Laboratoire de l'Informatique et du Parallélisme » Pobyso

def spo_polynomial_to_polynomials_list_3(p, alpha, N, columnsWidth=0):

    """

    From p, alpha, N build a list of polynomials...

    TODO: more in depth rationale...

    Our goal is to introduce each monomial with the smallest coefficient.

    Parameters

    ----------

    p: the (bivariate) polynomial;

    pRing: the ring over which p is defined;

    alpha:

    N:

    columsWidth: if == 0, no information is displayed, otherwise data is 

                 printed in colums of columnsWitdth width.

    """

    pRing = p.parent()

    knownMonomials = []

    polynomialsList = []

    pVariables = p.variables()

    iVariable = pVariables[0]

    tVariable = pVariables[1]

    polynomialAtPower = pRing(1)

    currentPolynomial = pRing(1)

    pIdegree = p.degree(iVariable)

    pTdegree = p.degree(tVariable)

    currentIdegree = currentPolynomial.degree(iVariable)

    nAtAlpha = N^alpha

    nAtPower = nAtAlpha

    polExpStr = ""

    # We work from p^0 * N^alpha to p^alpha * N^0

    for pPower in xrange(0, alpha + 1):

        # pPower == 0 is a special case. We introduce all the monomials in i 

        # up to i^pIdegree.

        if pPower == 0:

            # Notice who iPower runs up to i^pIdegree.

            for iPower in xrange(0, pIdegree + 1): 

                # No t power is taken into account as we limit our selves to

                # degree 1 in t and make no "t-shifts".

                if columnsWidth != 0:

                    polExpStr = spo_expression_as_string(iPower, 

                                                         0, 

                                                         0, 

                                                         alpha)

                    print "->", polExpStr

                currentExpression = iVariable^iPower * nAtAlpha

                # polynomialAtPower == 1 here. Next line should be commented

                # out but it does not work! Some conversion problem?

                currentPolynomial = pRing(currentExpression)

                polynomialsList.append(currentPolynomial) 

            # End for iPower.

        else: # pPower > 0: (p^1..p^alpha)

            # This where we introduce the p^pPower * N^(alpha-pPower)

            # polynomial. This is also where the t^pPower monomials shows up for

            # the first time. It app

            if columnsWidth != 0:

                polExpStr = spo_expression_as_string(0, 0, pPower, alpha-pPower)

                print "->", polExpStr

            currentPolynomial = polynomialAtPower * nAtPower

            polynomialsList.append(currentPolynomial) 

            # Exit when pPower == alpha

            if pPower == alpha:

                return((knownMonomials, polynomialsList))

            # This is where the "i-shifts" take place. Mixed terms, i^k * t^l

            # (that were introduced at a previous

            # stage or are introduced now) are only shifted to already existing 

            # ones with the notable exception of i^iPower * t^pPower, which

            # must be manually introduced.

            # p^pPower is "shifted" to higher degrees in i as far as 

            # possible, up to of the degree in i of p^(pPower+1).

            # These "pure" i^k monomials can only show up with i multiplications.

            for iPower in xrange(1, pIdegree + 1):

                # The i^iPower * t^pPower monomial. Notice the alpha exponent

                # for N.

                internalIpower = iPower

                for tPower in xrange(pPower,0,-1):

                    if columnsWidth != 0:

                        polExpStr = spo_expression_as_string(internalIpower, \

                                                             tPower,  \

                                                             0, \

                                                             alpha)

                        print "->", polExpStr

                    currentExpression = i^internalIpower * t^tPower * nAtAlpha

                    currentPolynomial = pRing(currentExpression)

                    polynomialsList.append(currentPolynomial) 

                    internalIpower += pIdegree

                # End for tPower

                # The i^iPower * p^pPower * N^(alpha-pPower) i-shift.

                if columnsWidth != 0:

                    polExpStr = spo_expression_as_string(iPower, \

                                                         0,      \

                                                         pPower, \

                                                         alpha-pPower)

                    print "->", polExpStr

                currentExpression = i^iPower * nAtPower

                currentPolynomial = pRing(currentExpression) * polynomialAtPower

                polynomialsList.append(currentPolynomial) 

            # End for iPower

        polynomialAtPower *= p  

        nAtPower /= N

    # End for pPower loop

    return((knownMonomials, polynomialsList))

# End spo_polynomial_to_proto_matrix_3