Rebased on 7.6.beta6

src/doc/en/reference/discrete_geometry/index.rst

@@ -0,0 +1,120 @@
+Combinatorial and Discrete Geometry
+===================================
+
+Sage includes classes for hyperplane arrangements, polyhedra, toric varieties
+(including polyhedral cones and fans), triangulations and some other helper
+classes and functions.
+
+Hyperplane arrangements
+-----------------------
+
+.. toctree::
+:maxdepth: 1
+
+sage/geometry/hyperplane_arrangement/arrangement
+sage/geometry/hyperplane_arrangement/library
+sage/geometry/hyperplane_arrangement/hyperplane
+sage/geometry/hyperplane_arrangement/affine_subspace
+sage/geometry/hyperplane_arrangement/plot
+
+Polyhedral computations
+-----------------------
+
+Polyhedra
+~~~~~~~~~
+
+.. toctree::
+:maxdepth: 1
+
+sage/geometry/polyhedron/library
+sage/geometry/polyhedron/constructor
+sage/geometry/polyhedron/parent
+sage/geometry/polyhedron/representation
+sage/geometry/polyhedron/plot
+sage/geometry/polyhedron/face
+sage/geometry/polyhedron/cdd_file_format
+
+Lattice polyhedra
+~~~~~~~~~~~~~~~~~
+
+.. toctree::
+:maxdepth: 1
+
+sage/geometry/lattice_polytope
+sage/geometry/polyhedron/lattice_euclidean_group_element
+sage/geometry/polyhedron/palp_database
+sage/geometry/polyhedron/ppl_lattice_polygon
+sage/geometry/polyhedron/ppl_lattice_polytope
+
+Toric geometry
+~~~~~~~~~~~~~~
+
+.. toctree::
+   :maxdepth: 1
+
+   sage/geometry/toric_lattice
+   sage/geometry/cone
+   sage/geometry/fan
+   sage/geometry/fan_morphism
+   sage/geometry/point_collection
+   sage/geometry/toric_plotter
+   sage/rings/polynomial/groebner_fan
+
+Base classes for polyhedra
+~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. toctree::
+   :maxdepth: 1
+
+   sage/geometry/polyhedron/base
+   sage/geometry/polyhedron/base_QQ
+   sage/geometry/polyhedron/base_ZZ
+   sage/geometry/polyhedron/base_RDF
+
+Backends for Polyhedra
+~~~~~~~~~~~~~~~~~~~~~~
+
+.. toctree::
+   :maxdepth: 1
+
+   sage/geometry/polyhedron/backend_cdd
+   sage/geometry/polyhedron/backend_field
+   sage/geometry/polyhedron/backend_normaliz
+   sage/geometry/polyhedron/backend_ppl
+   sage/geometry/polyhedron/double_description
+   sage/geometry/polyhedron/double_description_inhomogeneous
+
+
+Triangulations
+--------------
+
+.. toctree::
+   :maxdepth: 1
+
+   sage/geometry/triangulation/point_configuration
+   sage/geometry/triangulation/base
+   sage/geometry/triangulation/element
+
+Miscellaneous
+-------------
+
+.. toctree::
+   :maxdepth: 1
+
+   sage/geometry/linear_expression
+   sage/geometry/newton_polygon
+   sage/geometry/ribbon_graph
+   sage/geometry/pseudolines
+
+Helper functions
+----------------
+
+.. toctree::
+   :maxdepth: 1
+
+   sage/geometry/fan_isomorphism
+   sage/geometry/hasse_diagram
+   sage/geometry/integral_points
+   sage/geometry/hyperplane_arrangement/check_freeness
+
+.. include:: ../footer.txt

src/doc/en/reference/hyperbolic_geometry/conf.py

@@ -0,0 +1 @@
+../conf_sub.py

src/doc/en/reference/hyperbolic_geometry/index.rst

@@ -0,0 +1,14 @@
+Hyperbolic Geometry
+===================
+
+.. toctree::
+   :maxdepth: 1
+
+   sage/geometry/hyperbolic_space/hyperbolic_point
+   sage/geometry/hyperbolic_space/hyperbolic_isometry
+   sage/geometry/hyperbolic_space/hyperbolic_geodesic
+   sage/geometry/hyperbolic_space/hyperbolic_model
+   sage/geometry/hyperbolic_space/hyperbolic_interface
+
+
+.. include:: ../footer.txt

src/doc/en/reference/index.rst

@@ -83,7 +83,8 @@ Calculus
 Geometry and Topology
 ---------------------
 
-* :doc:`Combinatorial Geometry <geometry/index>`
+* :doc:`Combinatorial and Discrete Geometry <discrete_geometry/index>`
+* :doc:`Hyperbolic Geometry <hyperbolic_geometry/index>`
 * :doc:`Cell Complexes and their Homology <homology/index>`
 * :doc:`Differential Forms <tensor/index>`
 * :doc:`Manifolds <manifolds/index>`

src/sage/geometry/polyhedron/backend_normaliz.py

@@ -2,6 +2,11 @@
 """
 The Normaliz backend for polyhedral computations
 
+.. NOTE::
+
+    This backend requires `PyNormaliz <https://pypi.python.org/pypi/PyNormaliz/1.5>`_.
+    To install PyNormaliz, type :code:`sage -i pynormaliz` in the terminal.
+
 AUTHORS:
 
 - Matthias Köppe (2016-12): initial version
@@ -441,7 +446,7 @@ def integral_points(self, threshold=10000):
         INPUT:
 
         - ``threshold`` -- integer (default: 10000); use the naïve
-        algorithm as long as the bounding box is smaller than this
+          algorithm as long as the bounding box is smaller than this
 
         OUTPUT:
 

src/sage/geometry/polyhedron/base.py

@@ -2940,7 +2940,7 @@ def face_truncation(self, face, linear_coefficients=None, cut_frac=None):
         ``linear_coefficients``.
 
         To determine how deep the truncation is done, the method uses the
-        parameter ``cut_frac``. By default it is equal to `\frac{1}{3}. Once
+        parameter ``cut_frac``. By default it is equal to `\frac{1}{3}`. Once
         the normal vector of the cutting hyperplane is chosen, the vertices of
         polyhedron are evaluated according to the corresponding linear
         function. The parameter `\frac{1}{3}` means that the cutting

src/sage/geometry/polyhedron/constructor.py

@@ -57,6 +57,14 @@
     sage: triangle.vertices()
     (A vertex at (-1, 0), A vertex at (1, 0), A vertex at (0, 2))
 
+.. SEEALSO::
+
+    If one only needs to keep track of a system of linear system of
+    inequalities, one should also consider the class for mixed integer linear
+    programming.
+
+    - :mod:`Mixed Integer Linear Programming <sage.numerical.mip>`
+
 
 Unbounded Polyhedra
 -------------------
@@ -188,14 +196,44 @@
     A 2-dimensional polyhedron in (Number Field in sqrt3 with defining 
     polynomial x^2 - 3)^2 defined as the convex hull of 3 vertices
 
+Base classes
+------------
+
+Depending on the chosen base ring, a specific class is used to represent the polyhedron object.
+
+.. SEEALSO::
+
+    - :mod:`Base class for polyhedra <sage.geometry.polyhedron.base.Polyhedron_base>`
+    - :mod:`Base class for polyhedra over integers <sage.geometry.polyhedron.base_ZZ.Polyhedron_ZZ>`
+    - :mod:`Base class for polyhedra over rationals <sage.geometry.polyhedron.base_QQ.Polyhedron_QQ>`
+    - :mod:`Base class for polyhedra over RDF <sage.geometry.polyhedron.base_RDF.Polyhedron_RDF>`
+
+The most important base class is **Base class for polyhedra** from which other base classes and backends inherit.
+
+Backends
+--------
+
+There are different backends available to deal with polyhedron objects.
+
+.. SEEALSO::
+
+    - :mod:`cdd backend for polyhedra <sage.geometry.polyhedron.backend_cdd.Polyhedron_cdd>`
+    - :mod:`field backend for polyhedra <sage.geometry.polyhedron.backend_field.Polyhedron_field>`
+    - :mod:`normaliz backend for polyhedra <sage.geometry.polyhedron.backend_normaliz.Polyhedron_normaliz>`
+    - :mod:`ppl backend for polyhedra <sage.geometry.polyhedron.backend_ppl.Polyhedron_ppl>`
+
+.. NOTE::
+
+    Depending on the backend used, it may occur that different methods are
+    available or not.
 
 Appendix
 --------
 
 REFERENCES:
 
     Komei Fukuda's `FAQ in Polyhedral Computation
-    <http://www.ifor.math.ethz.ch/~fukuda/polyfaq/polyfaq.html>`_
+    <https://www.inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html>`_
 
 AUTHORS: