There are some pictures that may give a lot of information about a semigroup. This is the case of the egg-box picture of the D-classes, the right Cayley graph of a finite monoid and the Schutzenberger graphs of a finite inverse monoid.
> DrawDClassOfElement ( arg ) | ( function ) |
This function takes as arguments a semigroup followed by a transformation which is the element whose D-class will be drawn. Optionally we can then specify n lists of elements and the elements of each list will be drawn in different colours. Finally, we may specify a string name the file that will be used to write the drawing of the class (in PostScript format) and if the last argument is the integer 1
then the elements will appear as transformations, otherwise they will appear as words. The idempotents will be marked with a * before them.
This last optional argument may also be the integer 2
and in this case the elements will appear as integers, where i
represents the element Elements(S)[i]
.
gap> DrawDClassOfElement(poi3, Transformation([1,4,3,4])); gap> DrawDClassOfElement(poi3, Transformation([1,4,3,4]),1); gap> DrawDClassOfElement(poi3, Transformation([1,4,3,4]), [Transformation( [ 2, 3, 4, 4 ] )],1); gap> DrawDClassOfElement(poi3, Transformation([1,4,3,4]), [Transformation( [ 2, 3, 4, 4 ] ), Transformation( [ 2, 4, 3, 4 ] )], [Transformation( [ 2, 4, 3, 4 ] )],1); gap> DrawDClassOfElement(poi3, Transformation([1,4,3,4]), [Transformation( [ 2, 4, 3, 4 ] )],"Dclass",1); |
This is the image produced by the first command in the previous example:
> DrawDClasses ( arg ) | ( function ) |
This function is similar to the previous one, except that this one draws all the D-classes of the semigroup given as the first argument. It then takes optionally n lists of elements and the elements of each list will be drawn in different colours. It also accepts a string specifying the name of the file in which the drawing will be written and the last, optional, argument, the integer 1
, to specify whether the elements will appear as words or as transformations as in the previous function. The idempotents will be marked with a * before them.
This last optional argument may also be the integer 2
and in this case the elements will appear as integers, where i
represents the element Elements(S)[i]
.
gap> DrawDClasses(poi3,"DClasses"); gap> DrawDClasses(poi3, [Transformation( [ 2, 3, 4, 4 ] ), Transformation( [ 2, 4, 3, 4 ] )], [Transformation( [ 2, 4, 3, 4 ] )],1); |
This is the image produced by the first command in the previous example:
> DrawRightCayleyGraph ( S ) | ( function ) |
Draws the right Cayley graph of a finite monoid or semigroup S.
> DrawCayleyGraph ( S ) | ( function ) |
This function is a synonym of DrawRightCayleyGraph
(3.3-1).
For example, the command DrawCayleyGraph(b21);
would produce the following image (where state i
represents the element Elements(S)[i]
, the neutral element is colored in "light blue" and all other idempotents are colored in "light coral"):
> DrawSchutzenbergerGraphs ( S ) | ( function ) |
Draws the Schutzenberger graphs of the inverse semigroup S.
For example, DrawSchutzenbergerGraphs(poi3);
would produce the following:
By default, when a drawing is requested, it is outputted in PostScript format. Since graphviz
allows other output formats (see http://www.graphviz.org/doc/info/output.html), it is possible to also request a drawing in a format other than PostScript.
> DrawingsListOfExtraFormats | ( global variable ) |
This is a global variable which holds the valid output formats for a drawing. It currently has the value: ["dia", "fig", "gd", "gd2", "gif", "hpgl", "jpg", "mif", "mp", "pcl", "pic", "plain", "plain-ext", "png", "ps", "ps2", "svg", "svgz", "vrml", "vtx", "wbmp", "none"]
(see http://www.graphviz.org/doc/info/output.html for their description).
> DrawingsExtraFormat | ( global variable ) |
This is a global variable which holds the alternative output format for a drawing. By default its value is "none"
which indicates that just PostScript will be used as the output format.
If its value becomes one of those in DrawingsListOfExtraFormats
(3.5-1), then besides the PostScript file, it will also be created a file in the alternative format.
To change this variable's value, please use SetDrawingsExtraFormat
(3.5-3).
> SetDrawingsExtraFormat ( f ) | ( function ) |
This function is used to set the value of DrawingsExtraFormat
(3.5-2) to the format f which is one of DrawingsListOfExtraFormats
(3.5-1).
gap> DrawingsExtraFormat; "none" gap> SetDrawingsExtraFormat("jpg"); gap> DrawingsExtraFormat; "jpg" gap> DrawRightCayleyGraph(poi3); Displaying file: /tmp/tmp.tpJqvI/cayleygraph.dot.ps The extra output format file: /tmp/tmp.tpJqvI/cayleygraph.dot.jpg has also been created. |
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