.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a and b</code></strong></span></dt><dd><p lang="en">
Logical and. Returns true if both
<code class="varname">a</code> and <code class="varname">b</code> are true,
else returns false. If given numbers, nonzero numbers
are treated as true.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a or b</code></strong></span></dt><dd><p lang="en">
Logical or.
Returns true if either
<code class="varname">a</code> or <code class="varname">b</code> is true,
else returns false. If given numbers, nonzero numbers
are treated as true.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a xor b</code></strong></span></dt><dd><p lang="en">
Logical xor.
Returns true if exactly one of
<code class="varname">a</code> or <code class="varname">b</code> is true,
else returns false. If given numbers, nonzero numbers
are treated as true.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>not a</code></strong></span></dt><dd><p lang="en">
Logical not. Returns the logical negation of <code class="varname">a</code>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>-a</code></strong></span></dt><dd><p lang="en">
Negation operator. Returns the negative of a number or a matrix (works element-wise on a matrix).
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>&a</code></strong></span></dt><dd><p lang="en">
Variable referencing (to pass a reference to a variable).
See <a class="xref" href="ch06s08.html" title="Referenzen">the section called “Referenzen”</a>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>*a</code></strong></span></dt><dd><p lang="en">
Variable dereferencing (to access a referenced variable).
See <a class="xref" href="ch06s08.html" title="Referenzen">the section called “Referenzen”</a>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a'</code></strong></span></dt><dd><p lang="en">
Matrix conjugate transpose. That is, rows and columns get swapped and we take complex conjugate of all entries. That is
if the i,j element of <code class="varname">a</code> is x+iy, then the j,i element of <strong class="userinput"><code>a'</code></strong> is x-iy.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a.'</code></strong></span></dt><dd><p lang="en">
Matrix transpose, does not conjugate the entries. That is,
the i,j element of <code class="varname">a</code> becomes the j,i element of <strong class="userinput"><code>a.'</code></strong>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a@(b,c)</code></strong></span></dt><dd><p lang="en">
Get element of a matrix in row <code class="varname">b</code> and column
<code class="varname">c</code>. If <code class="varname">b</code>,
<code class="varname">c</code> are vectors, then this gets the corresponding
rows, columns or submatrices.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a@(b,)</code></strong></span></dt><dd><p lang="en">
Get row of a matrix (or multiple rows if <code class="varname">b</code> is a vector).
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a@(b,:)</code></strong></span></dt><dd><p>Gleiches wie oben.</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a@(,c)</code></strong></span></dt><dd><p lang="en">
Get column of a matrix (or columns if <code class="varname">c</code> is a
vector).
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a@(:,c)</code></strong></span></dt><dd><p>Gleiches wie oben.</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a@(b)</code></strong></span></dt><dd><p lang="en">
Get an element from a matrix treating it as a vector. This will
traverse the matrix row-wise.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a:b</code></strong></span></dt><dd><p lang="en">
Build a vector from <code class="varname">a</code> to <code class="varname">b</code> (or specify a row, column region for the <code class="literal">@</code> operator). For example to get rows 2 to 4 of matrix <code class="varname">A</code> we could do
</p><pre lang="en" class="programlisting">A@(2:4,)
</pre><p lang="en">
as <strong class="userinput"><code>2:4</code></strong> will return a vector
<strong class="userinput"><code>[2,3,4]</code></strong>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a:b:c</code></strong></span></dt><dd><p lang="en">
Build a vector from <code class="varname">a</code> to <code class="varname">c</code>
with <code class="varname">b</code> as a step. That is for example
</p><pre lang="en" class="programlisting">genius> 1:2:9
=
`[1, 3, 5, 7, 9]
</pre><p lang="en">
</p><p lang="en">
When the numbers involved are floating point numbers, for example
<strong class="userinput"><code>1.0:0.4:3.0</code></strong>, the output is what is expected
even though adding 0.4 to 1.0 five times is actually just slightly
more than 3.0 due to the way that floating point numbers are
stored in base 2 (there is no 0.4, the actual number stored is
just ever so slightly bigger). The way this is handled is the
same as in the for, sum, and prod loops. If the end is within
<strong class="userinput"><code>2^-20</code></strong> times the step size of the endpoint,
the endpoint is used and we assume there were roundoff errors.
