Improve the output of repr_pretty for Polyhedron

[jipilab]

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.

[jipilab]

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

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New commits:

​7cf1a56

first version