====================================================================
Hexadecimal Expansion
====================================================================

All rationals have repeating hexadecimal expansions.  The operation
hex returns these expansions of type HexadecimalExpansion.  Operations
to access the individual numerals of a hexadecimal expansion can be
obtained by converting the value to RadixExpansion(16).  More examples
of expansions are available in the DecimalExpansion, BinaryExpansion,
and RadixExpansion.

This is a hexadecimal expansion of a rational number. ::

  r := hex(22/7)
      ___
    3.249
                      Type: HexadecimalExpansion

Arithmetic is exact. ::

  r + hex(6/7)
    4
                      Type: HexadecimalExpansion

The period of the expansion can be short or long ::

  [hex(1/i) for i in 350..354]
       _______________    _________      _____    ______________________
   [0.00BB3EE721A54D88, 0.00BAB6561, 0.00BA2E8, 0.00B9A7862A0FF465879D5F,
       _____________________________
    0.00B92143FA36F5E02E4850FE8DBD78]
                      Type: List HexadecimalExpansion

or very long! ::

  hex(1/1007)
     _______________________________________________________________________
   0.0041149783F0BF2C7D13933192AF6980619EE345E91EC2BB9D5CCA5C071E40926E54E8D
     ______________________________________________
     DAE24196C0B2F8A0AAD60DBA57F5D4C8536262210C74F1
                      Type: HexadecimalExpansion

These numbers are bona fide algebraic objects. ::

  p := hex(1/4)*x**2 + hex(2/3)*x + hex(4/9)
        2     _      ___
    0.4x  + 0.Ax + 0.71C
                      Type: Polynomial HexadecimalExpansion

  q := D(p, x)
             _
    0.8x + 0.A
                      Type: Polynomial HexadecimalExpansion

  g := gcd(p, q)
          _
    x + 1.5
                      Type: Polynomial HexadecimalExpansion

See Also:

* )help RadixExpansion
* )help BinaryExpansion
* )help DecimalExpansion
* )show HexadecimalExpansion