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Version 0.5.4
1) polycount has a few bugs for very small problem (i.e. 2 lines in R2, or all lines are parallel). An error message will be thrown if users try to use polycount for arrangement with dim > 2.
2) NICERd: added an option to turn off acceleration. If hyperplanes are not in general position, an error will be thrown to tell user to turn off acceleration. This is a temporary measure, at the end of the day, would like to figure out a way to accelerate even when hyperplanes are degenerate (ie. all through origin, or less extreme).
3) NICER: intended to be used for dim = 2, now will throw an error if user feed in hyperplanes of dim > 2. Same with polyzone, which is also constructed for dim = 2.
4) Added a demo on arrangement for dim = 2.
Version 0.5.5
1) witness function: seems there is a mosek bug. Try the following problem, mosek gives optimal answer (0,0,0), while (-2,1,1) is clearly giving a larger objective value.
Interior = list()
Interior$sense = "max"
Interior$c = c(0,0,1)
blx = c(-Inf,-Inf,0)
bux = c(Inf,Inf,1)
Interior$bx = rbind(blx, bux)
S = diag(c(-1,1,1))
A0 = cbind(c(1,0,-1),c(0,1,-1))
A = cbind(S%*%A0, matrix(-1,3,1))
Interior$A = Matrix(A, sparse=TRUE)
buc = c(rep(Inf,3))
blc = c(rep(0,3))
Interior$bc = rbind(blc, buc)
r = mosek(Interior)
Fix (Mosek responded that it is indeed a bug for Mosek 7 and 8 (not for Mosek 9),
email correspondence Sept 28,2020) and suggested changing
Interior$A = as(A, 'dgCMatrix').