stla

# hSepString :: HSep -> String
# hSepString hsep = case hsep of
#   HSepEmpty    -> ""
#   HSepSpaces k -> replicate k ' '
#   HSepString s -> s
hSepString <- function(hsep) {
  sep <- attr(hsep, "sep")
  switch(
    sep,
    "empty" = "",

stla

# -- | Given the cardinalities of some finite sets, we list all possible
# -- Venn diagrams.
# --
# -- Note: we don't include the empty zone in the tables, because it's always empty.
# --
# -- Remark: if each sets is a singleton set, we get back set partitions:
# --
# -- > > [ length $ enumerateVennDiagrams $ replicate k 1 | k<-[1..8] ]
# -- > [1,2,5,15,52,203,877,4140]
# -- >

stla

rg <- function(a, b) {
  if(a <= b) a:b else integer(0L)
}

KostkaNumber <- function(lambda, mu) {
  lambda <- as.integer(lambda)
  mu     <- as.integer(mu)
  wmu  <- sum(mu)
  wlam <- sum(lambda)
  if(wlam == 0L) {

stla

insertWith <- function(f, mp, key, value) {
  if(key %in% names(mp)) {
    mp[[key]] <- f(value, mp[[key]])
  } else {
    mp[[key]] <- value
  }
  mp
}

zip3 <- function(v1, v2, v3) {

stla

insertWith <- function(f, mp, key, value) {
  if(key %in% names(mp)) {
    mp[[key]] <- f(value, mp[[key]])
  } else {
    mp[[key]] <- value
  }
  mp
}

drop <- function(n, x) {

stla

/*
Weierstrass p-function and its first three derivatives.
Author: Stéphane Laurent.
Depends on math.js <https://mathjs.org/> 
  and jacobi.js <https://gist.github.com/stla/955af9c1c2713a47883bc927a759bdc7>.
*/

var weierstrass = (function () {

  const jtheta1 = jacobi.jtheta1;

stla

/*
Carlson elliptic integrals and incomplete elliptic integrals.
Author: Stéphane Laurent.
Depends on math.js <https://mathjs.org/>.
*/

var ellipticIntegrals = (function () {

  let CarlsonRF = function(x, y, z, err) {
    if(err <= 0) {

stla

/*
Jacobi theta functions.
Author: Stéphane Laurent.
The functions jtheta1, jtheta2, jtheta3 and jtheta4 are the Jacobi theta 
functions. The function jtheta1 is 1-antiperiodic, and the functions 
jtheta2, jtheta3 and jtheta4 are 1-periodic.
The function jthetaAB is the Jacobi theta function with characteristics.
The function jtheta1Prime0 is the derivative at 0 of jtheta1.
*/

stla

import Meshes
using MeshViz
using GLMakie
using Makie
using Printf

# vectors obtained by changing signs of the given vectors
function changesOfSigns(vecs)
  N = length(vecs[1])
  signs = Iterators.product(ntuple(i -> (-1, 1), N)...)

stla

import Meshes
using LinearAlgebra
using MeshViz
using GLMakie
using Makie
using Printf

# beta factor
function betaF(A, s)
  1.0 / √(1 + LinearAlgebra.norm_sqr(A) / (s*s))