Improve the output of repr_pretty_Hrepresentation for Polyhedron

[jplab]

Following #22572, we can improve the output of the pretty print:

    sage: Cube = polytopes.cube()
    sage: TCube = Cube.truncation()
    sage: Nice_repr = TCube.repr_pretty_Hrepresentation(separator='\n')
    sage: print(Nice_repr)
    1 >= x0
    1 >= x1
    3*x1 + 7 >= 3*x0 + 3*x2
    x0 + 1 >= 0
    x1 + 1 >= 0
    3*x0 + 7 >= 3*x1 + 3*x2
    3*x0 + 3*x1 + 7 >= 3*x2
    3*x0 + 3*x2 + 7 >= 3*x1
    3*x0 + 3*x1 + 3*x2 + 7 >= 0
    x2 + 1 >= 0
    1 >= x2
    3*x1 + 3*x2 + 7 >= 3*x0
    3*x2 + 7 >= 3*x0 + 3*x1
    7 >= 3*x0 + 3*x1 + 3*x2

In the new version it gives:

    sage: print(TCube.Hrepresentation_str())
                    -x0 >= -1 
                    -x1 >= -1 
    -3*x0 + 3*x1 - 3*x2 >= -7 
                     x0 >= -1 
                     x1 >= -1 
     3*x0 - 3*x1 - 3*x2 >= -7 
     3*x0 + 3*x1 - 3*x2 >= -7 
     3*x0 - 3*x1 + 3*x2 >= -7 
     3*x0 + 3*x1 + 3*x2 >= -7 
                     x2 >= -1 
                    -x2 >= -1 
    -3*x0 + 3*x1 + 3*x2 >= -7 
    -3*x0 - 3*x1 + 3*x2 >= -7 
    -3*x0 - 3*x1 - 3*x2 >= -7

    sage: print(TCube.Hrepresentation_str(latex=True))
    \begin{array}{rcl}
                                   -x_{0} & \geq & -1 \\
                                   -x_{1} & \geq & -1 \\
    -3 \, x_{0} + 3 \, x_{1} - 3 \, x_{2} & \geq & -7 \\
                                    x_{0} & \geq & -1 \\
                                    x_{1} & \geq & -1 \\
     3 \, x_{0} - 3 \, x_{1} - 3 \, x_{2} & \geq & -7 \\
     3 \, x_{0} + 3 \, x_{1} - 3 \, x_{2} & \geq & -7 \\
     3 \, x_{0} - 3 \, x_{1} + 3 \, x_{2} & \geq & -7 \\
     3 \, x_{0} + 3 \, x_{1} + 3 \, x_{2} & \geq & -7 \\
                                    x_{2} & \geq & -1 \\
                                   -x_{2} & \geq & -1 \\
    -3 \, x_{0} + 3 \, x_{1} + 3 \, x_{2} & \geq & -7 \\
    -3 \, x_{0} - 3 \, x_{1} + 3 \, x_{2} & \geq & -7 \\
    -3 \, x_{0} - 3 \, x_{1} - 3 \, x_{2} & \geq & -7 
    \end{array}

The style parameter allows to change the way to print the H-relations:

sage: P = polytopes.permutahedron(3)
sage: print(P.Hrepresentation_str(style='<='))
-x0 - x1 - x2 == -6 
      x1 + x2 <=  5 
           x2 <=  3 
           x1 <=  3 
          -x1 <= -1 
     -x1 - x2 <= -3 
          -x2 <= -1
sage: print(P.Hrepresentation_str(style='positive'))
x0 + x1 + x2 == 6       
           5 >= x1 + x2 
           3 >= x2      
           3 >= x1      
          x1 >= 1       
     x1 + x2 >= 3       
          x2 >= 1

In order to make the function more apparent, deprecation of the current function is perhaps a good idea and change the name to Hrepresentation_str.

Depends on #22572

CC: @videlec @mo271 @tscrim

Component: geometry

Keywords: days93, IMA-PolyGeom

Author: Jean-Philippe Labbé

Branch: b1ae583

Reviewer: Moritz Firsching, Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/24837

[jplab]

Dependencies: #22572

[jplab]

comment:1

Once the tutorial is merged in #22572, we should change the "tips" page accordingly...

