In corybrunson/atheory: A-theory

library(atheory)

A-homotopy

Only the first homotopy group has been algorithmized. It is called by the a1rk function.

g <- graph(c(1,2, 2,3, 3,4, 4,5, 5,1), directed = FALSE)
plot(g)
a1rk(g)

h <- add_vertices(g, 4)
h <- add_edges(h, c(2,6, 6,7, 7,8, 8,9, 9,1))
plot(h)
a1rk(h)

platonics <- c("tetrahedron",
               "cubical", "octahedron",
               "dodecahedron", "icosahedron")
for (platonic in platonics) {
  print(paste0("The ", platonic, " has rank:"))
  platonic_graph <- graph.famous(platonic)
  print(a1rk(platonic_graph))
}

Simplicial complexes are not a class of object; they're represented here as lists of vectors, where each vector contains the nodes that make up the simplex.

# This example and the next are taken from Barcelo & Laubenbacher (2005)
# http://www.sciencedirect.com/science/article/pii/S0012365X05002323
sc1 <- list(
  c(1,2,3),
  c(1,3,4),
  c(1,4,5),
  c(1,5,6),
  c(1,6,2)
)
sc1_graph <- sc_to_graph(sc1, q = 1)
plot(sc1_graph)
a1rk(sc1_graph)

sc2 <- c(sc1, list(c(1,2,5)))
sc2_graph <- sc_to_graph(sc2, q = 1)
plot(sc2_graph)
a1rk(sc2_graph)

corybrunson/atheory documentation built on May 13, 2019, 10:51 p.m.