algebrite/sources/rationalize.coffee

Computer Algebra System in Coffeescript

DEBUG_RATIONALIZE = false

Eval_rationalize = ->
  push(cadr(p1))
  Eval()
  rationalize()

rationalize = ->
  x = expanding
  yyrationalize()
  expanding = x

yyrationalize = ->
  theArgument = pop()

  if (istensor(theArgument))
    __rationalize_tensor(theArgument)
    return

  expanding = 0

  if (car(theArgument) != symbol(ADD))
    push(theArgument)
    return

  if DEBUG_RATIONALIZE then console.log("rationalize: this is the input expr: " + theArgument)

  # get new denominator

  push(one)
  multiply_denominators(theArgument)
  commonDenominator = pop()

  if DEBUG_RATIONALIZE then console.log("rationalize: this is the new denominator: " + commonDenominator)

  # multiply each term by new denominator

  push(zero)
  eachTerm = cdr(theArgument)
  while (iscons(eachTerm))
    if DEBUG_RATIONALIZE then console.log("term: " + car(eachTerm))
    push(commonDenominator)
    push(car(eachTerm))
    multiply()
    add()
    eachTerm = cdr(eachTerm)

  if DEBUG_RATIONALIZE then console.log("rationalize: original terms times new denominator: " + stack[tos - 1])

  # collect common factors

  Condense()

  if DEBUG_RATIONALIZE then console.log("rationalize: after factoring: " + stack[tos - 1])

  # divide by common denominator

  push(commonDenominator)
  divide()

  if DEBUG_RATIONALIZE then console.log("rationalize: after dividing by new denom. (and we're done): " + stack[tos - 1])

multiply_denominators = (p) ->
  if (car(p) == symbol(ADD))
    p = cdr(p)
    while (iscons(p))
      multiply_denominators_term(car(p))
      p = cdr(p)
  else
    multiply_denominators_term(p)

multiply_denominators_term = (p) ->
  if (car(p) == symbol(MULTIPLY))
    p = cdr(p)
    while (iscons(p))
      multiply_denominators_factor(car(p))
      p = cdr(p)
  else
    multiply_denominators_factor(p)

multiply_denominators_factor = (p) ->
  if (car(p) != symbol(POWER))
    return

  push(p)

  p = caddr(p)

  # like x^(-2) ?

  if (isnegativenumber(p))
    inverse()
    __lcm()
    return

  # like x^(-a) ?

  if (car(p) == symbol(MULTIPLY) && isnegativenumber(cadr(p)))
    inverse()
    __lcm()
    return

  # no match

  pop()

__rationalize_tensor = (theTensor) ->

  i = 0
  push(theTensor)

  Eval(); # makes a copy

  theTensor = pop()

  if (!istensor(theTensor)) # might be zero
    push(theTensor)
    return

  n = theTensor.tensor.nelem

  for i in [0...n]
    push(theTensor.tensor.elem[i])
    rationalize()
    theTensor.tensor.elem[i] = pop()

  check_tensor_dimensions theTensor

  push(theTensor)



__lcm = ->
  save()

  p1 = pop()
  p2 = pop()

  push(p1)
  push(p2)
  multiply()
  push(p1)
  push(p2)
  gcd()
  divide()

  restore()