In [1]:
# load the package badic (you can install it with "sage -pip install badic [--user]")
from badic import *
In [2]:
#########################################
# choose a Pisot number and an alphabet #
#########################################
pi = x^3-x^2-x-1 # Tribonacci number
#pi = x^3-2*x^2-x-1
m = BetaAdicSet(pi, [0,1]) #choose the alphabet
print(m)
pm = m.b.parent().places()[1] # choose a place (will be usefull in the function approx)
print(pm)
m.plot()
b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 1 state and 2 letters Ring morphism: From: Number Field in b with defining polynomial x^3 - x^2 - x - 1 with b = -0.4196433776070806? - 0.6062907292071993?*I To: Complex Field with 53 bits of precision Defn: b |--> -0.419643377607080 + 0.606290729207199*I
Out[2]:
In [3]:
m = m.reduced() # permit to represent each point of the set by a single word
print(m)
m.plot()
b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 4 states and 2 letters
Out[3]:
In [14]:
######################################
# Rauzy fractal approximating a disk #
######################################
# the first argument of approx() is the precision,
# and the second one is the characteristic function of the shape to approximate
# the shape must be not too big in order to be inside m
md = m.approx(13, lambda x: (pm(x).real())^2 + (pm(x).imag())^2 < .4 )
md.plot()
b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 201 states and 2 letters
Out[14]:
In [15]:
md = md.proj(m) # permits to get md as a subset of m
m.plot_list([md])
Out[15]:
In [16]:
# compute a domain exchange on this approximation of disk
lm = md.domain_exchange()
lm
Out[16]:
[(1, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 90 states and 2 letters), (b^2 - b, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 73 states and 2 letters), (b, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 117 states and 2 letters), (b + 1, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 76 states and 2 letters), (b^2, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 164 states and 2 letters), (b^2 + 1, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 75 states and 2 letters), (b^2 + b, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 38 states and 2 letters), (b^2 + b + 1, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 54 states and 2 letters)]
In [24]:
# plot it (nprec permits to choose the density of points drawn)
md.plot_list([a for t,a in lm], nprec=6)
Out[24]:
In [25]:
# plot it after exchange
md.plot_list([a.proj(m, t) for t,a in lm], nprec=6)
Out[25]:
In [29]:
# compute a substitution having md has Rauzy fractal
%time d = md.substitution()
d
CPU times: user 32.2 s, sys: 59.9 ms, total: 32.3 s Wall time: 32.3 s
Out[29]:
{1: [102, 20],
2: [5, 109],
3: [214, 32, 165],
4: [46, 110, 277, 79],
5: [280, 273, 281, 297],
6: [291, 252],
7: [242, 4],
8: [217, 3],
9: [186, 24],
10: [186, 7],
11: [263, 149],
12: [248, 87, 104, 75, 236],
13: [106, 23, 1, 89],
14: [291, 112, 239, 106, 23, 1, 89],
15: [291, 246, 239, 106, 278, 307, 57],
16: [291, 294, 239, 106, 23, 1, 89],
17: [291, 179, 106, 278, 307, 57],
18: [24],
19: [286],
20: [9],
21: [10],
22: [40],
23: [208],
24: [65, 144],
25: [32, 165],
26: [64, 21],
27: [12],
28: [14],
29: [15],
30: [16],
31: [17],
32: [276, 8, 156, 164],
33: [124, 10],
34: [282, 35, 165],
35: [8, 156, 164],
36: [231, 261],
37: [6, 123],
38: [229, 13],
39: [260, 24],
40: [257, 26],
41: [232, 88, 107, 71, 52],
42: [36, 142, 105, 132, 91],
43: [103, 22, 123],
44: [106, 23, 122],
45: [217, 240, 25],
46: [212, 158, 26],
47: [214, 282, 35],
48: [291, 294, 239, 106, 131, 89],
49: [289, 222, 142, 105, 132, 91],
50: [305, 46, 110, 277, 79],
51: [27],
52: [28],
53: [29],
54: [30],
55: [31],
56: [71],
57: [37],
58: [38],
59: [41],
60: [42],
61: [48],
62: [49],
63: [50],
64: [303, 47, 155, 124],
65: [305, 252, 110, 277],
66: [19, 223, 236],
67: [19, 308, 236],
68: [278, 307, 57],
69: [278, 203],
70: [292, 233, 109],
71: [288, 156, 21],
72: [45, 111, 164],
73: [46, 110, 277],
74: [250, 156, 164],
75: [286, 127],
76: [172, 33],
77: [173, 147],
78: [161, 123],
79: [115, 43],
80: [160, 44],
81: [300, 273, 241, 130, 176],
82: [273, 281, 74],
83: [305, 252, 110, 277, 135],
84: [305, 252, 110, 277, 79],
85: [61],
86: [62],
87: [76],
88: [77],
89: [78],
90: [79],
91: [80],
92: [81],
93: [83],
94: [84],
95: [221, 225, 141],
96: [278, 224, 57],
97: [292, 82, 109],
98: [300, 142, 241, 132, 177],
99: [192, 142, 105, 132, 91],
100: [98],
101: [99],
102: [136],
103: [51],
104: [52],
105: [53],
106: [54],
107: [55],
108: [176],
109: [58],
110: [85],
111: [86],
112: [219, 245],
113: [214, 282, 35, 165],
114: [273, 241, 130, 176],
115: [136, 39],
116: [290, 247, 238, 104],
117: [291, 246, 239, 106],
118: [186, 63],
119: [186, 93],
120: [186, 94],
121: [230, 128],
122: [102, 20, 78],
123: [110, 277, 79],
124: [121],