This is not perfect, but it handles the majority of the cases.
This check is done only from version 1.0.18 onwards, so execution
of your code may differ on older versions. If you want to avoid
dealing with this issue, use actual rational numbers, possibly
using the <code class="function">float</code> if you wish to get floating
point numbers in the end. For example
<strong class="userinput"><code>1:2/5:3</code></strong> does the right thing and
<strong class="userinput"><code>float(1:2/5:3)</code></strong> even gives you floating
point numbers and is ever so slightly more precise than
<strong class="userinput"><code>1.0:0.4:3.0</code></strong>.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>(a)i</code></strong></span></dt><dd><p lang="en">
Make <code class="varname">a</code> into an imaginary number (multiply <code class="varname">a</code> by the
imaginary). Normally the imaginary number <code class="varname">i</code> is
written as <strong class="userinput"><code>1i</code></strong>. So the above is equal to
</p><pre lang="en" class="programlisting">(a)*1i
</pre><p lang="en">
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>`a</code></strong></span></dt><dd><p lang="en">
Quote an identifier so that it doesn't get evaluated. Or
quote a matrix so that it doesn't get expanded.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>a swapwith b</code></strong></span></dt><dd><p lang="en">
Swap value of <code class="varname">a</code> with the value
of <code class="varname">b</code>. Currently does not operate
on ranges of matrix elements.
It returns <code class="constant">null</code>.
Available from version 1.0.13.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>increment a</code></strong></span></dt><dd><p lang="en">
Increment the variable <code class="varname">a</code> by 1. If
<code class="varname">a</code> is a matrix, then increment each element.
This is equivalent to <strong class="userinput"><code>a=a+1</code></strong>, but
it is somewhat faster. It returns <code class="constant">null</code>.
Available from version 1.0.13.
</p></dd><dt><span lang="en" class="term"><strong class="userinput"><code>increment a by b</code></strong></span></dt><dd><p lang="en">
Increment the variable <code class="varname">a</code> by <code class="varname">b</code>. If
<code class="varname">a</code> is a matrix, then increment each element.
This is equivalent to <strong class="userinput"><code>a=a+b</code></strong>, but
it is somewhat faster. It returns <code class="constant">null</code>.
Available from version 1.0.13.
</p></dd></dl></div><div class="note" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Note</h3><p lang="en">
The @() operator makes the : operator most useful. With this you can specify regions of a matrix. So that a@(2:4,6) is the rows 2,3,4 of the column 6. Or a@(,1:2) will get you the first two columns of a matrix. You can also assign to the @() operator, as long as the right value is a matrix that matches the region in size, or if it is any other type of value.
</p></div><div class="note" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Note</h3><p lang="en">
The comparison operators (except for the <=> operator, which behaves normally), are not strictly binary operators, they can in fact be grouped in the normal mathematical way, e.g.: (1<x<=y<5) is a legal boolean expression and means just what it should, that is (1<x and x≤y and y<5)
</p></div><div class="note" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Note</h3><p lang="en">
The unitary minus operates in a different fashion depending on where it
appears. If it appears before a number it binds very closely, if it appears in
front of an expression it binds less than the power and factorial operators.
So for example <strong class="userinput"><code>-1^k</code></strong> is really <strong class="userinput"><code>(-1)^k</code></strong>,
but <strong class="userinput"><code>-foo(1)^k</code></strong> is really <strong class="userinput"><code>-(foo(1)^k)</code></strong>. So
be careful how you use it and if in doubt, add parentheses.
</p></div></div><div class="navfooter"><hr><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="ch05s06.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="ch05.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="ch06.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Modulare Auswertung </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 6. Programmierung mit GEL</td></tr></table></div></body></html>
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