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* Update PyQNormaliz by adding lattice points, integer hull and volume  
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* Algebraic polytopes in Qnormaliz using eantic [[https://trac.sagemath.org/ticket/25097#25097]]: convex hull computation completed, improvement of Qnormaliz input and output, control of interrupts and parallelization via libQnormaliz  * Algebraic polytopes in Qnormaliz using eantic [[https://trac.sagemath.org/ticket/25097#25097]]: convex hull computation completed, improvement of Qnormaliz input and output, control of interrupts and parallelization via libQnormaliz, lattice points, integer hull and volume added. Qnormaliz should be essentially complete now. 
A Roadmap for Optimization and Polyhedral Geometry softwares interactions
(around Sage, (PyQ)Normaliz, SCIP, eantic, Polymake, and others)
This page is intended to describe the current status of development of Sage related to optimization and polyhedral geometry.
Future & Current Projects
 Extend the usage of Normaliz in Sage
 Extend the polyhedral geometry component of sage
 Polyhedral arrangements and complexes
Meetings
Sage Days 84 on Polytopes in Olot
Tickets
Here are some practical lists of tickets:
Tickets from the Sage Days 84 March 2017
Tickets from the IMA Coding Sprint  April 2018
Current tickets of the Geometry component
Metatickets
There are already a few metatickets related to this topic:
Polytopes, lattice (integer) point counting / enumeration, and their applications
Improvements to MixedIntegerLinearProgram, its backends, and InteractiveLinearProgram
To do
Test the algebraic polytopes #25097
Make Polyhedron_normaliz accept algebraic stuff, related to #25097 (adapt _init_from_Hrepresentation)
 Add known irrational polytope to the library of polytopes
repr of NumberFields (the parents) should indicate its embedding if there is one #21161 (this ticket will help in debugging and have good feedback)
 Thematic Tutorial for Py(Q)Normaliz installation/Usage in Sage
 Increase documentation in Py(Q)Normaliz
 Update PyQNormaliz by adding lattice points, integer hull and volume
Deprecate the opacity argument for plot3d and use alpha #21984
Make Ehrhart (quasi)polynomial accessible through normaliz (and consisten with the current one) #18957
Adjust the new features of the normaliz backend to the latest version #25091 #25090
Progress Report Timeline
April 2018
Sage
Here are improvements realized during the Coding Sprints at the IMA in Minneapolis to objects related to polyhedron in Sage:
Thematic tutorial on polyhedron in Sage #22572
Make features of normaliz accessible #25091
number_field_elements_from_algebraics should create embedded number field elements #20181 Sagedevel discussion
Helper functions and improvements in the normaliz backend #25097
Change error message in construction of polyhedron object #24835
Improve the output of repr_pretty for Polyhedron #24837
Implement stacking onto a face of a polyhedron #24847
Implement join of polytopes #24848
Implement one point suspension and face split of polyhedron #24886
The polar of a polyhedron should carry the backend used #25081
Construct RationalPolyhedralFan from possibly overlapping cones #25122
polygon3d ignores the "alpha" (and equivalent "opacity") argument #25095
Update normaliz 3.5.3 and pynormaliz 1.12 in Sage. Now Positive review. #22984
PolyhedralComplex: preliminary implementation, see #20877
(Q)Normaliz
http://normaliz.uniosnabrueck.de
Upgrade normaliz to 3.5.3 and pynormaliz to 1.12 #22984: repair of performance loss
Upgrade normaliz to 3.5.4 and pynormaliz to 1.16 #25090: Ehrhart series and triangulation of polytope also for inhomogeneous input
Algebraic polytopes in Qnormaliz using eantic #25097: convex hull computation completed, improvement of Qnormaliz input and output, control of interrupts and parallelization via libQnormaliz, lattice points, integer hull and volume added. Qnormaliz should be essentially complete now.
fixed: getProjectionCone might segfault https://github.com/Normaliz/Normaliz/issues/180
fixed: BadInputException for ProjectCone https://github.com/Normaliz/Normaliz/issues/181
 General getters for cone properties. The getters can be used in future interfaces to make access to Normaliz cone properties easier
 resetGrading method for cone: Can be used to replace the grading and redo certain Normaliz computation without having to delete
 degree indepenent properties, such as hilbert bases.
