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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.
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