Differences

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--- tutorial:apps_matroid [2014/11/14 10:32] – [Other Constructions] schroeter
+++ user_guide:tutorials:apps_matroid [2019/01/25 09:38] – ↷ Page moved from user_guide:apps_matroid to user_guide:tutorials:apps_matroid oroehrig
@@ Line 1: / Line 1: @@
-====== Short Introduction to New Application ''matroid'' ======
+====== Short Introduction to application ''matroid'' ======
-The application ''matroid'' introduced with version 2.9.7 is in its infancy.  This tutorial is meant to show the main features available.
+**This tutorial is also available as a {{ user_guide:apps_matroid.ipynb |jupyter notebook}} for polymake 3.1.**
-To make ''matroid'' your current application start ''polymake'' with the option ''-A matroid'' or use the context switch ''%%application "matroid";%%'' from within the ''polymake'' shell.  A permanent setting can be stored with ''%%set_custom $default_application="matroid";%%''
+This tutorial is meant to show the main features for handling matroids available. To make ''matroid'' your current application start ''polymake'' with the option ''-A matroid'' or use the context switch
+<code>
+> application "matroid";
+</code>
+from within the ''polymake'' shell.  A permanent setting can be stored with ''%%set_custom $default_application="matroid";%%''
 ===== Constructing a Simple Matroid and Playing Around =====
@@ Line 10: / Line 14: @@
 <code>
-matroid > $M=new Matroid(POINTS=>[[1,0,0],[1,0,1],[1,1,0],[1,0,2]]);
+matroid > $M=new Matroid(VECTORS=>[[1,0,0],[1,0,1],[1,1,0],[1,0,2]]);
 </code>
@@ Line 16: / Line 20: @@
 <code>
-polytope > $M=new matroid::Matroid(POINTS=>[[1,0,0],[1,0,1],[1,1,0],[1,0,2]]);
+polytope > $M=new matroid::Matroid(VECTORS=>[[1,0,0],[1,0,1],[1,1,0],[1,0,2]]);
 </code>
@@ Line 24: / Line 28: @@
 4 3
 </code>
-{{ :tutorial:matroid_lattice_of_flats_example.png?nolink&200|}}
+{{ user_guide:matroid_lattice_of_flats_example.png?nolink&200|}}
-The ''POINTS'' are numbered consecutively, starting from zero.  The bases are encoded as sets of these ordinal numbers.
+The ''VECTORS'' are numbered consecutively, starting from zero.  The bases are encoded as sets of these ordinal numbers.
 <code>
@@ Line 49: / Line 53: @@
 You can also compute other properties, like
 <code>
-matroid > print $M->PAVING?"1":"0", " ", $M->BINARY?"1":"0", " ", $M->SERIES_PARALLEL?"1":"0", " ", $M->CONNECTED?"1":"0";
+matroid > print $M->PAVING?"1":"0", " ",
+matroid (2)> $M->BINARY?"1":"0", " ",
+matroid (3)> $M->SERIES_PARALLEL?"1":"0", " ",
+matroid (4)> $M->CONNECTED?"1":"0";
 1 0 0
@@ Line 62: / Line 69: @@
 Even the lattice of flats could be computed and visualised.
 <code>
-matroid > $lattice=$M->LATTICE_OF_FLATS; foreach (@{$lattice->nodes_of_dim(2)}){print $lattice->FACES->[$_]," "};
+matroid > $lattice=$M->LATTICE_OF_FLATS;
+matroid > foreach (@{$lattice->nodes_of_rank(2)}){print $lattice->FACES->[$_]," "};
 {0 2} {0 1 3} {1 2} {2 3}
@@ Line 92: / Line 100: @@
 <code>
-matroid > $C=new Matroid(POINTS=>polytope::cube(3)->VERTICES);
+matroid > $C=new Matroid(VECTORS=>polytope::cube(3)->VERTICES);
 matroid > print $C->N_BASES;
@@ Line 109: / Line 117: @@
 It is also possible to derive a new matroid from others.
 <code>
-matroid > $se=series_extension(uniform_matroid(2,3),0,uniform_matroid(1,3),0); # the arguments are two matroids and for each matroid a basepoint.The basepoints will be identified.
+matroid > # The arguments are two matroids and for each matroid a basepoint. The basepoints will be identified.
+matroid > $se=series_extension(uniform_matroid(2,3),0,uniform_matroid(1,3),0);
-matroid > print deletion($se,4)->POINTS;
+matroid > print deletion($se,4)->VECTORS;
 0 0
 1 0
@@ Line 119: / Line 128: @@
 matroid > $pe=parallel_extension(uniform_matroid(1,3),0,uniform_matroid(2,3),0);
-matroid > print dual(contraction($pe,4))->POINTS;
+matroid > print dual(contraction($pe,4))->VECTORS;
 0 0
 1 0