###
Convert complex z to rectangular form

  Input:    push  z

  Output:    Result on stack
###


DEBUG_RECT = false

Eval_rect = ->
  push(cadr(p1))
  Eval()
  rect()

rect = ->
  save()
  p1 = pop()
  input = p1

  if DEBUG_RECT then console.log "RECT of " + input

  if DEBUG_RECT then console.log "any clock forms in : " + input + " ? " + findPossibleClockForm(input)


  # if we assume real variables, then the
  # rect of any symbol is the symbol itself
  # (note that 'i' is not a symbol, it's made of (-1)^(1/2))
  # otherwise we have to leave unevalled
  if issymbol(p1)
    if DEBUG_RECT then console.log " rect: simple symbol: " + input
    if !isZeroAtomOrTensor(get_binding(symbol(ASSUME_REAL_VARIABLES)))
      push(p1)
    else
      push_symbol(YYRECT)
      push(p1)
      list(2)

  # TODO this is quite dirty, ideally we don't need this
  # but removing this creates a few failings in the tests
  # that I can't investigate right now.
  # --
  # if we assume all variables are real AND
  # it's not an exponential nor a polar nor a clock form
  # THEN rect(_) = _
  # note that these matches can be quite sloppy, one can find expressions
  # which shouldn't match but do
  # 
  else if !isZeroAtomOrTensor(get_binding(symbol(ASSUME_REAL_VARIABLES))) and
   !findPossibleExponentialForm(p1) and # no exp form?
   !findPossibleClockForm(p1) and # no clock form?
   !(Find(p1, symbol(SIN)) and Find(p1, symbol(COS)) and Find(p1, imaginaryunit)) # no polar form?
    if DEBUG_RECT then console.log " rect: simple symbol: " + input
    push(p1)

  # ib
  else if (car(p1) == symbol(MULTIPLY) and isimaginaryunit(cadr(p1)) and !isZeroAtomOrTensor(get_binding(symbol(ASSUME_REAL_VARIABLES))))
    push(p1)

  # sum
  else if (car(p1) == symbol(ADD))
    if DEBUG_RECT then console.log " rect - " + input + " is a sum "
    push_integer(0)
    p1 = cdr(p1)
    while (iscons(p1))
      push(car(p1))
      rect()
      add()
      p1 = cdr(p1)

  else
    # try to get to the rectangular form by doing
    # abs(p1) * (cos (theta) + i * sin(theta))
    # where theta is arg(p1)
    if DEBUG_RECT then console.log " rect - " + input + " is NOT a sum "

    push(p1);  # abs(z) * (cos(arg(z)) + i sin(arg(z)))
    abs()

    if DEBUG_RECT then console.log " rect - " + input + " abs: " + stack[tos-1].toString()
    push(p1)
    arg()
    if DEBUG_RECT then console.log " rect - " + input + " arg of " + p1 + " : " + stack[tos-1].toString()
    p1 = pop()
    push(p1)
    cosine()
    if DEBUG_RECT then console.log " rect - " + input + " cosine: " + stack[tos-1].toString()
    push(imaginaryunit)
    push(p1)
    sine()
    if DEBUG_RECT then console.log " rect - " + input + " sine: " + stack[tos-1].toString()
    multiply()
    if DEBUG_RECT then console.log " rect - " + input + " i * sine: " + stack[tos-1].toString()
    add()
    if DEBUG_RECT then console.log " rect - " + input + " cos + i * sine: " + stack[tos-1].toString()
    multiply()
  restore()
  if DEBUG_RECT then console.log "rect of " + input + " : " + stack[tos-1]