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<html><head><title>[SONATA] 7 Graphic ideal lattices (X-GAP only)</title></head>
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<h1>7 Graphic ideal lattices (X-GAP only)</h1><p>
<p>
If you run SONATA under XGAP it is possible to study ideal lattices of
nearrings graphically.
<p>
<a name = ""></a>
<li><code>GraphicIdealLattice( </code><var>nr</var><code>, </code><var>string</var><code> )</code>
<p>
The function <code>GraphicIdealLattice</code> computes one- and two-sided
nearring ideals and uses XGAP's graphic capabilities to draw the ideal
lattice of the nearring <var>nr</var>. The string <var>string</var> determines, which
ideals are shown:
<p>
If <var>string</var> contains the letter <code>l</code>, left ideals are shown, if
<var>string</var> contains the letter <code>r</code>, right ideals are shown, and if
<var>string</var> contains the letter <code>i</code>, two-sided ideals are shown.  Any
combination of these letters is possible.
<p>
Right ideals of the nearring are represented by squares, left ideals
by diamonds and two-sided ideals by circles. It is possible, that
two-sided ideals are shown as right or left ideals, if the two-sided
ideal property has not yet been tested.
<p>
Left clicking on an ideal allows one to select the ideal and determine
more information about the ideal. Choosing <code>Ideal type</code> from the
<code>Ideals</code>-menu determines, whether the selected ideal is two-sided (in
which case its shape changes to a circle immediately). On a right
click on an ideal a window opens showing more information about the
ideal, such as its size and the isomorphism class of the factor
nearring by the ideal (if it is two-sided). The information is
computed and displayed as soon as you click on the corresponding entry
in the window. Finally clicking on <code>Export ideal to GAP</code> makes the
ideal the last output of XGAP's main window, where you may then go on
working with it.
<p>
It is also possible to select several ideals at the same time pressing
the Ctrl-key while left clicking on the ideals. When several ideals
are selected it is possible to compute their sums and intersection
from the corresponding <code>Ideals</code>-menu entries. The result of the
computation is then indicated by green color.
<p>
<p>
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<P>
<address>SONATA manual<br>November 2008
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