documentation:latest:tropical:linesincubic

Available versions of this document: latest release, release 4.0, release 3.6, release 3.5, nightly master

Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2

from application tropical

This represents the result of the method lines_in_cubic. It contains: The tropical polynomial representing the surface, the surface itself as a Cycle and lists of lines and families of different types, each starting with LIST_… The object also has methods, starting with array_… that return the corresponding LIST_… as a perl array. The different (lists of) lines can be visualized nicely with visualize_in_surface.

Type Parameters:

Addition: Mode of tropical addition, must be Min or Max. There is on purpose no default value for it.

These count lines or families of lines in the cubic.# @category Defining properties

N_FAMILIES

The total number of families in LIST_FAMILY_FIXED_EDGE, LIST_FAMILY_FIXED_VERTEX, LIST_FAMILY_MOVING_EDGE and LIST_FAMILY_MOVING_VERTEX

Type:
Int
from extension:

N_ISOLATED

The total number of elements in LIST_ISOLATED_EDGE and LIST_ISOLATED_NO_EDGE

Type:
Int
from extension:

The polynomial and the corresponding cubic.

CUBIC

The surface containing the lines

Type:
Cycle<Addition>
from extension:

POLYNOMIAL

The homogeneous tropical polynomial defining the surface

Type:
Polynomial<TropicalNumber<Addition,Rational>,Int>
from extension:

These contain lists of certain (families of) lines.

LIST_FAMILY_FIXED_EDGE
Type:
Cycle<Addition>
from extension:
Methods of LIST_FAMILY_FIXED_EDGE:
representative

Returns a representative of the family.

from extension:

LIST_FAMILY_FIXED_VERTEX
Type:
Cycle<Addition>
from extension:
Methods of LIST_FAMILY_FIXED_VERTEX:
representative

Returns a representative of the family.

from extension:

LIST_FAMILY_MOVING_EDGE
Type:
Cycle<Addition>
from extension:
Methods of LIST_FAMILY_MOVING_EDGE:
representative

Returns a representative of the family.

from extension:

LIST_FAMILY_MOVING_VERTEX
Type:
Cycle<Addition>
from extension:
Methods of LIST_FAMILY_MOVING_VERTEX:
representative

Returns a representative of the family.

from extension:

LIST_ISOLATED_EDGE
Type:
Cycle<Addition>
from extension:

LIST_ISOLATED_NO_EDGE
Type:
Cycle<Addition>
from extension:

These contain lists of certain (families of) lines.

all_families()
Returns:
Cycle<Addition>
from extension:

all_isolated()
Returns:
Cycle<Addition>
from extension:

array_family_fixed_edge()
Returns:
Cycle<Addition>
from extension:

array_family_fixed_vertex()
Returns:
Cycle<Addition>
from extension:

array_family_moving_edge()
Returns:
Cycle<Addition>
from extension:

array_family_moving_vertex()
Returns:
Cycle<Addition>
from extension:

array_isolated_edge()
Returns:
Cycle<Addition>
from extension:

array_isolated_no_edge()
Returns:
Cycle<Addition>
from extension:

• documentation/latest/tropical/linesincubic.txt