125: [51, 294, 239],
126: [136, 9],
127: [139, 119],
128: [105, 132, 91],
129: [106, 131, 89],
130: [207, 156, 164],
131: [208, 102, 20],
132: [207, 111, 164],
133: [70, 147],
134: [154, 69],
135: [182, 43],
136: [60],
137: [92],
138: [100],
139: [101],
140: [93],
141: [94],
142: [133],
143: [134],
144: [135],
145: [220, 118],
146: [220, 119],
147: [221, 120],
148: [172, 156, 21],
149: [251, 156, 21],
150: [287, 145],
151: [286, 146],
152: [219, 245, 149],
153: [290, 178, 104],
154: [291, 179, 106],
155: [165],
156: [124],
157: [142],
158: [143],
159: [273, 281, 297, 58],
160: [51, 11],
161: [51, 40],
162: [186, 170],
163: [125, 129],
164: [162],
165: [163],
166: [137, 223, 236],
167: [138, 225, 141],
168: [139, 225, 140],
169: [241, 72, 177],
170: [242, 73, 90],
171: [241, 132, 177],
172: [303, 234, 108],
173: [306, 233, 109],
174: [125, 13],
175: [125, 44],
176: [174],
177: [175],
178: [218, 107, 148],
179: [274, 107, 149],
180: [181, 87, 104],
181: [184, 88, 107],
182: [136, 293, 18],
183: [183, 295, 243],
184: [180, 296, 244],
185: [136, 225, 18],
186: [136, 225, 140],
187: [71, 52],
188: [75, 236],
189: [151, 236],
190: [292, 159],
191: [2, 167],
192: [231, 166],
193: [59, 166],
194: [60, 186],
195: [92, 168],
196: [97, 95],
197: [116, 166],
198: [117, 68],
199: [153, 166],
200: [173, 95],
201: [190, 167],
202: [286, 168],
203: [126, 37],
204: [126, 78],
205: [258, 128],
206: [262, 171],
207: [217, 240, 34],
208: [213, 157, 169],
209: [291, 152, 106, 277, 204],
210: [291, 253, 106, 277, 204],
211: [291, 179, 106, 278, 203],
212: [191],
213: [193],
214: [196],
215: [197],
216: [198],
217: [199],
218: [200],
219: [201],
220: [205],
221: [206],
222: [166],
223: [168],
224: [185],
225: [186],
226: [209],
227: [210],
228: [211],
229: [291, 294, 239],
230: [289, 222, 142],
231: [248, 187],
232: [180, 189],
233: [273, 281, 297],
234: [214, 282, 298],
235: [226],
236: [227],
237: [228],
238: [148],
239: [149],
240: [214],
241: [216],
242: [305],
243: [235],
244: [236],
245: [237],
246: [274, 107],
247: [218, 107],
248: [232, 88, 107],
249: [232, 218, 107],
250: [215, 47, 155],
251: [303, 47, 155],
252: [212, 158, 149],
253: [274, 158, 149],
254: [273, 281, 298, 176],
255: [214, 282, 298, 176],
256: [249, 238, 104],
257: [191, 143],
258: [192, 142],
259: [193, 142],
260: [194, 140],
261: [195, 236],
262: [300, 142],
263: [201, 237],
264: [202, 236],
265: [215, 113],
266: [217, 113],
267: [70, 95],
268: [70, 167],
269: [154, 68],
270: [154, 96],
271: [259, 169],
272: [262, 169],
273: [267],
274: [268],
275: [269],
276: [270],
277: [271],
278: [272],
279: [284, 188],
280: [285, 264],
281: [275],
282: [276],
283: [248, 56, 104],
284: [248, 87, 104],
285: [248, 238, 104],
286: [304, 114],
287: [304, 254],
288: [303, 255],
289: [231],
290: [232],
291: [279],
292: [280],
293: [260],
294: [263],
295: [150],
296: [151],
297: [265, 156, 164],
298: [266, 156, 164],
299: [256, 166],
300: [283, 166],
301: [284, 67],
302: [285, 66],
303: [299],
304: [300],
305: [301],
306: [302],
307: [126],
308: [127]}
In [28]:
# check that the Rauzy fractal of this substitution is the one expected
s = WordMorphism(d)
s.rauzy_fractal_plot()
Out[28]:
In [32]:
########################################
# Rauzy fractal approximating a square #
########################################
# the first argument of approx() is the precision,
# and the second one is the characteristic function of the shape to approximate
# the shape must be not too big in order to be inside m
%time mc = m.approx(15, lambda x: abs(pm(x).real()) < .5 and abs(pm(x).imag()) < .5 )
mc
CPU times: user 3.14 s, sys: 3.99 ms, total: 3.14 s Wall time: 3.14 s
Out[32]:
b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 273 states and 2 letters
In [35]:
mc = mc.proj(m) # permits to have mc as a subset of m
print(mc)
m.plot_list([mc])
b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 262 states and 2 letters
Out[35]:
In [38]:
%time d = mc.substitution()
d
CPU times: user 50.5 s, sys: 188 ms, total: 50.7 s Wall time: 50.7 s
Out[38]:
{1: [244, 131, 200, 174],
2: [265, 160, 206],
3: [31, 1, 262],
4: [314, 72, 132, 265, 86],
5: [77, 174, 121],
6: [100, 278, 184, 74, 94],
7: [298, 308, 203, 277, 124, 217, 105],
8: [189, 244, 40, 77, 186, 121],
9: [255, 275, 239, 74],
10: [56, 69, 1, 262],
11: [25, 154, 241, 261],
12: [117, 258, 288],
13: [301, 66, 157],
14: [301, 66, 26],
15: [301, 20, 28],
16: [201, 140, 22],
17: [201, 290, 8],
18: [77, 186, 121],
19: [255, 304, 152, 239, 74, 93],
20: [196, 296, 291, 217, 105],
21: [129, 296, 123, 216, 106],
22: [244, 43, 77, 174, 121],
23: [33, 112, 273, 176],
24: [33, 112, 45, 254],
25: [117, 258, 232, 193, 219],
26: [314, 72, 132, 265, 86, 205],
27: [314, 145, 265, 86, 230],
28: [314, 147, 143, 273, 220],
29: [315, 21, 59, 273, 176],
30: [301, 20, 28, 274, 219],
31: [191, 280, 277, 126, 217, 80],
32: [192, 203, 277, 124, 217, 105],
