Révision 124 pobysoPythonSage/src/sageSLZ/sageSLZ.sage

sageSLZ.sage (revision 124)
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                        degree, targetHardnessToRound, alpha):
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    """
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    Check an Hard-to-round value.
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    TODO::
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    Full rewriting: this is hardly a draft.
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    """
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    polyApproxPrec = targetHardnessToRound + 1
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    polyTargetHardnessToRound = targetHardnessToRound + 1
......
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    """
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    # Check the parameters.
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    # RealNumbers only.
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    classTree = [number.__class__] + number.mro()
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    if not sage.rings.real_mpfr.RealNumber in classTree:
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    try:
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        classTree = [number.__class__] + number.mro()
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        if not sage.rings.real_mpfr.RealNumber in classTree:
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            return None
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    except AttributeError:
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        return None
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    # Non zero negative integers only for emin.
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    if emin >= 0 or int(emin) != emin:
......
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    For a given set of arguments (see below), compute a list
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    of "reduced polynomials" that could be used to compute roots
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    of the inputPolynomial.
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    INPUT:
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    - "inputPolynomial" -- (no default) a bivariate integer polynomial;
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    - "alpha" -- the alpha parameter of the Coppersmith algorithm;
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    - "N" -- the modulus;
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    - "iBound" -- the bound on the first variable;
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    - "tBound" -- the bound on the second variable.
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    OUTPUT:
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    A list of bivariate integer polynomial obtained using the Coppersmith
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    algorithm. The polynomials correspond to the rows of the LLL-reduce
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    reduced base that comply with the Coppersmith condition.
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    TODO::
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    Full rewrite, this is barely a draft.
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    """
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    # Arguments check.
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    if iBound == 0 or tBound == 0:
......
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    """
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    For a given set of arguments (see below), compute the polynomial modular
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    roots, if any.
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    """
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    # Arguments check.
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    if iBound == 0 or tBound == 0:
......
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    precision is reached.
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    The polynomial, the bounds, the center of the interval and the error
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    are returned.
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    OUTPU:
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    A tuple made of 4 Sollya objects:
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    - a polynomial;
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    - an range (an interval, not in the sense of number given as an interval);
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    - the center of the interval;
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    - the maximum error in the approximation of the input functionSo by the
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      output polynomial ; this error <= approxPrecSaS.
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    """
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    RRR = lowerBoundSa.parent()
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    intervalShrinkConstFactorSa = RRR('0.5')

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