Notes on partial triangulation census of 3-manifold implementation

partial census notes

# Given FPG on n nodes
# Take tree decomposition of FPG, arbitrarily assign a root

# Let "contains" consisting of n "true" bools
# Let seen := {}
# Take root bag and assign properties as follows:
#     Let bag.contains = contains
#     Let bag.toAdd = bag.contents \setminus seen
#     Let seen = seen + bag.contents
#     Let contains = contains \setminus seen
#     Iterate through children with same process

# Description:
#     bag.contains denotes the tetrahedra which will be in the triangulation at this stage of the enumeration (true if present, false if not)
#     bag.toAdd are the tetrahedra which are to be added at this stage of the enumeration
    


# Enumeration process, run at root node and recurses down:

# First create the "new" tetrahedra at this bag.
For i in bag.toAdd:
    now.triangulation.newSimplex( i.toString() ) # To avoid constant reindexing of tetrahedra, use descriptions to refer to them? Better idea?
    For j in {0,1,2,3}:
        if now.contains[ FPG.dest(i,j).simp ]:
            gluings.append( (NFacetSpec(i,j), FPG.dest(i,j) ) # Find the gluings which need to be tried here
# Start recursion call
start(0)

# new function
# Finds the next starter. The "i" denotes which child number we are currently iterating through.
def start(i) { 
    if i == number_of_children: # Iterated through all children, time to try gluing
        tryGluing(0)
        return
    int size_at_start = now.triangulation.size() # Used for backtracking
    for child_triangulation in child[i].iterator:
        child_triangulation.moveTo(now.triangulation) # Add on the bits from the child
        start(i+1); # Recurse
        # Backtrack by deleting tetrahedra. moveTo() will re-create them from next child triangulation
        while (now.triangulation.size() > size_at_start)
            now.triangulation.removeTetrahedronAt(now.triangulation.size())
    tryEdge(0)

# new function
# Tries the next gluing. The "i" indicates which gluing we are testing.
def tryEdge(i) {
    if i == number_of_edges: # Everything glued up, so store this
        store(now.triangulation)
        return
    e = edges[i]
    for g in possible_gluings: # Each of 6
	perm = makePerm(g, e[0].face, e[1].face) # Create the NPerm object from the gluing + faces
	tetA = getTet(e[0].simp) # Need to find the right tetrahedron from description to avoid reindexing.
        tetB = getTet(e[1].simp)
        tetA.joinTo(e[0].face,tetB, perm) # Glue
        if now.triangulation.isValidPartial(): # Test validity. No closed vertex links (unless all faces glued), no edges glued in reverse.
            tryEdge(i+1);
        tetA.simp.unjoin(e[0].face) # Backtrack