Use Case

classDiagram
    generator_rational --|> generator
    gen_rational_config_t --|> gen_config_t
    gen_rational_config_t *-- notation_tv
    generator_rational *-- gen_rational_config_t

    class generator {
        <<interface>>
    }

    class generator_rational {
<<>>
}

class gen_rational_config_t {
<<struct>>
+ notation_tv
}

class gen_config_t {
<<interface>>

}

class notation_tv{
<<>>
}

Language

C

Implements

• Generator Interface

Uses

• Notation Twist Vector

Libraries

N/A

Functionality

A rational tangle is given by alternating NE,SE and SE,SW twisting of the \(0\) tangle\({}^{[2]}\)\({}^{[1]}\). A canonical combinatorial description of a rational tangle can be given by the Twist Vector.

This module generates twist vectors and in doing so rational tangles. A normal flows go as:

Configuration

stateDiagram-v2
  state "Init local configuration" as Sc

    [*] --> Sc
    Sc --> [*]

Generate

stateDiagram-v2
  state "Get Combination of CN" as gen
  state join_state <<fork>>
  state is_even <<choice>>
  state no_combinations <<choice>>
  state "Print" as print {
  state "Set TV values" as stv
  state "Set CN value" as scv
    [*] --> stv
    stv --> scv
    scv --> [*]
  }

  state "Oddify Even combination" as even {
  state "shift array left"  as shiftL
  state "shift array right" as shiftR
  state "prepend 0" as pp0
    [*] --> shiftR
    shiftR --> pp0
    pp0 --> print
    print --> shiftL
    shiftL --> join_state


  }

    [*] --> gen
    gen --> no_combinations
  no_combinations --> is_even: if is not final combination
    no_combinations --> [*] : if is final combination

  is_even --> even: if tv.length % 2 == 0
    is_even --> print : if tv.length % 2 == 1
    print --> join_state
    join_state --> gen

Cite

1. Conway, J.H. “An Enumeration of Knots and Links, and Some of Their Algebraic Properties.” In Computational Problems in Abstract Algebra, 329–58. Elsevier, 1970. https://doi.org/10.1016/B978-0-08-012975-4.50034-5.
2. Kauffman, Louis H., and Sofia Lambropoulou. “On the Classification of Rational Knots,” 2002. https://doi.org/10.48550/ARXIV.MATH/0212011.