Laboratoire de l'Informatique et du Parallélisme » Pobyso

                # Add the coefficient to the proto matrix row and delete the 

def spo_polynomial_to_polynomials_list_6(p, alpha, N, iBound, tBound,

                                         columnsWidth=0):

    """

    From p, alpha, N build a list of polynomials use to create a base

    that will eventually be reduced with LLL.

    The bounds are computed for the coefficients that will be used to

    form the base.

    We try to introduce only one new monomial at a time, whithout trying to

    obtain a triangular matrix.

    There are many possibilities to introduce the monomials: our goal is also 

    to introduce each of them on the diagonal with the smallest coefficient.

    The method depends on the structure of the polynomial. Here it is adapted

    to the a_n*i^n + ... + a_1 * i - t + b form.     

    Parameters

    ----------

    p: the (bivariate) polynomial;

    alpha:

    N:

    iBound:

    tBound:

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

                 printed in colums of columnsWitdth width.

    """

    pRing = p.parent()

    polynomialsList = []

    pVariables = p.variables()

    iVariable = pVariables[0]

    tVariable = pVariables[1]

    polynomialAtPower = copy(p)

    currentPolynomial = pRing(1)     # Constant term.

    pIdegree = p.degree(iVariable)

    pTdegree = p.degree(tVariable)

    maxIdegree = pIdegree * alpha

    currentIdegree = currentPolynomial.degree(iVariable)

    nAtAlpha = N^alpha

    nAtPower = nAtAlpha

    polExpStr = ""

    #

    ## Shouldn't we start at tPower == 1 because polynomials without 

    #  t monomials are useless?

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

        ## Start at iPower == 0 because here there are i monomials

        #  in p even if iPower is zero.

        for iPower in xrange(0, alpha-tPower+1):

            if iPower + tPower <= alpha:

                print "iPower:", iPower, " tPower:", tPower

                q = pRing(iVariable * iBound)^iPower * ((p * N)^tPower)

                print q.monomials()

                polynomialsList.append(q)

    return polynomialsList

    """

    # We first introduce all the monomials in i alone multiplied by N^alpha.

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

        if columnsWidth !=0:

            polExpStr = spo_expression_as_string(iPower, iBound,

                                                 0, tBound, 

                                                 0, alpha)

            print "->", polExpStr

        currentExpression = iVariable^iPower * nAtAlpha * iBound^iPower

        currentPolynomial = pRing(currentExpression)

        polynomialsList.append(currentPolynomial)

    # End for iPower

    # We work from p^1 * N^alpha-1 to p^alpha * N^0

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

        # First of all the p^pPower * N^(alpha-pPower) polynomial.

        nAtPower /= N

        if columnsWidth !=0:

            polExpStr = spo_expression_as_string(0, iBound,

                                                 0, tBound,

                                                 pPower, alpha-pPower)

            print "->", polExpStr

        currentPolynomial = polynomialAtPower * nAtPower

        polynomialsList.append(currentPolynomial)

        # Exit when pPower == alpha

        if pPower == alpha:

            return polynomialsList

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

            iCurrentPower = pIdegree + iPower

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

                #print "tPower:", tPower

                if columnsWidth != 0:

                    polExpStr = spo_expression_as_string(iCurrentPower, iBound,

                                                         tPower, tBound, 

                                                         0, alpha)

                    print "->", polExpStr

                currentExpression = i^iCurrentPower * iBound^iCurrentPower * t^tPower * tBound^tPower *nAtAlpha 

                currentPolynomial = pRing(currentExpression)

                polynomialsList.append(currentPolynomial)

                iCurrentPower += pIdegree 

            # End for tPower 

        # We now introduce the mixed i^k * t^l monomials by i^m * p^n * N^(alpha-n)

            if columnsWidth != 0:

                polExpStr = spo_expression_as_string(iPower, iBound,

                                                     0, tBound, 

                                                     pPower, alpha-pPower)

                print "->", polExpStr

            currentExpression = i^iPower * iBound^iPower * nAtPower

            currentPolynomial = pRing(currentExpression) * polynomialAtPower

            polynomialsList.append(currentPolynomial) 

        # End for iPower

        polynomialAtPower *= p  

    # End for pPower loop

    """

    return polynomialsList 

# End spo_polynomial_to_proto_matrix_6