====== BigObject LinesInCubic<Addition> ======
//from application [[..:tropical|tropical]]//\\
\\
 This represents the result of the method ''[[..:tropical#lines_in_cubic |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 ''[[..:tropical#visualize_in_surface |visualize_in_surface]]''.

  ? Type Parameters:
  :: ''Addition'':  Mode of tropical addition, must be ''[[..:common#Min |Min]]'' or ''[[..:common#Max |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
----
{{anchor:n_families:}}
  ?  **''N_FAMILIES''**
  :: The total number of families in ''[[..:tropical:LinesInCubic#LIST_FAMILY_FIXED_EDGE |LIST_FAMILY_FIXED_EDGE]]'', ''[[..:tropical:LinesInCubic#LIST_FAMILY_FIXED_VERTEX |LIST_FAMILY_FIXED_VERTEX]]'',  ''[[..:tropical:LinesInCubic#LIST_FAMILY_MOVING_EDGE |LIST_FAMILY_MOVING_EDGE]]'' and ''[[..:tropical:LinesInCubic#LIST_FAMILY_MOVING_VERTEX |LIST_FAMILY_MOVING_VERTEX]]''
    ? Type:
    :''[[..:common#Int |Int]]''
    ? from extension:
    : [[:external_software|bundled:atint]]


----
{{anchor:n_isolated:}}
  ?  **''N_ISOLATED''**
  :: The total number of elements in ''[[..:tropical:LinesInCubic#LIST_ISOLATED_EDGE |LIST_ISOLATED_EDGE]]'' and ''[[..:tropical:LinesInCubic#LIST_ISOLATED_NO_EDGE |LIST_ISOLATED_NO_EDGE]]''
    ? Type:
    :''[[..:common#Int |Int]]''
    ? from extension:
    : [[:external_software|bundled:atint]]


----

==== Defining properties ====
 The polynomial and the corresponding cubic.
----
{{anchor:cubic:}}
  ?  **''CUBIC''**
  :: The surface containing the lines
    ? Type:
    :''[[..:tropical:Cycle |Cycle]]<Addition>''
    ? from extension:
    : [[:external_software|bundled:atint]]


----
{{anchor:polynomial:}}
  ?  **''POLYNOMIAL''**
  :: The homogeneous tropical polynomial defining the surface
    ? Type:
    :''[[..:common#Polynomial |Polynomial]]<[[..:common#TropicalNumber |TropicalNumber]]<Addition,[[..:common#Rational |Rational]]>,[[..:common#Int |Int]]>''
    ? from extension:
    : [[:external_software|bundled:atint]]


----

==== Lists of lines ====
 These contain lists of certain (families of) lines.
----
{{anchor:list_family_fixed_edge:}}
  ?  **''LIST_FAMILY_FIXED_EDGE''**
  ::
    ? Type:
    :''[[..:tropical:Cycle |Cycle]]<Addition>''
    ? from extension:
    : [[:external_software|bundled:atint]]
    ? Methods of LIST_FAMILY_FIXED_EDGE:
    :
      ?  **''representative''**
      :: Returns a representative of the family.
        ? from extension:
        : [[:external_software|bundled:atint]]


----
{{anchor:list_family_fixed_vertex:}}
  ?  **''LIST_FAMILY_FIXED_VERTEX''**
  ::
    ? Type:
    :''[[..:tropical:Cycle |Cycle]]<Addition>''
    ? from extension:
    : [[:external_software|bundled:atint]]
    ? Methods of LIST_FAMILY_FIXED_VERTEX:
    :
      ?  **''representative''**
      :: Returns a representative of the family.
        ? from extension:
        : [[:external_software|bundled:atint]]


----
{{anchor:list_family_moving_edge:}}
  ?  **''LIST_FAMILY_MOVING_EDGE''**
  ::
    ? Type:
    :''[[..:tropical:Cycle |Cycle]]<Addition>''
    ? from extension:
    : [[:external_software|bundled:atint]]
    ? Methods of LIST_FAMILY_MOVING_EDGE:
    :
      ?  **''representative''**
      :: Returns a representative of the family.
        ? from extension:
        : [[:external_software|bundled:atint]]


----
{{anchor:list_family_moving_vertex:}}
  ?  **''LIST_FAMILY_MOVING_VERTEX''**
  ::
    ? Type:
    :''[[..:tropical:Cycle |Cycle]]<Addition>''
    ? from extension:
    : [[:external_software|bundled:atint]]
    ? Methods of LIST_FAMILY_MOVING_VERTEX:
    :
      ?  **''representative''**
      :: Returns a representative of the family.
        ? from extension:
        : [[:external_software|bundled:atint]]


----
{{anchor:list_isolated_edge:}}
  ?  **''LIST_ISOLATED_EDGE''**
  ::
    ? Type:
    :''[[..:tropical:Cycle |Cycle]]<Addition>''
    ? from extension:
    : [[:external_software|bundled:atint]]


----
{{anchor:list_isolated_no_edge:}}
  ?  **''LIST_ISOLATED_NO_EDGE''**
  ::
    ? Type:
    :''[[..:tropical:Cycle |Cycle]]<Addition>''
    ? from extension:
    : [[:external_software|bundled:atint]]


----
===== Methods =====

==== Lists of lines ====
 These contain lists of certain (families of) lines.
----
{{anchor:all_families:}}
  ?  **''all_families()''**
  ::
    ? Returns:
    :''[[..:tropical:Cycle |Cycle]]<Addition>''
    ? from extension:
    : [[:external_software|bundled:atint]]


----
{{anchor:all_isolated:}}
  ?  **''all_isolated()''**
  ::
    ? Returns:
    :''[[..:tropical:Cycle |Cycle]]<Addition>''
    ? from extension:
    : [[:external_software|bundled:atint]]


----
{{anchor:array_family_fixed_edge:}}
  ?  **''array_family_fixed_edge()''**
  ::
    ? Returns:
    :''[[..:tropical:Cycle |Cycle]]<Addition>''
    ? from extension:
    : [[:external_software|bundled:atint]]


----
{{anchor:array_family_fixed_vertex:}}
  ?  **''array_family_fixed_vertex()''**
  ::
    ? Returns:
    :''[[..:tropical:Cycle |Cycle]]<Addition>''
    ? from extension:
    : [[:external_software|bundled:atint]]


----
{{anchor:array_family_moving_edge:}}
  ?  **''array_family_moving_edge()''**
  ::
    ? Returns:
    :''[[..:tropical:Cycle |Cycle]]<Addition>''
    ? from extension:
    : [[:external_software|bundled:atint]]


----
{{anchor:array_family_moving_vertex:}}
  ?  **''array_family_moving_vertex()''**
  ::
    ? Returns:
    :''[[..:tropical:Cycle |Cycle]]<Addition>''
    ? from extension:
    : [[:external_software|bundled:atint]]


----
{{anchor:array_isolated_edge:}}
  ?  **''array_isolated_edge()''**
  ::
    ? Returns:
    :''[[..:tropical:Cycle |Cycle]]<Addition>''
    ? from extension:
    : [[:external_software|bundled:atint]]


----
{{anchor:array_isolated_no_edge:}}
  ?  **''array_isolated_no_edge()''**
  ::
    ? Returns:
    :''[[..:tropical:Cycle |Cycle]]<Addition>''
    ? from extension:
    : [[:external_software|bundled:atint]]


----