text: # -*- coding: utf-8 -*-
  r"""
  Discrete Gaussian Samplers for `\ZZ[x]`
  
  This class realizes oracles which returns polynomials in `\ZZ[x]`
  where each coefficient is sampled independently with a probability
  proportional to `\exp(-(x-c)²/(2σ²))`.
  
  AUTHORS:
  
  - Martin Albrecht, Robert Fitzpatrick, Daniel Cabracas, Florian Göpfert,
    Michael Schneider: initial version
  
  EXAMPLE::
  
      sage: from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
      sage: sigma = 3.0; n=1000
      sage: l = [DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 64, sigma)() for _ in xrange(n)]
      sage: l = [vector(f).norm().n() for f in l]
      sage: mean(l), sqrt(64)*sigma
      (23.83..., 24.0...)
  
  """
  #******************************************************************************
  #
  #                        DGS - Discrete Gaussian Samplers
  #
  # Copyright (c) 2014, Martin Albrecht  <martinralbrecht+dgs@googlemail.com>
  # All rights reserved.
  #
  # Redistribution and use in source and binary forms, with or without
  # modification, are permitted provided that the following conditions are met:
  #
  # 1. Redistributions of source code must retain the above copyright notice, this
  #    list of conditions and the following disclaimer.
  # 2. Redistributions in binary form must reproduce the above copyright notice,
  #    this list of conditions and the following disclaimer in the documentation
  #    and/or other materials provided with the distribution.
  #
  # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
  # AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  # IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
  # DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
  # FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  # DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
  # SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
  # CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
  # OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
  # OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  #
  # The views and conclusions contained in the software and documentation are
  # those of the authors and should not be interpreted as representing official
  # policies, either expressed or implied, of the FreeBSD Project.
  #*****************************************************************************/
  from __future__ import absolute_import
  
  from sage.rings.all import RealField, RR, ZZ
  from .discrete_gaussian_integer import DiscreteGaussianDistributionIntegerSampler
  from sage.structure.sage_object import SageObject
  
  class DiscreteGaussianDistributionPolynomialSampler(SageObject):
      r"""
      Discrete Gaussian sampler for polynomials.
  
      EXAMPLE::
  
          sage: from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
          sage: DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 3.0)()
          3*x^7 + 3*x^6 - 3*x^5 - x^4 - 5*x^2 + 3
          sage: gs = DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 3.0)
          sage: [gs() for _ in range(3)]
          [4*x^7 + 4*x^6 - 4*x^5 + 2*x^4 + x^3 - 4*x + 7, -5*x^6 + 4*x^5 - 3*x^3 + 4*x^2 + x, 2*x^7 + 2*x^6 + 2*x^5 - x^4 - 2*x^2 + 3*x + 1]
  
      .. automethod:: __init__
      .. automethod:: __call__
      """
      def __init__(self, P, n, sigma):
          r"""
          Construct a sampler for univariate polynomials of degree ``n-1``
          where coefficients are drawn independently with standard deviation
          ``sigma``.
  
          INPUT:
  
          - ``P`` - a univariate polynomial ring over the Integers
          - ``n`` - number of coefficients to be sampled
          - ``sigma`` - coefficients `x` are accepted with probability
            proportional to `\exp(-x²/(2σ²))`. If an object of type
            :class:`sage.stats.distributions.discrete_gaussian_integer.DiscreteGaussianDistributionIntegerSampler`
            is passed, then this sampler is used to sample coefficients.
  
          EXAMPLE::
  
              sage: from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
              sage: DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 3.0)()
              3*x^7 + 3*x^6 - 3*x^5 - x^4 - 5*x^2 + 3
              sage: gs = DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 3.0)
              sage: [gs() for _ in range(3)]
              [4*x^7 + 4*x^6 - 4*x^5 + 2*x^4 + x^3 - 4*x + 7, -5*x^6 + 4*x^5 - 3*x^3 + 4*x^2 + x, 2*x^7 + 2*x^6 + 2*x^5 - x^4 - 2*x^2 + 3*x + 1]
          """
          if isinstance(sigma, DiscreteGaussianDistributionIntegerSampler):
              self.D = sigma
          else:
              self.D = DiscreteGaussianDistributionIntegerSampler(RR(sigma))
          self.n = ZZ(n)
          self.P = P
  
      def __call__(self):
          """
          Return a new sample.
  
          EXAMPLE::
  
              sage: from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
              sage: sampler = DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 12.0)
              sage: sampler()
              8*x^7 - 11*x^5 - 19*x^4 + 6*x^3 - 34*x^2 - 21*x + 9
          """
          coeffs = [self.D() for _ in range(self.n)]
          f = self.P(coeffs)
          return f
  
      def _repr_(self):
          """
          EXAMPLE::
  
              sage: from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
              sage: DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 3.0)
              Discrete Gaussian sampler for polynomials of degree < 8 with σ=3.000000 in each component
          """
          return "Discrete Gaussian sampler for polynomials of degree < %d with σ=%f in each component"%(self.n, self.D.sigma)
  