latte-count: Count integer points in a polytope

In dkahle/latter: Interface to 'LattE' and '4ti2'

Count integer points in a polytope

Description

latte_count uses LattE's count function to count the (integer) lattice points in a polytope and compute Ehrhart polynomials.

Usage

count_core(spec, dir = tempdir(), quiet = TRUE, mpoly = TRUE, ...)

latte_count(spec, dir = tempdir(), quiet = TRUE, mpoly = TRUE, ...)

latte_fcount(spec, dir = tempdir(), quiet = TRUE, mpoly = TRUE, ...)

Arguments

spec	Specification, see details and examples
dir	Directory to place the files in, without an ending /
quiet	Show latte output?
mpoly	When opts = "–ehrhart-polynomial", return the mpoly version of it
...	Additional arguments to pass to the function, see count –help at the command line to see examples. Note that dashes - should be specified with underscores _

Details

The specification should be one of the following: (1) a character string or strings containing an inequality in the mpoly expression format (see examples), (2) a list of vertices, (3) a list of A and b for the equation Ax <= b (see examples), or (4) raw code for LattE's count program. If a character vector is supplied, (1) and (4) are distinguished by the number of strings.

Behind the scenes, count works by writing a latte file and running count on it. If a specification other than a length one character is given to it (which is considered to be the code), count attempts to convert it into LattE code and then run count on it.

Value

The count. If the count is a number has less than 10 digits, an integer is returned. If the number has 10 or more digits, an integer in a character string is returned. You may want to use the gmp package's as.bigz to parse it.

Examples

if (has_latte()) {

spec <- c("x + y <= 10", "x >= 1", "y >= 1")
latte_count(spec) # 45
latte_count(spec, quiet = FALSE) # 45
latte_count(spec, dilation = 10) # 3321
latte_count(spec, homog = TRUE) # 45

# by default, the output from LattE is in
list.files(tempdir())
list.files(tempdir(), recursive = TRUE)

# ehrhart polynomials
latte_count(spec, ehrhart_polynomial = TRUE)
latte_count(spec, ehrhart_polynomial = TRUE, mpoly = FALSE)

# ehrhart series (raw since mpoly can't handle rational functions)
latte_count(spec, ehrhart_series = TRUE)

# simplified ehrhart series - not yet implemented
#latte_count(spec, simplified_ehrhart_polynomial = TRUE)

# first terms of the ehrhart series
latte_count(spec, ehrhart_taylor = 1)
# latte_count(spec, ehrhart_taylor = 2)
# latte_count(spec, ehrhart_taylor = 3)
# latte_count(spec, ehrhart_taylor = 4)

# multivariate generating function
latte_count(spec, multivariate_generating_function = TRUE)


# by vertices
spec <- list(c(1,1), c(10,1), c(1,10), c(10,10))
latte_count(spec)
latte_count(spec, vrep = TRUE)

code <- "
5 3
1 -1  0
1  0 -1
1 -1 -1
0  1  0
0  0  1
"
latte_count(code)


# for Ax <= b, see this example from the latte manual p.10
A <- matrix(c(
   1,  0,
   0,  1,
   1,  1,
  -1,  0,
   0, -1
), nrow = 5, byrow = TRUE)
b <- c(1, 1, 1, 0, 0)
latte_count(list(A = A, b = b))









}

dkahle/latter documentation built on March 22, 2023, 9:05 p.m.