33: [297, 312, 129, 296, 123, 216, 106],
34: [255, 275, 239, 74, 93, 223, 306],
35: [161, 312, 129, 296, 123, 216, 106],
36: [280, 277, 126, 151, 253],
37: [280, 277, 126, 217],
38: [310, 136, 264, 2],
39: [201, 140, 266, 5],
40: [296, 49, 253, 106],
41: [201, 140, 75, 18],
42: [261, 125, 299, 17],
43: [296, 123, 216, 106],
44: [255, 275, 239, 74, 93],
45: [255, 275, 239, 261, 93],
46: [255, 275, 239, 261, 125],
47: [167, 277, 6, 253, 156],
48: [13, 278, 184, 74, 94],
49: [13, 278, 184, 74, 249],
50: [242, 43, 144, 206],
51: [243, 43, 51, 45, 254],
52: [243, 43, 113, 9, 150, 254],
53: [243, 43, 112, 273, 176],
54: [117, 258, 288, 274, 219],
55: [117, 258, 288, 246, 219],
56: [191, 280, 277, 126, 217],
57: [315, 73, 43, 59, 273, 176],
58: [315, 73, 43, 112, 273, 176],
59: [315, 73, 43, 51, 273, 176],
60: [315, 21, 112, 273, 150, 254],
61: [315, 21, 112, 273, 176],
62: [296, 123, 71, 253, 106],
63: [201, 290, 70, 75, 18],
64: [167, 277, 128, 151, 253, 156],
65: [167, 277, 128, 217, 156],
66: [203, 277, 124, 217, 105],
67: [243, 43, 51, 273, 150, 254],
68: [243, 43, 51, 273, 176],
69: [80],
70: [189],
71: [249],
72: [165],
73: [129],
74: [177, 42],
75: [244, 62],
76: [205],
77: [35],
78: [24, 34],
79: [144, 206],
80: [31, 82],
81: [32, 157],
82: [244, 131, 200, 174, 260],
83: [10, 244, 131, 200, 174, 260],
84: [23, 44, 254],
85: [24, 44, 254],
86: [29, 44, 254],
87: [52, 46, 254],
88: [53, 45, 254],
89: [57, 44, 254],
90: [58, 44, 254],
91: [60, 44, 254],
92: [61, 44, 254],
93: [30, 225, 74],
94: [54, 225, 74],
95: [7, 4, 76],
96: [315, 21, 68],
97: [201, 47, 207],
98: [201, 64, 207],
99: [201, 65, 207],
100: [202, 66, 157],
101: [201, 149, 207],
102: [201, 187, 159],
103: [201, 290, 158],
104: [201, 36, 83],
105: [201, 37, 83],
106: [201, 187, 119],
107: [201, 36, 119],
108: [81, 278, 184, 74, 94],
109: [255, 304, 182, 74, 93],
110: [242, 43, 265, 160, 206],
111: [242, 62, 265, 160, 206],
112: [315, 21, 51, 273, 176],
113: [315, 21, 67, 273, 176],
114: [315, 21, 68, 273, 176],
115: [238, 229, 232, 209, 218, 168],
116: [117, 258, 232, 193, 219, 99],
117: [298, 308, 196, 296, 291, 217, 105],
118: [298, 308, 203, 296, 291, 217, 105],
119: [3, 244, 131, 200, 174, 260],
120: [80, 244, 131, 200, 174, 260],
121: [255, 275, 130, 261, 125, 223, 306],
122: [12, 305, 225, 74],
123: [13, 278, 184, 74],
124: [14, 278, 184, 74],
125: [15, 305, 225, 74],
126: [81, 278, 184, 74],
127: [95, 278, 184, 74],
128: [100, 278, 184, 74],
129: [310, 136, 264, 79],
130: [314, 198, 200, 78],
131: [277, 49, 253, 106],
132: [277, 49, 253, 107],
133: [3, 244, 131, 200, 174],
134: [80, 244, 131, 200, 174],
135: [164, 277, 49, 253, 155],
136: [204, 277, 48, 253, 155],
137: [165, 277, 49, 253, 107],
138: [204, 277, 48, 253, 170],
139: [167, 277, 6, 253, 189],
140: [280, 277, 6, 253, 189],
141: [242, 43, 52, 46, 254],
142: [242, 43, 144, 46, 254],
143: [243, 43, 29, 44, 254],
144: [243, 43, 113, 44, 254],
145: [165, 277, 123, 71, 253, 107],
146: [204, 277, 123, 151, 253, 170],
147: [165, 277, 123, 216, 107],
148: [204, 277, 123, 217, 170],
149: [167, 277, 128, 217, 171],
150: [93],
151: [94],
152: [97],
153: [98],
154: [99],
155: [56, 119],
156: [56, 120],
157: [244, 132, 265, 86, 205],
158: [189, 244, 131, 200, 174, 121],
159: [189, 244, 131, 200, 174, 260],
160: [113, 44, 254],
161: [115, 227, 295],
162: [116, 241, 261],
163: [118, 228, 232],
164: [310, 136, 50],
165: [310, 136, 110],
166: [310, 146, 111],
167: [310, 146, 142],
168: [201, 139, 207],
169: [201, 140, 208],
170: [201, 37, 119],
171: [201, 37, 120],
172: [163, 304, 224, 74],
173: [114, 19, 254],
174: [114, 109, 254],
175: [117, 258, 232],
176: [93, 223, 306],
177: [255, 283, 130],
178: [122, 215, 306],
179: [161, 312, 129],
180: [7, 26],
181: [117, 27],
182: [97, 314, 198, 200, 85],
183: [98, 314, 198, 200, 92],
184: [101, 314, 198, 200, 84],
185: [175, 284, 241, 261],
186: [96, 287, 109, 254],
187: [280, 277, 108, 253],
188: [56, 133, 262],
189: [56, 134, 262],
190: [190, 195, 233, 172, 216, 102],
191: [257, 285, 227, 295, 292, 235, 103],
192: [257, 286, 227, 295, 210, 235, 103],
193: [256, 304, 183, 261],
194: [175, 245, 225, 261],
195: [314, 135, 265, 88],
196: [310, 138, 264, 87],
197: [314, 145, 265, 86],
198: [279, 277, 49, 253, 188],
199: [166, 277, 49, 253, 188],
200: [179, 43],
201: [191],
202: [192],
203: [310, 138, 141],
204: [310, 138, 142],
205: [255, 275, 239, 261, 125, 214, 306],
206: [255, 275, 239, 261, 125, 223, 306],
207: [244, 131, 200, 173, 121],
208: [244, 131, 200, 174, 121],
209: [211, 304, 183, 74],
210: [212, 304, 225, 74],
211: [117, 228, 232],
212: [117, 197, 232],
213: [11, 263, 39],
214: [11, 269, 39],
215: [248, 263, 39],
216: [249, 222, 306],
217: [94, 222, 306],
218: [94, 213, 306],
219: [94, 215, 306],
220: [125, 214, 17],
221: [125, 300, 17],
222: [162, 302, 39],
223: [162, 269, 39],
224: [99, 314, 198, 200, 84],
