Laboratoire de l'Informatique et du Parallélisme » Pobyso

def spo_float_poly_of_float_to_rat_poly_of_rat(polyOfFloat):

    """

    Create a polynomial over the rationals from a polynomial over

    a RealField.

    Important warning: default Sage behavior is to convert coefficients

    using continued fractions instead of making a simple conversion

    with a powers of two at denominators (and possible simplification).

    Hence conversion is not exact but with a relative error around 10^(-521).

    """

    ratPolynomialRing = QQ[str(polyOfFloat.variables()[0])]

    return(ratPolynomialRing(polyOfFloat))

# End spo_float_poly_of_float_to_rat_poly_of_rat.

def spo_float_poly_of_float_to_rat_poly_of_rat_pow_two(polyOfFloat):

    """

    Create a polynomial over the rationals from a polynomial over

    a RealField where all denominators are

    powers of two.

    Allows for exact conversions (and lcm computation of the coefficients

    denominator).

    """

    polyVariable = polyOfFloat.variables()[0] 

    RPR = QQ[str(polyVariable)]

    polyCoeffs      = polyOfFloat.coefficients()

    #print polyCoeffs

    polyExponents   = polyOfFloat.exponents()

    #print polyExponents

    polyDenomPtwoCoeffs = []

    for coeff in polyCoeffs:

        polyDenomPtwoCoeffs.append(sno_float_to_rat_pow_of_two_denom(coeff))

        #print "Converted coefficient:", sno_float_to_rat_pow_of_two_denom(coeff),

        #print type(sno_float_to_rat_pow_of_two_denom(coeff))

    ratPoly = RPR(0)

    #print type(ratPoly)

    ## !!! CAUTION !!! Do not use the RPR(coeff * polyVariagle^exponent)

    #  construction.

    #  The coefficient becomes plainly wrong when exponent == 0.

    #  No clue as to why.

    for coeff, exponent in zip(polyDenomPtwoCoeffs, polyExponents):

        ratPoly += coeff * RPR(polyVariable^exponent)

    return ratPoly

# End slz_float_poly_of_float_to_rat_poly_of_rat.