Laboratoire de l'Informatique et du Parallélisme » Pobyso

def lcmm(rationalList = None):

    """ 

    Compute the lcm of an sequence (list, tuple) of numbers

    """

    # No argument.

    if rationalList is None:

        raise TypeError('lcmm takes a list of rationals')

    # Try the len function.

    try:

        listLength = len(rationalList)

    except Exception:

        print "lcmm:", rationalList, "does not understand the len() function."

        return(0)

    # An empty list: return 0

    if listLength == 0:

        return(0)

    # Only one element, return it, wahtever it is.

    if listLength == 1:

        return(rationalList[0])

    try:

        return(reduce(lcm, rationalList))

    except Exception:

        print "Exception raised in lcmm!"

        return(0)

def denominators(rationalList = None):

    """

    Compute the list of the denominators of a rational numbers list.

    """

    # No argument.

    if rationalList is None:

        raise TypeError('numerators takes a list of rationals.')

    try:

        listLength = len(rationalList)

    except Exception:

        print "denominators:", rationalList, \

                "does not understand the len() function."

        return([])

    if listLength == 0:

        return([])

    if listLength == 1:

        try:

            return(QQ(rationalList[0]).denominator())

        except Exception:

            print "denominators:", rationalList[0], \

                    "has no \"denominator()\" member." 

            return([])

    denominatorsList = []    

    for i in xrange(listLength):

        try:

            denominatorsList.append(QQ(rationalList[i]).denominator())

        except Exception:

            print "denominators:", rationalList[i], \

                    "has no \"denominator()\" member." 

            return([])

    return(denominatorsList)

def numerators(rationalList = None):

    """

    Compute the list of the numerators of a rational numbers list.

    """

    # No argument.

    if rationalList is None:

        raise TypeError('numerators takes a list of rationals.')

    try:

        listLength = len(rationalList)

    except Exception:

        print "numerators:", rationalList, \

                "does not understand the len() function."

        return([])

    if listLength == 0:

        return([])

    if listLength == 1:

        try:

            return(QQ(rationalList[0]).numerator())

        except Exception:

            print "denominators:", rationalList[0], \

                    "has no \"numerator()\" member." 

            return([])

    numeratorsList = []    

    for i in xrange(listLength):

        try:

            numeratorsList.append(QQ(rationalList[i]).numerator())

        except Exception:

            print "numerators:", rationalList[i], \

                    "has no \"numerator()\" member." 

            return([])

    return(numeratorsList)

  <li>when you get a too large error, reduce (e. g. divide by 2) the interval by

    lowering the upper bound until the computed error matches the target

  <li>this upper bound becomes the lower bound of the next interval, always

interval width too agressively.  There is no point in getting a too small approximation error since it multiplies the number of interval (and

lengthens the subsequent manipulations that are made on each sub-interval).</p>

<p>In step 3 you probably inutily compute polynomials for too large intervals

<p>The whole idea is to reduce the number of polynomial computations and get the

maximum width (compatible with the expected approwimaiton error).</p>

<p>Adjacent question: is it possible, given a the result of a previous

computation, to forecast the effect on the approximation precision of a degree

in(de)crease?</p>