Révision 90
| pobysoPythonSage/src/sageSLZ/sageSLZ.sage (revision 90) | ||
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""" |
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module: sageSLZ.sage |
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Sage core function needed for the implementation of SLZ. |
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Created on 2013-08 |
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moduleauthor:: S.T. |
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""" |
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print "sageSLZ loading..." |
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def slz_compute_polynomial_and_interval(functionSo, degreeSo, lowerBoundSa, |
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upperBoundSa, approxPrecSa, |
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variable1, |
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variable2): |
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""" |
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Creates a new polynomial with integer coefficients for use with the
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Coppersmith method. |
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Creates a new multivariate polynomial with integer coefficients for use
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with the Coppersmith method.
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A the same time it computes : |
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- 2^K (N); |
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- 2^k |
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- 2^k (bound on the second variable)
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- lcm |
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:param ratPolyOfInt: a polynomial with rational coefficients and integer |
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variables. |
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:param precision: the precision of the floating-point coefficients. |
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:param targetHardnessToRound: the hardness to round we want to check. |
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:param variable1: the first variable of the polynomial (an expression). |
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:param variable2: the second variable of the polynomial (an expression). |
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:returns: a 4 elements tuple: |
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- the polynomial; |
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- the module (N); |
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- the lcm used to compute the integral coefficients and the |
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module. |
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""" |
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# Create a new integer polynomial ring. |
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IP = PolynomialRing(ZZ, name=str(variable1) + "," + str(variable2)) |
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coefficientDenominators = sro_denominators(ratPolyCoefficients) |
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coefficientDenominators.append(2^precision) |
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coefficientDenominators.append(2^(targetHardnessToRound + 1)) |
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# Compute the lcm |
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leastCommonMultiple = lcm(coefficientDenominators) |
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# Compute the expression corresponding to the new polynomial |
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coefficientNumerators = sro_numerators(ratPolyCoefficients) |
| pobysoPythonSage/src/sageSLZ/sagePolynomialOperations.sage (revision 90) | ||
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return ((protoMatrixRows, knownMonomials)) |
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# End spo_polynomial_to_proto_matrix |
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def spo_proto_to_column_matrix(protoMatrixColumns): |
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def spo_proto_to_column_matrix(protoMatrixColumns, \ |
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knownMonomialsList, \ |
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boundVar1, \ |
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boundVar2): |
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""" |
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Create a column (each row holds the coefficients of one monomial) matrix. |
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protoMatrixRows. |
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baseMatrix = matrix(ZZ, numRows, numColumns) |
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for colIndex in xrange(0, numColumns): |
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for rowIndex in xrange(0, len(protoMatrixColumns[colIndex])): |
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baseMatrix[rowIndex, colIndex] = \ |
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protoMatrixColumns[colIndex][rowIndex] |
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if protoMatrixColumns[colIndex][rowIndex] != 0: |
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baseMatrix[rowIndex, colIndex] = \ |
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protoMatrixColumns[colIndex][rowIndex] * \ |
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knownMonomialsList[rowIndex](boundVar1, boundVar2) |
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return baseMatrix |
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# End spo_proto_to_column_matrix. |
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# |
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boundVar1, \ |
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boundVar2): |
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""" |
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Create a row (each column holds the coefficients of one monomial) matrix. |
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Create a row (each column holds the evaluation one monomial at boundVar1 and |
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boundVar2 values) matrix. |
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protoMatrixRows. |
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Parameters |
Formats disponibles : Unified diff