# pretty print



bake = ->
  h = 0
  s = 0
  t = 0
  x = 0
  y = 0
  z = 0

  expanding++

  save()

  p1 = pop()

  s = ispolyexpandedform(p1, symbol(SYMBOL_S))
  t = ispolyexpandedform(p1, symbol(SYMBOL_T))
  x = ispolyexpandedform(p1, symbol(SYMBOL_X))
  y = ispolyexpandedform(p1, symbol(SYMBOL_Y))
  z = ispolyexpandedform(p1, symbol(SYMBOL_Z))

  if (s == 1 && t == 0 && x == 0 && y == 0 && z == 0)
    p2 = symbol(SYMBOL_S)
    bake_poly()
  else if (s == 0 && t == 1 && x == 0 && y == 0 && z == 0)
    p2 = symbol(SYMBOL_T)
    bake_poly()
  else if (s == 0 && t == 0 && x == 1 && y == 0 && z == 0)
    p2 = symbol(SYMBOL_X)
    bake_poly()
  else if (s == 0 && t == 0 && x == 0 && y == 1 && z == 0)
    p2 = symbol(SYMBOL_Y)
    bake_poly()
  else if (s == 0 && t == 0 && x == 0 && y == 0 && z == 1)
    p2 = symbol(SYMBOL_Z)
    bake_poly()
  # don't bake the contents of some constructs such as "for"
  # because we don't want to evaluate the body of
  # such constructs "statically", i.e. without fully running
  # the loops.
  else if (iscons(p1)) and car(p1) != symbol(FOR)
    h = tos
    push(car(p1))
    p1 = cdr(p1)
    while (iscons(p1))
      push(car(p1))
      bake()
      p1 = cdr(p1)
    list(tos - h)
  else
    push(p1)

  restore()

  expanding--

polyform = ->
  h = 0

  save()

  p2 = pop()
  p1 = pop()

  if (ispolyexpandedform(p1, p2))
    bake_poly()
  else if (iscons(p1))
    h = tos
    push(car(p1))
    p1 = cdr(p1)
    while (iscons(p1))
      push(car(p1))
      push(p2)
      polyform()
      p1 = cdr(p1)
    list(tos - h)
  else
    push(p1)

  restore()

bake_poly = ->
  h = 0
  i = 0
  k = 0
  n = 0
  #U **a
  a = tos
  k = coeff(p2, p1)
  h = tos
  for i in[(k - 1)..0] by -1
    p1 = stack[a+i]
    bake_poly_term(i)
  n = tos - h
  if (n > 1)
    list(n)
    push(symbol(ADD))
    swap()
    cons()
  p1 = pop()
  moveTos tos - k
  push(p1)

# p1 points to coefficient of p2 ^ k

# k is an int
bake_poly_term = (k) ->
  h = 0
  n = 0

  if (isZeroAtomOrTensor(p1))
    return

  # constant term?

  if (k == 0)
    if (car(p1) == symbol(ADD))
      p1 = cdr(p1)
      while (iscons(p1))
        push(car(p1))
        p1 = cdr(p1)
    else
      push(p1)
    return

  h = tos

  # coefficient

  if (car(p1) == symbol(MULTIPLY))
    p1 = cdr(p1)
    while (iscons(p1))
      push(car(p1))
      p1 = cdr(p1)
  else if (!equaln(p1, 1))
    push(p1)

  # x ^ k

  if (k == 1)
    push(p2)
  else
    push(symbol(POWER))
    push(p2)
    push_integer(k)
    list(3)

  n = tos - h

  if (n > 1)
    list(n)
    push(symbol(MULTIPLY))
    swap()
    cons()