#-----------------------------------------------------------------------------
#
#  Hermite polynomial
#
#  Input:    tos-2    x  (can be a symbol or expr)
#
#      tos-1    n
#
#  Output:    Result on stack
#
#-----------------------------------------------------------------------------



hermite = ->
  save()
  yyhermite()
  restore()

# uses the recurrence relation H(x,n+1)=2*x*H(x,n)-2*n*H(x,n-1)

#define X p1
#define N p2
#define Y p3
#define Y1 p4
#define Y0 p5

yyhermite = ->

  n = 0

  p2 = pop()
  p1 = pop()

  push(p2)
  n = pop_integer()

  if (n < 0 || isNaN(n))
    push_symbol(HERMITE)
    push(p1)
    push(p2)
    list(3)
    return

  if (issymbol(p1))
    yyhermite2(n)
  else
    p3 = p1;      # do this when X is an expr
    p1 = symbol(SECRETX)
    yyhermite2(n)
    p1 = p3
    push(symbol(SECRETX))
    push(p1)
    subst()
    Eval()

yyhermite2 = (n) ->
  i = 0

  push_integer(1)
  push_integer(0)

  p4 = pop()

  for i in [0...n]

    p5 = p4

    p4 = pop()

    push(p1)
    push(p4)
    multiply()

    push_integer(i)
    push(p5)
    multiply()

    subtract()

    push_integer(2)
    multiply()