Table of Contents

BigObject LinesInCubic<Addition>

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.

Properties

Counts of lines

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:
bundled:atint

N_ISOLATED

The total number of elements in LIST_ISOLATED_EDGE and LIST_ISOLATED_NO_EDGE

Type:
Int
from extension:
bundled:atint

Defining properties

The polynomial and the corresponding cubic.

CUBIC

The surface containing the lines

Type:
Cycle<Addition>
from extension:
bundled:atint

POLYNOMIAL

The homogeneous tropical polynomial defining the surface

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

Lists of lines

These contain lists of certain (families of) lines.

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

Returns a representative of the family.

from extension:
bundled:atint

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

Returns a representative of the family.

from extension:
bundled:atint

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

Returns a representative of the family.

from extension:
bundled:atint

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

Returns a representative of the family.

from extension:
bundled:atint

LIST_ISOLATED_EDGE
Type:
Cycle<Addition>
from extension:
bundled:atint

LIST_ISOLATED_NO_EDGE
Type:
Cycle<Addition>
from extension:
bundled:atint

Methods

Lists of lines

These contain lists of certain (families of) lines.

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

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

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

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

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

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

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

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