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--- documentation:master:polytope [2026/09/17 12:17] – created - external edit 127.0.0.1
+++ documentation:master:polytope [2026/10/01 08:40] (current) – external edit 127.0.0.1
@@ Line 40: / Line 40: @@
 {{anchor:circuits2matrix:}}
   ?  **''circuits2matrix([[.:common#Set |Set]]<[[.:common#Pair |Pair]]<[[.:common#Set |Set]]<[[.:common#Int |Int]]>,[[.:common#Set |Set]]<[[.:common#Int |Int]]%%>>%%> co)''**
-  :: Convert ''[[.:polytope:VectorConfiguration#CIRCUITS |CIRCUITS]]'' or ''[[.:polytope:VectorConfiguration#COCIRCUITS |COCIRCUITS]]'' to a 0/+1/-1 matrix, with one row for each circuit/cocircuit,  and as many columns as there are VECTORs/POINTS.
+  :: Convert ''[[.:polytope:Polytope#CIRCUITS |CIRCUITS]]'' or ''[[.:polytope:Polytope#COCIRCUITS |COCIRCUITS]]'' to a 0/+1/-1 matrix, with one row for each circuit/cocircuit,  and as many columns as there are VECTORs/POINTS.
     ? Parameters:
     :: ''[[.:common#Set |Set]]<[[.:common#Pair |Pair]]<[[.:common#Set |Set]]<[[.:common#Int |Int]]>,[[.:common#Set |Set]]<[[.:common#Int |Int]]%%>>%%>'' ''co'': /circuits a set of circuits or cocircuits
@@ Line 361: / Line 361: @@
 {{anchor:affine_float_coords:}}
   ?  **''affine_float_coords([[.:polytope:Polytope |Polytope]] P)''**
-  :: Dehomogenize the [[.:polytope:Polytope#VERTICES |vertex coordinates]] and convert them to Float
+  :: Dehomogenize the [[.:polytope:SchlegelDiagram#VERTICES |vertex coordinates]] and convert them to Float
     ? Parameters:
     :: ''[[.:polytope:Polytope |Polytope]]'' ''P'': source object
@@ Line 521: / Line 521: @@
 {{anchor:center_distance:}}
   ?  **''center_distance([[.:polytope:Polytope |Polytope]] p)''**
-  :: Compute the mean or median distance of the ''[[.:polytope:Polytope#VERTICES |VERTICES]]'' to the ''[[.:polytope:Polytope#VERTEX_BARYCENTER |VERTEX_BARYCENTER]]''.
+  :: Compute the mean or median distance of the ''[[.:polytope:SchlegelDiagram#VERTICES |VERTICES]]'' to the ''[[.:polytope:Polytope#VERTEX_BARYCENTER |VERTEX_BARYCENTER]]''.
     ? Parameters:
     :: ''[[.:polytope:Polytope |Polytope]]'' ''p''
@@ Line 2913: / Line 2913: @@
     :: <code perl> > $p = SIM_body(new Vector(sequence(3,1)));
  > $s = new Polytope(POINTS=>$p->VERTICES->minor(All,~[$p->CONE_DIM]));
+</code>
+----
+{{anchor:agv_cube:}}
+  ?  **''agv_cube([[.:common#Int |Int]] n)''**
+  :: Produce the n-dimensional polytope with 2n facets underlying the linear program cex_n(t) of Allamigeon, Gaubert and Vandame, https://dl.acm.org/doi/10.1145/3519935.3519997 , for which every self-concordant barrier interior point method requires at least 2^n-1 iterations.
+    ? Parameters:
+    :: ''[[.:common#Int |Int]]'' ''n'': defining parameter
+    ? Options:
+    :
+    :: ''[[.:common#Rational |Rational]]'' ''eval_ratio'': parameter for evaluating the puiseux rational functions
+    :: ''[[.:common#Int |Int]]'' ''eval_exp'': to evaluate at eval_ratio^eval_exp, default: 1
+    :: ''[[.:common#Float |Float]]'' ''eval_float'': parameter for evaluating the puiseux rational functions
+    ? Returns:
+    :''[[.:polytope:Polytope |Polytope]]<[[.:common#PuiseuxFraction |PuiseuxFraction]]<[[.:common#Max |Max]],[[.:common#Rational |Rational]],[[.:common#Rational |Rational]]%%>>%%''
+    ? Example:
+    :: This yields a 3-polytope over the field of Puiseux fractions.
+    :: <code perl> > $p = agv_cube(3);
+</code>
+    ? Example:
+    :: This yields a rational 3-polytope with the same combinatorics.
+    :: <code perl> > $p = agv_cube(3,eval_ratio=>4);
 </code>