--Returns a function which takes a sequence of polynomial coefficients and
--returns two functions which evaluate the polynomial and its derivative, respectively
return function( coefs )
  local fixedPoint = coefs[0] or error( "Must have constant coefficient!" )
  --Interpolant, naive
  return function(x) 

    x = x - fixedPoint
    local y = fixedPoint
    local pow = 1
    local fact = 1
    for i = 1, #coefs do
      pow = pow * x
      fact = fact / i
      y = y + pow * fact * coefs[i]
    end
    return y
  end, 

  --Derivative, naive
  function(x) 

    x = x - fixedPoint
    local y = 0
    local pow = 1
    local fact = 1
    for i = 1, #coefs do
      y = y + pow * fact * coefs[i]
      pow = pow * x
      fact = fact / i
    end
    return y
  end


end