unit test GreenXpolynomial expansion

inst/essais/essai-GreenPolynomial-chiLambdaRho2.R

@@ -1,13 +1,12 @@
 library(jack)
 
-mu <- c(2, 1, 1)
-rho <- c(2, 2)
+mu <- c(2, 1, 1, 1)
+rho <- c(2, 2, 1)
 
 chi_lambda_rho <- function(lambda, rho) {
   jack:::chi_lambda_mu_rho(lambda, integer(0), rho)
 }
 
-
 listOfDominatingPartitions <- function(mu) {
   kappas <- jack:::listOfDominatedPartitions(partitions::conjugate(mu))
   lapply(kappas, partitions::conjugate)

tests/testthat/helper-15.R

@@ -0,0 +1,8 @@
+chi_lambda_rho <- function(lambda, rho) {
+  chi_lambda_mu_rho(lambda, integer(0), rho)
+}
+
+listOfDominatingPartitions <- function(mu) {
+  kappas <- listOfDominatedPartitions(partitions::conjugate(mu))
+  lapply(kappas, partitions::conjugate)
+}

tests/testthat/test-GreenPolynomials.R

@@ -31,6 +31,38 @@ test_that("Some Green X-polynomials (comparison with Sage)", {
 })
 
 
+test_that("Green X-polynomial expansion", {
+
+  mu  <- c(2, 1, 1, 1)
+  rho <- c(2, 2, 1)
+
+  lambdas <- listOfDominatingPartitions(mu)
+
+  KFpolys <- lapply(lambdas, function(lambda) { 
+    KostkaFoulkesPolynomial(lambda, mu)
+  })
+
+  chis <- lapply(lambdas, function(lambda) {
+    chi_lambda_rho(lambda, rho)
+  })
+
+  toAdd <- mapply(
+    function(chi, KFpoly) {
+      chi * KFpoly
+    },
+    chis, KFpolys,
+    USE.NAMES = FALSE, SIMPLIFY = FALSE
+  )
+
+  obtained <- Reduce(`+`, toAdd)
+
+  muAsString <- partitionAsString(mu)
+  expected <- GreenXpolynomials(rho = rho)[[muAsString]][["polynomial"]]
+
+  expect_true(obtained == expected)
+})
+
+
 test_that("A Green Q-polynomial (rho = lambda = [2,2])", {
   # comparison with https://elad.zelingher.com/mathapps/gln/GreenPolynomials.html
   GreenQpolys <- GreenQpolynomials(c(2, 2))