Implement non-spherical discrete Gaussian sampling

Author: grhkm21

src/doc/en/reference/references/index.rst

@@ -5021,6 +5021,11 @@ REFERENCES:
              small Schroeder paths*, JCTA 125 (2014), 357-378,
              :doi:`10.1016/j.jcta.2014.04.002`
 
+.. [Pei2010] Peikert, C. (2010). An Efficient and Parallel Gaussian Sampler for
+             Lattices. In: Rabin, T. (eds) Advances in Cryptology – CRYPTO 2010.
+             CRYPTO 2010. Lecture Notes in Computer Science, vol 6223. Springer,
+             Berlin, Heidelberg. :doi:`10.1007/978-3-642-14623-7_5`
+
 .. [Pen2012] \R. Pendavingh, On the evaluation at `(-i, i)` of the
              Tutte polynomial of a binary matroid. Preprint:
              :arxiv:`1203.0910`

src/sage/stats/all.py

@@ -2,6 +2,7 @@
 from .r import ttest
 from .basic_stats import (mean, mode, std, variance, median, moving_average)
 from .hmm import all as hmm
+from .distributions import (DGI, DGL, DGP)
 
 # We lazy_import the following modules since they import numpy which
 # slows down sage startup

src/sage/stats/distributions/__init__.py

@@ -0,0 +1,3 @@
+from .discrete_gaussian_integer import DGI
+from .discrete_gaussian_lattice import DGL
+from .discrete_gaussian_polynomial import DGP

src/sage/stats/distributions/discrete_gaussian_integer.pyx

@@ -494,3 +494,6 @@ cdef class DiscreteGaussianDistributionIntegerSampler(SageObject):
             'Discrete Gaussian sampler over the Integers with sigma = 3.000000 and c = 2.000000'
         """
         return f"Discrete Gaussian sampler over the Integers with sigma = {self.sigma:.6f} and c = {self.c:.6f}"
+
+
+DGI = DiscreteGaussianDistributionIntegerSampler