This directory, available both on the LattE website and as part of the
LattE integrale distribution (in the directory code/maple), contains
LattE's Maple programs, which can be used independently.


Conebyconeapproximations_08_11_2010.mpl

  It contains Maple code for computing the highest coefficients of
  Ehrhart quasi-polynomials, using the algorithm of this paper:

  - Velleda Baldoni, Nicole Berline, Jesus A. De Loera, Matthias
    Koeppe, and Michele Vergne, Computation of the highest
    coefficients of weighted Ehrhart quasi-polynomials of rational
    polyhedra, Foundations of Computational Mathematics 12 (2012),
    435-469, doi:10.1007/s10208-011-9106-4

  These functions are also accessible using LattE's "integrate"
  function; see the LattE manual.

  It can also compute the canonical cone-by-cone patched
  quasi-polynomial defined in the paper:

  - Velleda Baldoni, Nicole Berline, Jesus A. De Loera, Matthias
    Koeppe, and Michele Vergne, Three Ehrhart Quasi-polynomials, 2014.


m-knapsack.mpl

  It contains Maple code for computing the highest coefficients of
  Ehrhart quasi-polynomials of knapsack polytopes, using the algorithm
  of the papers:

  - Velleda Baldoni, Nicole Berline, Jesus A. De Loera, Brandon
    E. Dutra, Matthias Koeppe, and Michele Vergne, Top degree
    coefficients of the denumerant, 25th International Conference on
    Formal Power Series and Algebraic Combinatorics (FPSAC 2013),
    DMTCS proc. AS, Discrete Mathematics and Theoretical Computer
    Science (DMTCS), 2013, pp. 1149-1160, available from
    http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAS0197/4324
    
  - Velleda Baldoni, Nicole Berline, Jesus A. De Loera, Matthias
    Koeppe, and Michele Vergne, Coefficients of Sylvester's denumerant,
    eprint arXiv:1312.7147 [math.CO], 2013

  LattE integrale also contains a native C++ implementation of the
  same algorithm.  It is MUCH faster, so we recommend that for any
  production use.  See the LattE manual.


RealBarvinok-mars-exemples-2014-03-10.mpl

  It contains Maple code for computing intermediate generating
  functions S^L (by means of Brion-Vergne decomposition) and
  intermediate Ehrhart quasi-polynomials, using the algorithms in:

  - Velleda Baldoni, Nicole Berline, Matthias Koeppe, and Michele
    Vergne, Intermediate sums on polyhedra: Computation and real
    Ehrhart theory, Mathematika 59 (2013), no. 1, 1-22,
    doi:10.1112/S0025579312000101

  It also contains Maple code for computing the canonical Barvinok
  patched generating function and quasi-polynomial for a simplex,
  as described in:

  - Velleda Baldoni, Nicole Berline, Jesus A. De Loera, Matthias
    Koeppe, and Michele Vergne, Three Ehrhart Quasi-polynomials, 2014.


3-ehrhart-polynomials-paper-examples.mpl

  Computational examples from the paper:

  - Velleda Baldoni, Nicole Berline, Jesus A. De Loera, Matthias
    Koeppe, and Michele Vergne, Three Ehrhart Quasi-polynomials, 2014.


The other files are part of LattE's build system and can be ignored.

