Solve irrational numbers.

ir-solve.js

//Matrix used to solve sets of numbers in x^n.
//This matrix can be enlarged to higher dimensional numbers past root of 5.

var SMat = [
  [01,0,0,0,0,0],
  [05,1,0,0,0,0],
  [10,4,1,0,0,0],
  [10,6,3,1,0,0],
  [05,4,3,2,1,0],
  [01,1,1,1,1,1]
];

//Calculate sums with the matrix.

function calc( v )
{
  var m = [], o = [], sum = 0;
  
  var s = SMat.length - v.length;
  
  for( var i1 = s; i1 < SMat.length; i1++ )
  {
    m = SMat[i1];
    
    for( var i2 = s; i2 < m.length; i2++ )
    {
      sum += m[i2] * v[i2-s];
    }
    
    o[i1-s] = sum; sum = 0;
  }
  
  return( o );
}

//Reverse sums with the matrix.

function rcalc( v )
{
  var m = [], o = [], sum = 0;
  
  var s = SMat.length - v.length;
  
  for( var i1 = s; i1 < SMat.length; i1++ )
  {
    m = SMat[i1]; sum = v[i1-s];
    
    for( var i2 = 0; i2 < o.length; i2++ )
    {
      sum -= m[i2+s] * o[i2];
    }
    
    o[i1-s] = sum;
  }
  
  return( o );
}

//Calculate each A part in number.

function calcA( v, n )
{
  var r1 = [], r2 = [];
  var o = [], a = -1;
  
  for( var i = 0, c = true; i < n; i++ )
  {
    r2 = r1 = v; while( ( c && r2[r2.length-1] <= 0 ) || ( !c && r2[r2.length-1] >= 0 ) )
    {
      ++a; r1 = r2; r2 = calc( r1 );
    }
    
    o[i] = a; a = -1; c = !c; v = r1.reverse();

    if( (c ? -v[0] : v[0]) >= 0 ){ break; }
  }
  
  return( o );
}

//Put the number together.

function calcNum( a )
{
  var num = a[a.length-1];
  
  for( var i = a.length - 2; i >= 0; i-- )
  {
    num = a[i] + 1/num;
  }
  
  return( num );
}

//Take the number apart.

function getParts( num, n )
{
  var a = [], r = 0;
  
  for( var i = 0; i < n; i++ )
  {
    a[a.length] = r = num & -1; num=1/(num-r);
  }
  
  return( a );
}

//Create and solve number patterns.
//cube root 2 vector.

var vect = [1,0,0,-2];

//cube root 2 vector to 12 parts.

var parts = calcA( vect, 12 );

/*Some other calculations you can do.
vect = [1,0,0,0,0,-911]; root 5 of 911.
vect = [2,0,0,0,0,-911]; root 5 of 911÷2.
vect = [1,0,-23]; square root of 23.
vect = [1,0,0,0,-0.5]; root 4 of 0.5.
To go higher than the root of 5 you will
Have to expand the SMat matrix.*/

//Put parts into number Value.

var val = calcNum( parts );

//Display parts and number value.

alert( "parts = " + parts + "\r\nval = " + val + "" );

//Take the number value apart to 12 parts.

var nParts = getParts( val, 12 );

alert( "take val apart: " + val + "\r\nparts = " + nParts + "" );

//When we take a number apart we can translate its parts back into its vector combination.