enumerate group elements
This commit is contained in:
Florian Stecker
parent
fc4dfa195d
commit
55f0c2d093
133
automaton.py
133
automaton.py
@ -1,9 +1,9 @@
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#!/usr/bin/python
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# 0 is infinity
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coxeter_matrix = [[1, 2, 3],
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[2, 1, 0],
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[3, 0, 1]]
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coxeter_matrix = [[1, 5, 5],
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[5, 1, 5],
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[5, 5, 1]]
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import math
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from copy import copy
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@ -26,6 +26,18 @@ class Root:
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def __copy__(self):
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return Root(self.id, self.rank, self.depth, self.v.copy(), self.neighbors.copy())
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class Groupelement:
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def __init__(self, id, rank, word):
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self.id = id
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self.rank = rank
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self.word = word
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self.length = len(word)
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self.left = [None]*rank
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self.right = [None]*rank
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self.node = None
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self.lex_node = None
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self.inverse = None
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# compute <alpha_k, beta> where alpha_k is one of the simple roots and beta any root
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def form_gen_root(form, k, root):
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rank = len(form)
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@ -152,71 +164,84 @@ def generate_automaton(small_roots, lex_reduced = False):
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id += 1
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edges.append((nodes[node], nodes[newnode], k))
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return (nodes, levels, edges)
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graph = [[None for i in range(rank)] for j in range(len(nodes))]
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for (fr,to,gen) in edges:
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graph[fr][gen] = to
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return graph
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# main program
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form = [[-math.cos(math.pi/m) if m > 0 else -1 for m in row] for row in coxeter_matrix]
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rank = len(coxeter_matrix)
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small_roots = find_small_roots(form)
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nodes, levels, edges = generate_automaton(small_roots, lex_reduced = False)
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nodes_lex, levels_lex, edges_lex = generate_automaton(small_roots, lex_reduced = True)
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graph = generate_automaton(small_roots, lex_reduced = False)
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graph_lex = generate_automaton(small_roots, lex_reduced = True)
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#for r in small_roots:
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# print((r.id,r.v,[n.id if n else -1 for n in r.neighbors]))
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group = [Groupelement(0, rank, tuple())]
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group[0].inverse = group[0]
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group[0].node = group[0].lex_node = 0
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revedges = sorted(edges, key = lambda x:x[1])
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adjlist = {}
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revadjlist = {}
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for efrom, eto, egen in edges:
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if not efrom in adjlist:
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adjlist[efrom] = [-1]*rank
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adjlist[efrom][egen] = eto
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if not eto in revadjlist:
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revadjlist[eto] = [-1]*rank
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revadjlist[eto][egen] = efrom
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words = [([], 0)]
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depth = 0
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i = 0
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while len(words[i][0]) < 10:
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curword = words[i][0]
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curnode = words[i][1]
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for gen, nextnode in enumerate(adjlist[curnode]):
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if nextnode < 0:
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continue
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nextword = curword.copy()
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nextword.append(gen)
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words.append((nextword, nextnode))
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size = 1
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while True:
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current = group[i]
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i+=1
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#print(sorted([x[1] for x in words]))
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#print(["".join([chr(ord('a')+x) for x in w[0]]) for w in words])
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if current.length >= 10:
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break
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levelnodes = []
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for n,id in nodes.items():
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level = levels[n]
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if level >= len(levelnodes):
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levelnodes.append([])
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levelnodes[level].append(id)
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for gen, new_lex_node in enumerate(graph_lex[current.lex_node]):
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if new_lex_node:
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new_element = Groupelement(size, rank, current.word + (gen,))
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new_element.lex_node = new_lex_node
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new_element.node = graph[current.node][gen]
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group.append(new_element)
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size += 1
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print("digraph test123 {")
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print('rankdir="TB"')
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# w = w_1 t, w s = w_1
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# right multiplication (and left in case it does the same as a right mult)
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for k in range(rank):
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for (level,ns) in enumerate(levelnodes):
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print('{rank = "same";', end = ' ')
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for n in ns:
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print("{id:d};".format(id=n), end = ' ')
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print('}')
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# if right multiplication by k decreases length
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if not graph[new_element.node][k]:
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word = list(new_element.word)
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longer_suffix = group[0]
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while len(word) > 0:
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letter = word.pop()
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shorter_suffix = longer_suffix
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longer_suffix = shorter_suffix.left[letter]
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# w = w_1 t w_2, w_2 s_k = t w_2
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# in the case word = [] longer_suffix could be None
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# found it
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if len(word) == 0 or shorter_suffix.right[k] == longer_suffix:
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# finish word
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while len(word) > 0:
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shorter_suffix = shorter_suffix.left[word.pop()]
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new_element.right[k] = shorter_suffix
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shorter_suffix.right[k] = new_element
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colors = ['red', 'darkgreen', 'blue', 'orange']
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# find inverse and left multiply
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inverse = group[0]
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word = list(new_element.word)
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while len(word) > 0:
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inverse = inverse.right[word.pop()]
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if not inverse:
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break
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if inverse:
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new_element.inverse = inverse
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inverse.inverse = new_element
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for k in range(rank):
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if inverse.right[k]:
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other = inverse.right[k].inverse
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new_element.left[k] = other
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other.left[k] = new_element
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if new_element.right[k]:
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other = new_element.right[k].inverse
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inverse.left[k] = other
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other.left[k] = inverse
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for e in edges:
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print("{fr:d} -> {to:d} [color={color}];".format(
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fr = e[0],
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to = e[1],
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color = colors[e[2]]))
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print("}")
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length = 0
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for i in range(1,len(group)+1):
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if i == len(group) or group[i].length > group[i-1].length:
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print("{number:d} elements up to length {length:d}".format(number = i, length = group[i-1].length))
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