To do list: Tropical Geometry in Oscar

[YueRen]

This is a general to do list for the tropical package in branch yr/tropicalGeometry to keep track of all the tasks:

Major:

• add support for multiplicities (via attributes)
• add support for the tropical projective space (via flag in attributes which primarily affects how information is presented to the user)

Minor:

Hypersurfaces:

• improve tropical hypersurfaces: cache tropical polynomial via attributes
• improve tropical hypersurfaces: cache algebraic polynomial (if applicable) via attributes
• improve tropical hypersurfaces: cache initial forms via attribute (mainly as exercise to work towards caching initial ideals of tropical varieties)

Curves:

• add constructor: embedded tropical curve from edges + vertices
• add constructor embedded tropical curve from tropical variety (if dim=1)
• add constructor: abstract tropical curve from edges + vertex weights

Linear Spaces:

• add constructor: tropical linear space from Pluecker vector
• add constructor: tropical linear space from tropical / algebraic polynomial (if deg=1)
• add constructor: tropical linear space from tropical / algebraic matrix
• add constructor: tropical linear space from tropical variety (if deg=1)

General:

• improve intersect + stably_intersect: allow as input more than 2 tropical varieties
• add constructor: tropical hypersurface via algebraic polynomial
• improve all tropical: add visualization routines
• improve all tropical: add dual graphs routines
• improve polyhedral fans + complexes: add general support for symmetries (via existing polymake-internal functions)

[wdecker]

@YueRen Great! I am looking forward to follow the progress you are going to make!

With regard to identifiers etc we should coordinate naming with toric geometry and algebraic geometry.

[YueRen]

A lot of the things were implemented with #2832 so I will close this issue.