 documentation of QNormaliz written
 extensive tests of QNormaliz
 link from libQnormaliz to libnormaliz in preparation for lattice point computation in algebraic polytopes
 further attempts to improve QNormaliz output (not yet complete)
 work on the C++ wrapper of eantic
 Normaliz 3.5.4 released
Py(Q)Normaliz
https://pypi.python.org/pypi/PyNormaliz https://github.com/Normaliz/PyNormaliz
PyNormaliz (last version is 1.17):
 All computation goals and output properties from Normaliz 3.5.4 are supported
It is possible to give functions RationalHandler, VectorHandler, and MatrixHandler to NmzResult to construct rationals, vectors, and matrices
Some documentation in the sources of NormalizModule.cpp
 Functionality to copy cone
Functionality to reset grading of a cone in PyNormaliz
PyQNormaliz (current beta is 0.2, not available on PIPy):
 All QNormaliz compute targets can be accessed
 Input of number_field data as string
 Input of number_field elements as list of 2tuples, or as string
Ouput handlers RationalHandler, NumberfieldElementHandler, VectorHandler, and MatrixHandler
See example worksheet: https://nbviewer.jupyter.org/github/sebasguts/PyQNormaliz/blob/master/examples/Dodecahedron.ipynb
Upgrade normaliz to 3.5.3 and pynormaliz to 1.12 #22984
Upgraded pynormaliz to 1.16 https://github.com/Normaliz/PyNormaliz
Started PyQNormaliz. https://github.com/sebasguts/PyQNormaliz
PyScipOpt
https://github.com/SCIPInterfaces/PySCIPOpt
Sage devel discussion
Polymake
Upgrade polymake to version 3.2r2 (current interface breaks) #24905
Sage 8.2
 Improvements:
 Library of polytopes accepts a backend parameter
 Fixed _facet_adjacency_matrix of nonfulldim. polyhedron
 Optimize count lattice points of polytopes
 New methods for polyhedron:
 get_integral_point
Sage 8.1
 Improvements:
 Fixed equation handling in .to_linear_program and integral_points_count
 Fixed sage_input to include the backend used
 Improved the polyhedron constructor
 Fixed .affine_hull() raising an assertion error
 Volume function handling better the different measures depending on the engine used
Sage 8.0
Here is a sample of changes related to Polyhedral Geometry in this release.
 Highlights:
 Integration with Latte (function .integrate() )
 New class for Voronoi Diagrams
 Backend polymake for polyhedron
 Improvements:
Fixed CartesianProduct with distinct dimensions
 Fixed an error in .is_lattice_polytope()
 Fixed overflow in integral_points()
 Fixed normaliz backend with empty polyhedron
 New methods for Polyhedron:
 integral_points_count()
Sage 7.6
Here is a sample of changes related to Polyhedral Geometry in this release:
 Improvements:
 documentation of Combinatorial and Discrete Geometry
 combinatorial_automorphism_group
 Fixes on .volume()
 Fixes in integral_points()
 New methods for Polyhedron:
 .is_inscribed()
 .neighborliness()
 .is_neighborly()
 .normal_fan()
 .face_fan()
 .is_combinatorially_isomorphic()
 .face_truncation()
New methods for SimplicialComplexes:
 star of a face
 stellar subdivision
 Generic interface to latte integrale:
 count points
A list of other Polyhedral Geometry softwares
What are other softwares dealing with polyhedral geometry? Here is a nonexhaustive list.
 Maple:
https://www.maplesoft.com/support/help/Maple/view.aspx?path=PolyhedralSets%2fPolyhedralSet (seems to be only rational and implemented in 2015).
http://qhull.org/ (seems old?)
https://www.maplesoft.com/products/maple/new_features/Maple2018/ComputationalGeometry.aspx
https://www.maplesoft.com/support/help/Maple/view.aspx?path=PolyhedralSets
 CGAL:
 A paper:
Jing & Maza https://dl.acm.org/citation.cfm?id=3177798
 Matlab:
 Matematica: