discrete mathematics

div-rel.rb

# make Rel in Hasse diagram
# 0 and 1 are trivial and omitted

require 'prime'

Graph = Data.define(:nodes, :edges) do
  def initialize(nodes: [], edges: [])
    super
  end
end

# main
d = Graph.new
Prime.each(9) do |pn|
  cod = d.nodes.map { |from| from*pn }
  # destructive!
  d.edges
   .concat(d.nodes.zip(cod))
   .concat(cod.map{ |to| [pn,to] })
  # destructive!
  d.nodes
   .append(pn)
   .concat(cod)
end
# add square numbers
ss = d.nodes.map { it*it }
d.edges.concat(d.nodes.zip(ss))
d.nodes.concat(ss)
# print
pp d

Vectors of Prime Factors

• 1; 0,1; 0,0,1; ...
• 2; 1,1; 0,2; 1,0,1; ...
• 3; 1,1,1; 2,1; 1,2; ...
• ...

---
title: Divisor Relation
---
flowchart
	0 -->|⊃| 1
	1 -->|⊃| 2
	1 -->|⊃| 3
	1 -->|⊃| 4
	2 -->|⊃| 4
	1 -->|⊃| 5
	1 -->|⊃| 6
	2 -->|⊃| 6
	3 -->|⊃| 6
	1 -->|⊃| 7
	1 -->|⊃| 8
	2 -->|⊃| 8
	4 -->|⊃| 8
	1 -->|⊃| 9
	3 -->|⊃| 9
	1 -->|⊃| 10
	2 -->|⊃| 10
	5 -->|⊃| 10

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