addcomb-js

AddComb.js is a javascript library for additive combinatorics calculation.

The Online Interface allows for full functionality of AddComb.js.

Use

To use AddComb.js, include the script in your html file.

<script src="https://PetereFrancis.com/addcomb-js/AddComb.min.js"></script>

Examples

The main bit of important code is the sumset calculations and the 7 "Chapter" functions.

Sumsets

To do sumset calculations, first create a new set object (FastSet for cyclic groups of order at most 31, otherwise GeneralSet). Then add contents to your set and call the appropriate sumset method.

// I want to create the set {1, 2, 3} and
// find its 2 fold restricted sumset in Z_13
let fs = new FastSet();
fs.add_all([1, 2, 3]);
let sumset1 = fs.hfold_restricted_sumset(2, 13);

// I want to create the set {(1,3), (2,14), (3,10)} and
// find its [0,3] fold signed sumset in Z_5 x Z_15
let gs = new GeneralSet();
fs.add_all([[1,3], [2,14], [3,10]]);
let sumset = fs.hfold_signed_sumset([0,3], [2,15]);

The same can be accomplished by creating a Computer object to complete the computation asynchronously:

// I want to create the set {(1,3), (2,14), (3,10)} and
// find its [0,3] fold signed sumset in Z_5 x Z_15
let computer = new Computer();
computer.start({
  purpose: 'sumset',
  info: {
    H_string: '[0,3]',
    set_contents: '(1,3), (2,14), (3,10)',
    restricted: false,
    signed: true,
    sizes: '13x15'
  },
  oncomplete: function(response) {
    console.log(response.data.sumset); // FastSet or GeneralSet, depending
    console.log(response.data.verbose_string);
  },
  onerror: function(response) {
    console.log(response.data.msg);
  },
  ontimeout: function(response) {
    console.log(response.data.msg);
  },
  timeout: 60000 // ms to continue computation before timeout
})

Chapter Functions

To execute chapter functions, you must first create a group object. By convention, the chapter functions usually take the group as an argument, but here, the group is an object and the chapter functions are all methods. If a verbose element is supplied, verbose printing will be allowed.

The verbose printing will be in the developer console during the computation, and once complete, will be added to the innerHTML verbose_element (the later must be done manually if using a Computer object).

<textarea id='verbose'></textarea>
<script>
  let verbose_element = document.getElementById('verbose');

  // I want to find mu^(Z_2xZ_15, {1, 2}) with verbose printing
  let group_2_15 = new Group([2,15], verbose_element);
  let result1 = group_2_15.mu({
    restricted: true,
    signed: false,
    H: new Set([1,2]),
    verbose: true
  });

  // I want to find nu±(Z_29, 5, [0,7]) without verbose printing
  let group_29 = new Group([29], verbose_element);
  let result2 = group.mu({
    restricted: false,
    signed: true,
    H: [0,7],
    verbose: false
  });

</script>

The same can be accomplished by creating a Computer object to complete the computation asynchronously:

<script src="AddComb.js"></script>
<textarea id='verbose'></textarea>
<script>
  let verbose_element = document.getElementById('verbose');

  // I want to find mu^(Z_2xZ_15, {1, 2}) with verbose printing
  let computer = new Computer();
  computer.start({
    purpose: 'function',
    info: {
      func:'mu',
      arg:'1,2',
      restricted:true,
      signed:false,
      sizes:'2x15',
      verbose:true
    },
    oncomplete: function(response) {
      verbose.innerHTML += response.data.verbose_string;
    },
    onerror: function(response) {
      console.log(response.data.msg);
    },
    ontimeout: function(response) {
      console.log(response.msg);
    },
    timeout: 10000 // ms to continue computation before timeout
  });


  // I want to find nu±(Z_29, 5, [0,7]) without verbose printing
  let computer = new Computer();
  computer.start({
    purpose: 'function',
    info: {
      func:'nu',
      arg:'5,[0,7]',
      restricted:false,
      signed:true,
      sizes:'29',
      verbose:false
    },
    oncomplete: function(response) {
      console.log(response.data.res);
    },
    onerror: function(response) {
      console.log(response.data.msg);
    },
    ontimeout: function(response) {
      console.log(response.msg);
    },
    timeout: 10000
  });

</script>