225: [99, 314, 198, 200, 92],
226: [192, 203, 296, 291, 217, 105],
227: [314, 199, 265, 90],
228: [314, 137, 265, 86],
229: [314, 137, 265, 89],
230: [255, 275, 239, 261, 125, 214, 17],
231: [255, 275, 239, 261, 125, 299, 17],
232: [230],
233: [231],
234: [250, 270, 41],
235: [250, 270, 307],
236: [250, 270, 63],
237: [192, 196, 296, 291, 217, 105],
238: [192, 196, 296, 127, 217, 104],
239: [314, 198, 200, 85],
240: [314, 198, 200, 91],
241: [314, 198, 200, 92],
242: [297, 313, 38],
243: [297, 312, 129],
244: [297, 311, 165],
245: [193, 219],
246: [256, 304, 153, 241, 261],
247: [175, 245, 154, 241, 261],
248: [25, 225, 261],
249: [54, 225, 261],
250: [55, 225, 261],
251: [201, 289, 70, 207],
252: [201, 290, 70, 208],
253: [222, 306],
254: [223, 306],
255: [226, 228, 232],
256: [237, 228, 232],
257: [238, 229, 232],
258: [314, 147, 143],
259: [255, 283, 130, 261, 125, 299, 17],
260: [255, 275, 130, 261, 125, 223, 17],
261: [259],
262: [260],
263: [247, 303, 39],
264: [242, 43],
265: [243, 43],
266: [244, 43],
267: [255, 281, 239, 261, 125, 299, 17],
268: [256, 281, 240, 261, 125, 300, 17],
269: [185, 303, 16],
270: [185, 303, 39],
271: [256, 281, 240, 261],
272: [256, 282, 241, 261],
273: [255, 275, 239, 261],
274: [256, 276, 241, 261],
275: [274, 178, 97],
276: [274, 178, 98],
277: [271, 221],
278: [272, 178],
279: [310, 148, 111],
280: [310, 148, 142],
281: [246, 178, 97],
282: [246, 178, 98],
283: [193, 178, 97],
284: [193, 219, 99],
285: [209, 218, 168],
286: [209, 218, 251],
287: [273, 176],
288: [273, 220],
289: [167, 277, 6, 253],
290: [280, 277, 6, 253],
291: [180, 278, 184, 74],
292: [181, 304, 225, 74],
293: [189, 244, 40],
294: [189, 244, 62],
295: [267],
296: [268],
297: [257, 285, 227, 295],
298: [257, 286, 227, 295],
299: [248, 269, 39],
300: [248, 270, 39],
301: [298, 308],
302: [194, 303, 16],
303: [194, 303, 39],
304: [274, 178],
305: [274, 219],
306: [201, 290, 293, 18],
307: [201, 290, 294, 18],
308: [210, 235, 103],
309: [210, 236, 103],
310: [297, 309],
311: [210, 234, 103],
312: [210, 234, 169],
313: [210, 234, 252],
314: [297, 311],
315: [297, 312]}
In [39]:
s = WordMorphism(d)
s.rauzy_fractal_plot()
Out[39]:
In [4]:
########################################
# Rauzy fractal approximating a gabian #
########################################
from badic.beta_adic import ImageIn
im = ImageIn("/home/mercatpaul/gabian.png")
im
Out[4]:
Image of size 573x628
In [22]:
#compute a beta-adic set approximating the image
w = im.width()
h = im.height()
ma = max(w,h)
mg = m.approx(17, lambda x: (conjugate(pm(x))+.5*(1+I)+.1*I)*ma in im)
print(mg)
b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 486 states and 2 letters
In [23]:
m.plot_list([mg])
Out[23]:
In [24]:
# make the language of mg be a sublanguage of the one of m
mg = mg.proj(m)
mg
Out[24]:
b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 551 states and 2 letters
In [25]:
# compute a domain exchange describing the beta-adic set
%time lm = mg.domain_exchange()
print(len(lm))
lm
CPU times: user 15.7 s, sys: 11.9 ms, total: 15.7 s Wall time: 15.7 s 17
Out[25]:
[(b + 1, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 122 states and 2 letters), (b^2, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 199 states and 2 letters), (b^2 + b, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 31 states and 2 letters), (b^2 + b + 1, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 207 states and 2 letters), (b^2 + 2*b + 1, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 54 states and 2 letters), (2*b^2 + b, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 25 states and 2 letters), (2*b^2 + b + 1, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 95 states and 2 letters), (2*b^2 + 2*b + 1, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 225 states and 2 letters), (3*b^2 + 2*b + 1, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 211 states and 2 letters), (3*b^2 + 3*b + 2, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 227 states and 2 letters), (4*b^2 + 3*b + 2, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 155 states and 2 letters), (4*b^2 + 4*b + 2, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 24 states and 2 letters), (5*b^2 + 4*b + 2, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 63 states and 2 letters), (5*b^2 + 5*b + 3, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 100 states and 2 letters), (6*b^2 + 5*b + 3, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 122 states and 2 letters), (6*b^2 + 6*b + 4, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 37 states and 2 letters), (7*b^2 + 6*b + 4, b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 39 states and 2 letters)]
In [26]:
# plot it
mg.plot_list([a for t,a in lm], nprec=7)
Out[26]:
In [27]:
# plot it after exchange
mg.plot_list([a.proj(mg, t) for t,a in lm], nprec=7)
Out[27]:
In [28]:
