### circexp =====================================================================

Tags
----
scripting, JS, internal, treenode, general concept

Parameters
----------
x

General description
-------------------

Returns expression x with circular and hyperbolic functions converted to exponential forms. Sometimes this will simplify an expression.

###


Eval_circexp = ->
  push(cadr(p1))
  Eval()

  circexp()

  # normalize

  Eval()

circexp = ->
  i = 0
  h = 0
  save()
  p1 = pop()

  if (car(p1) == symbol(COS))
    push(cadr(p1))
    expcos()
    restore()
    return

  if (car(p1) == symbol(SIN))
    push(cadr(p1))
    expsin()
    restore()
    return

  if (car(p1) == symbol(TAN))
    p1 = cadr(p1)
    push(imaginaryunit)
    push(p1)
    multiply()
    exponential()
    p2 = pop()
    push(imaginaryunit)
    push(p1)
    multiply()
    negate()
    exponential()
    p3 = pop()
    push(p3)
    push(p2)
    subtract()
    push(imaginaryunit)
    multiply()
    push(p2)
    push(p3)
    add()
    divide()
    restore()
    return

  if (car(p1) == symbol(COSH))
    p1 = cadr(p1)
    push(p1)
    exponential()
    push(p1)
    negate()
    exponential()
    add()
    push_rational(1, 2)
    multiply()
    restore()
    return

  if (car(p1) == symbol(SINH))
    p1 = cadr(p1)
    push(p1)
    exponential()
    push(p1)
    negate()
    exponential()
    subtract()
    push_rational(1, 2)
    multiply()
    restore()
    return

  if (car(p1) == symbol(TANH))
    p1 = cadr(p1)
    push(p1)
    push_integer(2)
    multiply()
    exponential()
    p1 = pop()
    push(p1)
    push_integer(1)
    subtract()
    push(p1)
    push_integer(1)
    add()
    divide()
    restore()
    return

  if (iscons(p1))
    h = tos
    while (iscons(p1))
      push(car(p1))
      circexp()
      p1 = cdr(p1)
    list(tos - h)
    restore()
    return

  if (p1.k == TENSOR)
    push(p1)
    copy_tensor()
    p1 = pop()
    for i in [0...p1.tensor.nelem]
      push(p1.tensor.elem[i])
      circexp()
      p1.tensor.elem[i] = pop()
    push(p1)
    restore()
    return

  push(p1)
  restore()