---

New commits:

7cf1a56

first version

[jplab]

Commit: 7cf1a56

[jplab]

Branch: u/jipilab/24837

[jplab]

Author: Jean-Philippe Labbé

[jplab]

Description changed:

--- 
+++ 
@@ -1,20 +1,76 @@
 Following #22572, we can improve the output of the pretty print:
 
 ```
+    sage: Cube = polytopes.cube()
+    sage: TCube = Cube.truncation()
     sage: Nice_repr = TCube.repr_pretty_Hrepresentation(separator='\n')
-sage: print(Nice_repr)
-1 >= x0
-1 >= x1
-3*x1 + 7 >= 3*x0 + 3*x2
-x0 + 1 >= 0
-x1 + 1 >= 0
-3*x0 + 7 >= 3*x1 + 3*x2
-3*x0 + 3*x1 + 7 >= 3*x2
-3*x0 + 3*x2 + 7 >= 3*x1
-3*x0 + 3*x1 + 3*x2 + 7 >= 0
-x2 + 1 >= 0
-1 >= x2
-3*x1 + 3*x2 + 7 >= 3*x0
-3*x2 + 7 >= 3*x0 + 3*x1
-7 >= 3*x0 + 3*x1 + 3*x2
+    sage: print(Nice_repr)
+    1 >= x0
+    1 >= x1
+    3*x1 + 7 >= 3*x0 + 3*x2
+    x0 + 1 >= 0
+    x1 + 1 >= 0
+    3*x0 + 7 >= 3*x1 + 3*x2
+    3*x0 + 3*x1 + 7 >= 3*x2
+    3*x0 + 3*x2 + 7 >= 3*x1
+    3*x0 + 3*x1 + 3*x2 + 7 >= 0
+    x2 + 1 >= 0
+    1 >= x2
+    3*x1 + 3*x2 + 7 >= 3*x0
+    3*x2 + 7 >= 3*x0 + 3*x1
+    7 >= 3*x0 + 3*x1 + 3*x2
 ```
+
+In the new version it gives:
+
+```
+    sage: print(TCube.Hrepresentation_str())
+                    -x0 >= -1 
+                    -x1 >= -1 
+    -3*x0 + 3*x1 - 3*x2 >= -7 
+                     x0 >= -1 
+                     x1 >= -1 
+     3*x0 - 3*x1 - 3*x2 >= -7 
+     3*x0 + 3*x1 - 3*x2 >= -7 
+     3*x0 - 3*x1 + 3*x2 >= -7 
+     3*x0 + 3*x1 + 3*x2 >= -7 
+                     x2 >= -1 
+                    -x2 >= -1 
+    -3*x0 + 3*x1 + 3*x2 >= -7 
+    -3*x0 - 3*x1 + 3*x2 >= -7 
+    -3*x0 - 3*x1 - 3*x2 >= -7
+
+    sage: print(TCube.Hrepresentation_str(latex=True))
+    \begin{array}{rcl}
+                                   -x_{0} & \geq & -1 \\
+                                   -x_{1} & \geq & -1 \\
+    -3 \, x_{0} + 3 \, x_{1} - 3 \, x_{2} & \geq & -7 \\
+                                    x_{0} & \geq & -1 \\
+                                    x_{1} & \geq & -1 \\
+     3 \, x_{0} - 3 \, x_{1} - 3 \, x_{2} & \geq & -7 \\
+     3 \, x_{0} + 3 \, x_{1} - 3 \, x_{2} & \geq & -7 \\
+     3 \, x_{0} - 3 \, x_{1} + 3 \, x_{2} & \geq & -7 \\
+     3 \, x_{0} + 3 \, x_{1} + 3 \, x_{2} & \geq & -7 \\
+                                    x_{2} & \geq & -1 \\
+                                   -x_{2} & \geq & -1 \\
+    -3 \, x_{0} + 3 \, x_{1} + 3 \, x_{2} & \geq & -7 \\
+    -3 \, x_{0} - 3 \, x_{1} + 3 \, x_{2} & \geq & -7 \\
+    -3 \, x_{0} - 3 \, x_{1} - 3 \, x_{2} & \geq & -7 
+    \end{array}
+```
+
+The `style` parameter allows to change the way to print the H-relations:
+
+```
+sage: P = polytopes.permutahedron(3)
+sage: print(P.Hrepresentation_str(style='<='))
+-x0 - x1 - x2 == -6 
+      x1 + x2 <=  5 
+           x2 <=  3 
+           x1 <=  3 
+          -x1 <= -1 
+     -x1 - x2 <= -3 
+          -x2 <= -1
+```
+
+In order to make the function more apparent, deprecation of the current function is perhaps a good idea and change the name to `Hrepresentation_str`.

[jplab]

Description changed:

--- 
+++ 
@@ -71,6 +71,14 @@
           -x1 <= -1 
      -x1 - x2 <= -3 
           -x2 <= -1
+sage: print(P.Hrepresentation_str(style='positive'))
+x0 + x1 + x2 == 6       
+           5 >= x1 + x2 
+           3 >= x2      
+           3 >= x1      
+          x1 >= 1       
+     x1 + x2 >= 3       
+          x2 >= 1
 ```
 
 In order to make the function more apparent, deprecation of the current function is perhaps a good idea and change the name to `Hrepresentation_str`.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

132c27a

Merge branch 'develop' into 24837

[sagetrac-git]

Changed commit from 7cf1a56 to 132c27a