# give the list of pieces of the domain exchange to substitution() in order to avoid recomputing it
# !! takes time !!
%time d,la = mg.substitution(lt=[(a.a,t) for t,a in lm], get_aut=True)
print("number of pieces : %s" % len(la))
print(d)
CPU times: user 11min 49s, sys: 501 ms, total: 11min 49s
Wall time: 11min 49s
number of pieces : 310
{1: [115, 285, 121, 58, 303], 2: [79, 143, 221, 6, 285, 121, 52, 281, 303], 3: [118, 284, 247, 225, 283, 310, 57, 277, 79, 204, 308, 243, 164, 148, 259, 97, 75, 273, 125, 166, 295, 302], 4: [292, 307, 205], 5: [47, 75, 272, 78, 68, 295, 302], 6: [118, 284, 247, 225, 283, 310, 57, 277], 7: [293, 139, 309, 257, 301, 223, 147, 305, 91, 34, 156], 8: [180, 189, 309, 257, 171, 147, 144, 137, 278, 162, 283, 310], 9: [12, 309, 257, 171, 147, 144, 137, 278, 162, 283, 310], 10: [176, 231, 289, 128, 53, 292, 307, 205, 116, 285, 245, 51, 36, 27, 274, 79, 71, 308, 243, 109, 148, 200, 161, 75, 232, 254, 166, 295, 302], 11: [176, 231, 289, 146, 292, 307, 151, 185, 116, 285, 245, 51, 283, 310, 27, 2, 5, 79, 71, 308, 243, 109, 148, 200, 161, 75, 306, 90, 254, 166, 295, 302, 124, 107], 12: [176, 231, 289, 146, 292, 307, 151, 185, 116, 285, 245, 51, 283, 310, 64, 5, 79, 71, 308, 243, 109, 148, 200, 161, 75, 306, 90, 254, 166, 295, 302, 124, 107], 13: [119, 165, 297, 309, 257, 170, 147, 305, 92, 183, 118, 284, 247, 225, 283, 310, 57, 277, 79, 204, 308, 243, 164, 148, 259, 97, 75, 273, 125, 166, 295, 302, 238, 107, 289, 215], 14: [176, 231, 289, 128, 53, 292, 307, 205, 116, 285, 245, 51, 36, 27, 274, 79, 71, 308, 243, 109, 148, 200, 161, 75, 232, 254, 166, 295, 302, 124, 107, 289, 260], 15: [120, 192, 310, 129, 53], 16: [119, 135, 257, 170, 147, 305, 92, 84, 44], 17: [243, 132, 259, 97, 75, 273, 125, 166, 295, 302], 18: [13, 172, 281, 303, 46, 75, 272, 84, 155, 8, 295, 302], 19: [77, 4, 33, 114, 296, 301, 253, 305, 92, 84, 155, 201], 20: [16, 287, 304, 96, 148, 112, 35, 43, 15, 232, 78, 100, 167, 280, 302], 21: [40, 33, 114, 296, 301, 253, 305, 92, 84, 155, 201], 22: [10, 82, 114, 296, 301, 94, 290, 305, 92, 84, 155, 201, 278, 230, 283, 310, 26, 174], 23: [10, 82, 114, 296, 301, 94, 290, 234, 84, 155, 201, 278, 230, 283, 310, 26, 174], 24: [11, 309, 257, 171, 147, 305, 93, 34, 156, 137, 278, 162, 283, 310, 22, 277], 25: [12, 309, 257, 171, 147, 144, 137, 278, 162, 283, 310, 23, 277], 26: [14, 193, 301, 94, 290, 305, 92, 84, 155, 201, 278, 230, 283, 310, 26, 174], 27: [77, 4, 33, 114, 296, 301, 253, 305, 92, 84, 155, 201, 278, 230, 283, 310, 26, 174], 28: [293, 159, 189, 309, 257, 301, 42, 147, 144, 137, 278, 162, 283, 310, 23, 277], 29: [40, 33, 114, 296, 301, 253, 305, 92, 84, 155, 201, 278, 230, 283, 310, 26, 174], 30: [77, 4, 33, 114, 296, 301, 253, 305, 92, 84, 155, 201, 278, 191, 310, 26, 174, 79, 143], 31: [278, 230, 283, 310, 26, 174, 79, 143, 115, 285, 121, 58, 303, 60, 272, 78, 68, 295, 302], 32: [292, 307, 151, 186, 24, 304, 246, 237, 298, 310, 30, 1, 80, 79, 71, 308, 244, 304, 153, 148, 217, 85, 90, 255, 166, 295, 302], 33: [116, 285, 245, 51, 36, 27, 274, 79, 71, 308, 243, 109, 148, 200, 161, 75, 232, 254, 166, 295, 302, 124, 107, 289, 260], 34: [242, 304, 153, 288, 145], 35: [26, 300, 48, 79, 212], 36: [239, 299, 20, 289, 266], 37: [278, 230, 283, 310, 26, 174], 38: [278, 230, 283, 310, 26, 174, 79, 143], 39: [119, 165, 297, 309, 257, 170, 147, 305, 92, 183], 40: [176, 231, 289, 128, 53, 292, 307, 205], 41: [278, 191, 310, 26, 174, 79, 143], 42: [123, 285, 95, 148, 172, 35, 45, 75, 272, 78, 157, 54, 295, 302], 43: [13, 172, 281, 303, 61, 306, 150, 84, 155, 8, 83], 44: [75, 273, 182, 188, 302, 124, 299, 20, 289, 67, 81], 45: [39, 3, 288, 172, 281, 303, 46, 75, 272, 84, 155, 8, 295, 302], 46: [39, 3, 288, 172, 281, 303, 46, 75, 272, 84, 155, 118, 302], 47: [39, 3, 288, 172, 281, 303, 46, 75, 272, 84, 155, 202], 48: [221, 6, 285, 17, 76, 52, 35, 47, 75, 272, 78, 154, 169, 295, 302], 49: [39, 6, 285, 250, 52, 281, 303, 46, 75, 272, 78, 154, 55, 295, 302], 50: [221, 86, 121, 52, 281, 303, 60, 272, 78, 68, 295, 302], 51: [294, 203, 308, 220, 287, 304, 96, 148, 112, 35, 43, 15, 306, 90, 125, 167, 280, 302], 52: [293, 264, 7, 286, 301, 222, 147, 233, 34, 99, 149, 88, 279, 227, 283, 310], 53: [79, 211, 39, 6, 285, 250, 52, 281, 303, 46, 75, 272, 78, 154, 55, 295, 302], 54: [293, 159, 189, 309, 257, 301, 42, 147, 144, 137, 278, 162, 283, 310], 55: [293, 159, 189, 309, 257, 301, 42, 147, 144, 149, 88, 278, 162, 283, 310], 56: [14, 114, 296, 301, 94, 290, 305, 92, 84, 155, 201, 278, 230, 283, 310, 26, 174], 57: [14, 114, 296, 301, 253, 305, 