Xholon - Mathematical Objects

README.md

Xholon - Mathematical Ojects

List and describe all the mathematical objects in Xholon.

This will include ojects of type:

• set
• list
• poset, toset
• arrow, function, morphism
• category
• group
• ...

Include official math definitions.

Sets

xholonWorkbook.xml

<?xml version="1.0" encoding="UTF-8"?>
<!--Xholon Workbook http://www.primordion.com/Xholon/gwt/ MIT License, Copyright (C) Ken Webb, Fri Jul 14 2023 23:22:13 GMT-0400 (GMT-04:00)-->
<XholonWorkbook>

<Notes><![CDATA[
Xholon
------
Title: Xholon - Mathematical Objects
Description: 
Url: http://www.primordion.com/Xholon/gwt/
InternalName: e0b3e2231362250928cfc75eb399f90f
Keywords: 

My Notes
--------
14 July 2023

See brief notes in my notebook for 13 July 2023.

Use Xholon visit() to generate Sets, etc.

Use Julia to regenerate the Xholon tree
 - given the set of all Xholon nodes; a list
  + the set of all BT parent-child pairs

maybe write it as Julia data structures
 - data frames
 - Catlab formats

References
----------
(1) https://www.primordion.com/Xholon/gwt/wb/editwb.html?app=568ffc4faf650b8e8ef4317bc0bc561b&src=gist
    Xholon visit - experiments

]]></Notes>

<markdown><![CDATA[
##Xholon - Mathematical Ojects

List and describe all the mathematical objects in Xholon.
Provide a JS function that generates each mathematical object from the Xholon tree.

This will include ojects of type:
- set
- list
- poset, toset
- arrow, function, morphism
- category
- group
- ...

Include official math definitions.

###Sets
* set of all nodes in the complete Xholon tree
* set of all BT parent-child pairs
* set of all XML-type parent-child pairs

###Morphisms
* can be represented as pairs

]]></markdown> 

<_-.XholonClass>
  <PhysicalSystem/>
  
  <Block/>
  <Experiment>
    <One/>
    <Two/>
    <Three/>
    <Four/>
    <Five/>
    <Six/>
    <Seven/>
  </Experiment>
  
</_-.XholonClass>

<xholonClassDetails>
  <!--<Block>
    <port name="height" connector="Height"/>
  </Block>-->
</xholonClassDetails>

<PhysicalSystem>
  <Block/>
  <Experiment/>
  <One/>
</PhysicalSystem>

<Experimentbehavior implName="org.primordion.xholon.base.Behavior_gwtjs"><![CDATA[

// functions for use with visit()
const funk = x => x + 5;

// build child-parent pair
const buildPair = node => `[${node.name().substring(0, 5)}, ${node.parent() ? node.parent().name().substring(0, 5) : "null"}]`;

var me, count, arrId, arrName, arrPairs, setId, beh = {
  postConfigure: function() {
    me = this.cnode.parent();
    me.println(funk(6));
    count = 0;
    arrId = [];
    arrName = [];
    arrPairs = [];
    $wnd.xh.root().append(this.cnode.remove());
    //me.visit(this.cnode); // 1
    $wnd.xh.root().visit(this.cnode); // 4
    //$wnd.xh.app().visit(this.cnode); // 485
    me.println(count); // 4
    me.println(arrId); // 0,45,46,47
    me.println(arrName); // lots
    me.println(arrPairs); // 
    setId = new Set(arrId);
    me.println(setId); // 
  },
  //act: function() {
    //me.println(this.toString());
  //},
  visit: function(visitor) {
    count++;
    arrId.push(visitor.id());
    arrName.push(visitor.name().substring(0, 5));
    //const a = visitor.name().substring(0, 5);
    //const b = visitor.parent() ? visitor.parent().name().substring(0, 5) : "null";
    //arrPairs.push(`[${a}, ${b}]`);
    arrPairs.push(buildPair(visitor));
    return true;
  }
}
//# sourceURL=Experimentbehavior.js
]]></Experimentbehavior>

<SvgClient><Attribute_String roleName="svgUri"><![CDATA[data:image/svg+xml,
<svg width="100" height="50" xmlns="http://www.w3.org/2000/svg">
  <g>
    <title>Experiment</title>
    <rect id="PhysicalSystem/Experiment" fill="#98FB98" height="50" width="50" x="25" y="0"/>
    <g>
      <title>Experiment</title>
      <rect id="PhysicalSystem/Experiment" fill="#6AB06A" height="50" width="10" x="80" y="0"/>
    </g>
  </g>
</svg>
]]></Attribute_String><Attribute_String roleName="setup">${MODELNAME_DEFAULT},${SVGURI_DEFAULT}</Attribute_String></SvgClient>

</XholonWorkbook>