Laboratoire de l'Informatique et du Parallélisme » Pobyso

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

print "sagePolynomialOperations loading..."

                                            knownMonomials, 

                                            protoMatrixRows, 

                                            columnsWidth=0):

    """

    add the coefficients of the protoMatrix (a list of proto matrix 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.

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

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

    """

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

    pMonomials.reverse()

    pCoefficients.reverse()

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

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

                    currentPolynomial = pRing(currentExpression)

                    pMonomials = currentPolynomial.monomials()

                    pCoefficients = currentPolynomial.coefficients()

                    spo_add_polynomial_coeffs_to_matrix_row(pMonomials, 

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

                print "->", polExpStr

            currentPolynomial = polynomialAtPower * nAtPower

            pMonomials = currentPolynomial.monomials()

            pCoefficients = currentPolynomial.coefficients()

            spo_add_polynomial_coeffs_to_matrix_row(pMonomials, 

                    print "->", polExpStr

                currentExpression = i^iPower * nAtPower

                currentPolynomial = pRing(currentExpression) * polynomialAtPower

                pMonomials = currentPolynomial.monomials()

                pCoefficients = currentPolynomial.coefficients()

                spo_add_polynomial_coeffs_to_matrix_row(pMonomials,      \

                    print "->", polExpStr

                currentExpression = i^(iPower * pIdegree) * t^tPower * nAtAlpha

                currentPolynomial = pRing(currentExpression)

                pMonomials = currentPolynomial.monomials()

                pCoefficients = currentPolynomial.coefficients()

                spo_add_polynomial_coeffs_to_matrix_row(pMonomials, 

                        print "->", polExpStr

                    currentExpression = i^iPower * t^outerTpower * nAtAlpha

                    currentPolynomial = pRing(currentExpression)

                    pMonomials = currentPolynomial.monomials()

                    pCoefficients = currentPolynomial.coefficients()

                    spo_add_polynomial_coeffs_to_matrix_row(pMonomials, 

                            currentExpression = \

                                    i^(iPower) * t^(innerTpower) * nAtAlpha

                            currentPolynomial = pRing(currentExpression)

                            pMonomials = currentPolynomial.monomials()

                            pCoefficients = currentPolynomial.coefficients()

                            spo_add_polynomial_coeffs_to_matrix_row(pMonomials, 

                    currentExpression = i^iShift * t^outerTpower * nAtPower

                    currentPolynomial = pRing(currentExpression) * \

                                            polynomialAtPower

                    pMonomials = currentPolynomial.monomials()

                    pCoefficients = currentPolynomial.coefficients()

                    spo_add_polynomial_coeffs_to_matrix_row(pMonomials, 

    return ((protoMatrixRows, knownMonomials, polynomialsList))

# End spo_polynomial_to_proto_matrix

    """

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

    matrix (an array of "rows") to be converted into a "true" matrix and 

    eventually by reduced by fpLLL.

    """

    pRing = p.parent()

    knownMonomials = []

    polynomialsList = []

    pVariables = p.variables()

    iVariable = pVariables[0]

                # 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)

                print "->", polExpStr

            currentPolynomial = polynomialAtPower * nAtPower

            polynomialsList.append(currentPolynomial) 

            # 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 

                    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.

                currentExpression = i^iPower * nAtPower

                currentPolynomial = pRing(currentExpression) * polynomialAtPower

                polynomialsList.append(currentPolynomial) 

            # End for iPower

        polynomialAtPower *= p  

        nAtPower /= N

    # End for pPower loop

# End spo_polynomial_to_proto_matrix_2

def spo_proto_to_column_matrix(protoMatrixColumns, \