92, 84, 155, 201, 278, 230, 283, 310, 26, 174], 58: [293, 264, 7, 286, 301, 222, 147, 233, 34, 99, 149, 88, 279, 227, 283, 310, 26, 300, 48], 59: [77, 265, 114, 296, 301, 253, 305, 92, 84, 155, 201, 278, 230, 283, 310, 26, 174], 60: [39, 3, 288, 172, 281, 303, 46, 75, 272, 84, 155, 202, 120, 231, 298, 310, 129, 53], 61: [39, 3, 288, 172, 281, 303, 46, 75, 272, 84, 155, 118, 302, 120, 231, 298, 310, 129, 53], 62: [77, 264, 257, 301, 252, 234, 34, 99, 137, 278, 226, 283, 310, 26, 300, 48, 79, 211], 63: [119, 190, 309, 257, 170, 147, 305, 92, 183, 118, 284, 247, 225, 283, 310, 57, 277, 79, 204, 308], 64: [77, 4, 33, 114, 296, 301, 253, 305, 92, 84, 155, 201, 278, 230, 283, 310, 26, 174, 79, 143, 221, 6, 285, 121, 52, 281, 303], 65: [77, 4, 33, 114, 296, 301, 253, 305, 92, 84, 155, 201, 278, 191, 310, 26, 174, 79, 143, 115, 285, 121, 58, 303], 66: [77, 4, 33, 114, 296, 301, 253, 234, 84, 155, 201, 278, 191, 310, 26, 174, 79, 143, 221, 86, 121, 52, 281, 303], 67: [77, 4, 33, 114, 296, 301, 253, 234, 84, 155, 201, 278, 191, 310, 26, 174, 79, 143, 63, 121, 52, 281, 303], 68: [75, 306, 72, 188, 302, 124, 107, 298, 310, 67, 81, 293, 140, 309, 257, 301, 42, 147, 144, 149, 88, 278, 162, 283, 310], 69: [75, 306, 72, 188, 302, 124, 107, 289, 67, 81, 180, 189, 309, 257, 171, 147, 144, 137, 278, 162, 283, 310], 70: [75, 306, 72, 188, 302, 124, 107, 298, 310, 67, 81, 293, 140, 309, 257, 301, 42, 147, 144, 149, 88, 278, 162, 283, 310, 23, 277], 71: [292, 307, 151, 186, 24, 304, 246, 237, 298, 310, 30, 1, 80, 79, 71, 308, 244, 304, 153, 148, 217, 85, 90, 255, 166, 295, 302, 124, 299, 20], 72: [116, 304, 246, 175, 36, 29, 108, 79, 71, 308, 242, 109, 288, 199, 160, 75, 273, 182, 166, 295, 302, 124, 107, 289, 207], 73: [77, 4, 33, 193, 301, 253, 234, 84, 155, 201, 278, 191, 310, 26, 174, 79, 143, 221, 86, 121, 52, 281, 303, 60, 272, 78, 70, 302], 74: [292, 307, 151, 185, 116, 285, 245, 51, 283, 310, 27, 2, 5, 79, 71, 308, 243, 109, 148, 200, 161, 75, 306, 90, 254, 166, 295, 302, 124, 107, 289, 260], 75: [120, 231, 298, 310, 129, 53], 76: [238, 107, 298, 310, 136, 50], 77: [176, 231, 289, 128, 53], 78: [242, 109, 288, 199, 160], 79: [176, 231, 289, 62, 104], 80: [60, 272, 78, 68, 295, 302], 81: [60, 272, 78, 70, 302], 82: [124, 107, 289, 260], 83: [23, 277, 79, 209], 84: [242, 109, 288, 145], 85: [120, 192, 310, 129, 53, 292, 216], 86: [118, 284, 247, 225, 283, 310, 57, 277, 79, 204, 308], 87: [115, 285, 121, 58, 303, 60, 272, 78, 68, 295, 302], 88: [117, 284, 278, 162, 283, 310, 23, 277, 79, 138, 308], 89: [122, 285, 251, 172, 281, 303, 46, 75, 272, 84, 155, 8, 295, 302], 90: [116, 304, 246, 175, 283, 310, 29, 108, 79, 71, 308], 91: [116, 304, 249, 175, 36, 21, 31, 79, 158, 163, 282, 308], 92: [116, 304, 249, 175, 36, 21, 37, 108, 79, 158, 163, 282, 308], 93: [116, 304, 249, 175, 36, 21, 38, 87, 79, 158, 163, 282, 308], 94: [123, 228, 148, 172, 281, 303, 45, 75, 272, 78, 157, 28, 302], 95: [243, 164, 148, 259, 97, 75, 273, 125, 166, 295, 302], 96: [243, 164, 148, 259, 97, 75, 273, 78, 100, 188, 302], 97: [13, 172, 281, 303, 61, 272, 84, 155, 8, 295, 302], 98: [13, 172, 281, 303, 61, 272, 84, 155, 8, 83], 99: [75, 306, 72, 188, 302, 124, 299, 20, 289, 67, 81], 100: [75, 273, 182, 188, 302, 124, 107, 298, 310, 67, 81], 101: [75, 273, 182, 188, 302, 124, 107, 289, 67, 81], 102: [221, 6, 285, 121, 52, 281, 303, 60, 272, 78, 68, 295, 302], 103: [221, 6, 285, 121, 52, 35, 47, 75, 272, 78, 154, 169, 295, 302], 104: [39, 86, 250, 52, 281, 303, 61, 272, 78, 154, 55, 295, 302], 105: [79, 203, 308, 16, 6, 304, 96, 148, 112, 35, 43, 75, 232, 78, 100, 167, 280, 302], 106: [294, 262, 16, 287, 304, 96, 148, 112, 35, 43, 15, 232, 125, 167, 280, 302], 107: [294, 262, 16, 287, 304, 96, 148, 112, 35, 43, 15, 232, 78, 100, 167, 280, 302], 108: [79, 143, 115, 285, 121, 58, 303, 60, 272, 78, 68, 295, 302], 109: [79, 263, 243, 164, 148, 173, 35, 97, 75, 273, 78, 100, 166, 295, 302], 110: [79, 263, 243, 164, 148, 259, 97, 75, 273, 78, 100, 188, 302], 111: [79, 212, 122, 285, 251, 172, 281, 303, 46, 75, 272, 84, 155, 8, 295, 302], 112: [293, 264, 126, 301, 181, 233, 34, 99, 149, 88, 279, 227, 283, 310], 113: [293, 74, 257, 301, 223, 147, 305, 91, 34, 156, 137, 278, 225, 283, 310], 114: [293, 74, 257, 301, 223, 147, 233, 34, 156, 137, 278, 225, 283, 310], 115: [119, 190, 309, 257, 170, 147, 305, 92, 183, 118, 284, 247, 225, 283, 310, 57, 277], 116: [179, 189, 309, 257, 171, 147, 305, 93, 34, 156, 137, 278, 162, 283, 310, 22, 277], 117: [180, 189, 309, 257, 171, 147, 144, 117, 284, 278, 162, 283, 310, 23, 