Laboratoire de l'Informatique et du Parallélisme » Pobyso

load "/home/storres/recherche/arithmetique/pobysoPythonSage/src/sageSLZ/sageMatrixOperations.sage"

def spo_polynomial_to_matrix(p, pRing, alpha, N, columnWidth=0):

    """

    From a (bivariate) polynomial and some other parameters build a matrix

    to be reduced by fpLLL.

    The matrix is such as those found in Boneh-Durphy and Stehlé.

    p: the (bivariate) polynomial

    alpha:

    N:

    """

    pVariables = p.variables()

    iVariable = pVariables[0]

    tVariable = pVariables[1]

    polynomialAtPower = P(1)

    currentPolynomial = P(1)

    pIdegree = p.degree(pVariables[0])

    pTdegree = p.degree(pVariables[1])

    currentIdegree = currentPolynomial.degree(i)

    nAtPower = N^alpha

    # 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 but one

        # in, those in t necessary to be able to introduce

        # p. We arbitrary choose to introduce the highest degree monomial in i

        # with p. We also introduce all the mixed i^k * t^l monomials with

        # k < p.degree(i) and l <= p.degree(t)

        if pPower == 0:

            # iter1: power of i

            # Notice how i^pIdegree is excluded.

            for iPower in xrange(0, pIdegree):

                # iter5: power of t.

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

                    if columnWidth != 0:

                        print "->", spo_expression_as_string(iPower,

                                                             tPower,

                                                             pPower,

                                                             alpha)

                    currentExpression = iVariable^iPower * \

                                        tVariable^tPower * nAtPower

                    # polynomialAtPower == 1 here. Next line should be commented out but it does not work!

                    # Some convertion problem?

                    currentPolynomial = pRing(currentExpression) * \

                                        polynomialAtPower

                    pMonomials = currentPolynomial.monomials()

                    pCoefficients = currentPolynomial.coefficients()

                    spo_add_polynomial_coeffs_to_matrix(pMonomials, pCoefficients, knownMonomials, protoMatrixRows, monomialLengthChars)

                # End iter5.

            # End for iter1.

    else: # Next runs (p^1..p^alpha)

        pass

# End spo_polynomial_to_matrix

def spo_add_polynomial_coeffs_to_matrix(pMonomials,

                                        pCoefficients,

                                        knownMonomials,

                                        protoMatrixRows,

                                        columnWidth=0):

    """

    For a given polynomial (under the form of monomials and coefficents lists),

    add the coefficients of the protoMatrix (a list of proto rows).

    Coefficients are added to the protoMatrix row in the order imposed by the

    monomials discovery list (the knownMonomials list) built as construction

    goes on.

    As a bonus data can be printed out for a visual check.

    pMonomials     : the list of the monomials coming form some polynomial;

    pCoefficients  : the list of the corresponding coefficients to add to

                     the protoMatrix in the exact same order as the monomials;

    knownMonomials : the list of the already knonw monomials;

    protoMatrixRows: a list of lists, each one holding the coefficients of the

                     monomials

    columnWith     : the width, in characters, of the displayed column ; if 0,

                     do display anything.

    """

    # We have started with the smaller degrees in the first variable.

    pMonomials.reverse()

    pCoefficients.reverse()

    # New empty proto matrix row.

    protoMatrixRowCoefficients = []

    # We work according to the order of the already known monomials

    # No known monomials yet: add the pMonomials to knownMonomials

    # and add the coefficients to the proto matrix row.

    if len(knownMonomials) == 0:

        for pmIdx in xrange(0, len(pMonomials)):

            knownMonomials.append(pMonomials[pmIdx])

            protoMatrixRowCoefficients.append(pCoefficients[pmIdx])

            if columnWidth != 0:

                monomialAsString = str(pCoefficients[pmIdx]) + " " + \

                                   str(pMonomials[pmIdx])

                print monomialAsString, " " * \

                      (columnWidth - len(monomialAsString)),

    # There are some known monomials. We search for them in pMonomials and

    # add their coefficients to the proto matrix row.

    else:

        for knownMonomialIndex in xrange(0,len(knownMonomials)):

            # We lazily use an exception here since pMonomials.index() function

            # may fail throwing the ValueError exception.

            try:

                indexInPmonomials = \

                    pMonomials.index(knownMonomials[knownMonomialIndex])

                if columnWidth != 0:

                    monomialAsString = str(pCoefficients[indexInPmonomials]) + \

                        " " + str(knownMonomials[knownMonomialIndex])

                    print monomialAsString, " " * \

                        (columnWidth - len(monomialAsString)),

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

                # known monomial from the current pMonomial list

                #(and the corresponding coefficient as well).

                protoMatrixRowCoefficients.append(pCoefficients[indexInPmonomials])

                del pMonomials[indexInPmonomials]

                del pCoefficients[indexInPmonomials]

            # The knownMonomials element is not in pMonomials

            except ValueError:

                protoMatrixRowCoefficients.append(0)

                if columnWidth != 0:

                    monomialAsString = "0" + " "+ \

                        str(knownMonomials[knownMonomialIndex])

                    print monomialAsString, " " * \

                        (columnWidth - len(monomialAsString)),

        # End for knownMonomialKey loop.

        # We now append the remaining monomials of pMonomials to knownMonomials

        # and the corresponding coefficients to proto matrix row.

        for pmIdx in xrange(0, len(pMonomials)):

            knownMonomials.append(pMonomials[pmIdx])

            protoMatrixRowCoefficients.append(pCoefficients[pmIdx])

            if columnWidth != 0:

                monomialAsString = str(pCoefficients[pmIdx]) + " " \

                    + str(pMonomials[pmIdx])

                print monomialAsString, " " * \

                    (columnWidth - len(monomialAsString)),

        # End for pmIdx loop.

    # Add the new list row elements to the proto matrix.

    protoMatrixRows.append(protoMatrixRowCoefficients)

    if columnWidth != 0:

        print

# End spo_add_polynomial_coeffs_to_matrix

def spo_expression_as_string(powI, powT, powP, alpha):

    """

    Computes a string version of the i^k + t^l + p^m + N^n expression for

    output.

    """

    expressionAsString =""

    if powI != 0:

        expressionAsString += "i^" + str(powI)

    if powT != 0:

        if len(expressionAsString) != 0:

            expressionAsString += " * "

        expressionAsString += "t^" + str(powT)

    if powP != 0:

        if len(expressionAsString) != 0:

            expressionAsString += " * "

        expressionAsString += "p^" + str(powP)

    if (alpha - powP) != 0 :

        if len(expressionAsString) != 0:

            expressionAsString += " * "

        expressionAsString += "N^" + str(alpha - powP)

    return(expressionAsString)

# End spo_expression_as_string.