277], 118: [180, 189, 309, 257, 171, 147, 144, 137, 278, 162, 283, 310, 23, 277], 119: [176, 133, 128, 53, 292, 307, 151, 185, 116, 285, 245, 51, 283, 310, 27, 2, 5], 120: [178, 195, 198, 89, 75, 273, 84, 101, 8, 295, 284, 247, 224, 283, 310, 59, 274], 121: [243, 132, 259, 97, 75, 273, 125, 166, 295, 302, 238, 107, 298, 310, 136, 50], 122: [119, 165, 297, 309, 257, 170, 147, 305, 92, 183, 118, 284, 247, 225, 283, 310, 57, 277], 123: [119, 165, 297, 309, 257, 170, 147, 305, 92, 84, 44, 118, 284, 247, 225, 283, 310, 57, 277], 124: [178, 229, 288, 131, 303, 18, 75, 273, 84, 101, 25, 302, 248, 106, 298, 310, 59, 275], 125: [242, 109, 288, 199, 160, 75, 273, 182, 188, 302, 124, 107, 298, 310, 67, 81], 126: [293, 139, 309, 257, 301, 223, 147, 305, 91, 34, 156, 137, 278, 225, 283, 310, 56, 174], 127: [79, 71, 308, 244, 304, 153, 148, 217, 85, 90, 255, 166, 295, 302, 124, 299, 20], 128: [77, 264, 257, 301, 94, 147, 305, 92, 34, 99, 137, 278, 226, 283, 310, 26, 300, 48], 129: [77, 264, 257, 301, 252, 305, 92, 34, 99, 137, 278, 226, 283, 310, 26, 174], 130: [293, 264, 126, 301, 222, 147, 305, 91, 34, 99, 137, 279, 227, 283, 310, 26, 300, 48], 131: [293, 264, 126, 301, 222, 147, 233, 34, 99, 137, 279, 227, 283, 310, 26, 300, 48], 132: [79, 204, 308, 243, 164, 148, 259, 97, 75, 273, 78, 100, 188, 302, 238, 107, 289, 136, 50], 133: [79, 203, 308, 243, 110, 148, 200, 43, 75, 232, 125, 167, 280, 302, 239, 107, 289, 266], 134: [79, 204, 308, 243, 110, 148, 200, 98, 75, 273, 125, 188, 302, 239, 107, 289, 267], 135: [79, 71, 308, 243, 109, 148, 200, 161, 75, 232, 254, 166, 295, 302, 124, 107, 289, 260], 136: [77, 265, 114, 296, 301, 253, 234, 84, 155, 201, 278, 230, 283, 310, 26, 174, 79, 143], 137: [180, 189, 309, 257, 171, 147, 144, 117, 284, 278, 162, 283, 310, 23, 277, 79, 138, 308], 138: [292, 307, 206, 24, 304, 246, 237, 289, 65, 80, 79, 71, 308, 244, 304, 153, 148, 217, 85, 90, 255, 166, 295, 302, 124, 107], 139: [292, 307, 151, 185, 116, 285, 245, 51, 283, 310, 27, 2, 5, 79, 71, 308, 243, 109, 148, 200, 161, 75, 306, 90, 254, 166, 295, 302, 124, 107], 140: [292, 307, 151, 185, 116, 285, 245, 51, 283, 310, 64, 5, 79, 71, 308, 243, 109, 148, 200, 161, 75, 306, 90, 254, 166, 295, 302, 124, 107], 141: [116, 304, 246, 236, 36, 27, 108, 79, 71, 308, 242, 109, 148, 218, 75, 306, 90, 255, 166, 295, 302, 124, 299, 20, 289, 261], 142: [77, 4, 33, 114, 296, 301, 253, 305, 92, 84, 155, 201, 278, 230, 283, 310, 26, 174, 79, 143, 115, 285, 121, 58, 303, 60, 272, 78, 68, 295, 302], 143: [292, 269, 24, 304, 246, 237, 289, 30, 87, 79, 71, 308, 244, 304, 153, 148, 217, 85, 90, 255, 188, 302, 124, 299, 20, 289, 73], 144: [292, 210, 116, 304, 249, 175, 36, 21, 38, 87, 79, 158, 163, 282, 308, 242, 304, 153, 288, 145, 75, 306, 152, 182, 188, 302, 124, 299, 20, 289, 67, 81], 145: [293, 264, 126, 301, 181, 233, 34, 99, 137, 279, 227, 283, 310, 26, 300, 48, 79, 212, 39, 86, 251, 172, 281, 303, 61, 272, 84, 69, 83], 146: [77, 264, 257, 301, 94, 147, 305, 92, 34, 99, 137, 278, 226, 283, 310, 26, 300, 48, 79, 211, 39, 6, 285, 250, 52, 281, 303, 46, 75, 272, 78, 154, 55, 295, 302], 147: [241, 105, 289, 196, 49], 148: [238, 107, 289, 136, 50], 149: [180, 189, 309, 257, 171, 147, 144], 150: [116, 304, 246, 175, 36, 21, 37, 108, 79, 32, 282, 308], 151: [116, 304, 246, 236, 36, 27, 108, 79, 71, 308], 152: [116, 304, 246, 175, 36, 29, 108, 79, 71, 308], 153: [243, 164, 148, 173, 35, 97, 75, 273, 78, 100, 166, 295, 302], 154: [75, 306, 72, 188, 302, 124, 107, 298, 310, 67, 81], 155: [75, 306, 72, 188, 302, 124, 107, 289, 67, 81], 156: [75, 306, 152, 182, 188, 302, 124, 299, 20, 289, 67, 81], 157: [75, 306, 152, 182, 188, 302, 124, 107, 289, 67, 81], 158: [292, 307, 151, 186, 24, 304, 246, 237, 298, 310, 30, 1, 80], 159: [292, 307, 151, 185, 116, 285, 245, 51, 283, 310, 64, 5], 160: [39, 86, 251, 172, 281, 303, 61, 272, 84, 69, 83], 161: [39, 86, 251, 172, 281, 303, 61, 272, 84, 155, 8, 83], 162: [294, 203, 308, 16, 287, 304, 96, 148, 200, 43, 85, 90, 125, 167, 280, 302], 163: [79, 71, 308, 244, 304, 153, 148, 217, 85, 90, 255, 166, 295, 302], 164: [79, 204, 308, 243, 164, 148, 259, 97, 75, 273, 78, 100, 188, 302], 165: [79, 71, 308, 243, 109, 148, 200, 161, 75, 232, 254, 166, 295, 302], 166: [293, 140, 309, 257, 301, 42, 147, 235, 34, 156, 137, 278, 162, 283, 310], 167: [293, 140, 309, 257, 301, 42, 147, 235, 34, 156, 149, 88, 278, 162, 283, 310], 168: [293, 140, 309, 257, 301, 42, 147, 144, 137, 278, 162, 283, 310], 169: [293, 140, 309, 257, 301, 42, 147, 144, 149, 88, 278, 162, 283, 310], 170: [79, 208, 123, 285, 95, 148, 172, 281, 303, 45, 75, 272, 78, 157, 54, 295, 302], 171: [79, 208, 123, 285, 95, 148, 172, 35, 45, 75, 272, 78, 157, 54, 295, 302], 172: [293, 264, 126, 301, 222, 147, 233, 34, 99, 137, 279, 227, 283, 310], 173: [293, 264, 126, 301, 222, 147, 233, 34, 99, 149, 88, 279, 227, 283, 310], 174: [79, 143, 221, 6, 285, 17, 76, 52, 35, 47, 75, 272, 78, 154, 169, 295, 302], 175: [294, 262, 220, 287, 304, 96, 148, 112, 35, 43, 85, 90, 125, 167, 280, 302], 176: [178, 195, 130, 111, 75, 306, 152, 84, 101, 8, 295, 284, 247, 224, 283, 310, 59, 274], 177: [177, 134, 256, 111, 291, 306, 152, 184, 118, 284, 247, 225, 283, 310, 57, 276], 178: [119, 135, 257, 170, 147, 305, 92, 183, 118, 284, 247, 225, 283, 310, 57, 277], 179: [176, 231, 289, 146, 292, 307, 151, 185, 116, 285, 245, 51, 283, 310, 27, 2, 5], 180: [176, 231, 289, 146, 292, 307, 151, 185, 116, 285, 245, 51, 283, 310, 64, 5], 181: [123, 228, 148, 172, 35, 45, 75, 272, 78, 157, 28, 302, 241, 105, 289, 196, 49], 182: [242, 109, 288, 199, 160, 75, 273, 182, 166, 295, 302, 124, 107, 289, 207], 183: [242, 109, 288, 145, 75, 273, 182, 188, 302, 124, 299, 20, 289, 67, 81], 184: [242, 109, 288, 145, 75, 273, 182, 188, 302, 124, 107, 289, 67, 81], 185: [242, 109, 148, 218, 75, 232, 255, 166, 295, 302, 124, 107, 289, 66, 81], 186: [242, 109, 148, 218, 75, 232, 255, 166, 295, 302, 124, 107, 289, 261], 187: [293, 140, 309, 257, 301, 42, 147, 144, 137, 278, 162, 283, 310, 23, 277], 188: [293, 140, 309, 257, 301, 42, 147, 235, 34, 156, 137, 278, 162, 283, 310, 23, 277], 189: [79, 71, 308, 243, 109, 148, 200, 161, 75, 306, 90, 254, 166, 295, 302, 124, 107], 190: [79, 71, 308, 243, 109, 148, 200, 161, 75, 232, 254, 166, 295, 302, 124, 107], 191: [294, 203, 308, 244, 110, 148, 200, 43, 15, 306, 90, 125, 167, 280, 302, 239, 299, 20], 192: [79, 203, 308, 243, 110, 148, 200, 43, 75, 232, 125, 167, 280, 302, 239, 107], 193: [293, 74, 257, 301, 223, 147, 233, 34, 156, 137, 278, 225, 283, 310, 56, 174], 194: [79, 204, 308, 243, 164, 148, 259, 97, 75, 273, 125, 188, 302, 238, 107, 289, 136, 50], 195: [79, 204, 308, 243, 164, 148, 259, 97, 75, 273, 125, 188, 302, 238, 107, 289, 215], 196: [77, 264, 113, 296, 301, 252, 305, 92, 34, 99, 137, 278, 226, 283, 310, 26, 174, 79, 211], 197: [77, 265, 114, 296, 301, 253, 305, 92, 84, 155, 201, 278, 230, 283, 310, 26, 174, 79, 143], 198: [293, 264, 126, 301, 222, 147, 305, 91, 34, 99, 137, 279, 227, 283, 310, 26, 300, 48, 79, 212], 199: [293, 264, 126, 301, 181, 233, 34, 99, 137, 279, 227, 283, 310, 26, 300, 48, 79, 212], 200: [293, 264, 126, 301, 181, 233, 34, 99, 149, 88, 279, 227, 283, 310, 26, 300, 48, 79, 212], 201: [180, 189, 309, 257, 171, 147, 144, 137, 278, 162, 283, 310, 23, 277, 79, 138, 308], 202: [180, 189, 309, 257, 171, 147, 144, 137, 278, 162, 283, 310, 23, 277, 79, 209], 203: [292, 307, 206, 24, 304, 246, 237, 289, 30, 1, 80, 79, 71, 308, 244, 304, 153, 148, 217, 15, 306, 90, 255, 166, 295, 302, 124, 299, 20], 204: [292, 307, 206, 24, 304, 246, 237, 289, 30, 1, 80, 79, 71, 308, 244, 304, 153, 148, 217, 85, 90, 255, 166, 295, 302, 124, 299, 20], 205: [116, 304, 246, 236, 36, 27, 108, 79, 71, 308, 242, 109, 148, 218, 75, 232, 255, 166, 295, 302, 124, 107, 289, 66, 81], 206: [116, 304, 246, 236, 36, 27, 108, 79, 71, 308, 242, 109, 148, 218, 75, 232, 255, 166, 295, 302, 124, 107, 289, 261], 207: [77, 4, 33, 114, 296, 301, 253, 234, 84, 155, 201, 278, 191, 310, 26, 174, 79, 143, 63, 121, 52, 281, 303, 60, 272, 78, 70, 302], 208: [292, 307, 206, 24, 304, 246, 237, 289, 19, 41, 87, 79, 158, 127, 308, 244, 304, 153, 148, 217, 85, 90, 255, 166, 295, 302, 124, 299, 20, 289, 73], 209: [292, 307, 206, 24, 304, 246, 237, 289, 65, 80, 79, 71, 308, 244, 304, 153, 148, 217, 85, 90, 255, 166, 295, 302, 124, 107, 289, 73], 210: [292, 307, 141, 116, 304, 246, 236, 36, 142, 79, 71, 308, 242, 109, 148, 218, 75, 306, 90, 255, 166, 295, 302, 124, 299, 20, 289, 261], 211: [292, 269, 24, 304, 246, 237, 289, 19, 41, 87, 79, 158, 127, 308, 244, 304, 153, 148, 217, 85, 90, 255, 188, 302, 124, 299, 20, 289, 73], 212: [292, 269, 24, 304, 246, 237, 289, 19, 41, 87, 79, 158, 127, 308, 244, 304, 153, 148, 217, 85, 90, 255, 188, 302, 124, 107, 289, 73], 213: [77, 264, 113, 296, 301, 252, 305, 92, 34, 99, 137, 278, 226, 283, 310, 26, 174, 79, 211, 39, 6, 285, 250, 52, 281, 303, 46, 75, 272, 78, 154, 55, 295, 302], 214: [77, 265, 114, 296, 301, 253, 305, 92, 84, 155, 201, 278, 230, 283, 310, 26, 174, 79, 143, 221, 6, 285, 121, 52, 281, 303, 60, 272, 78, 68, 295, 302], 215: [77, 265, 114, 296, 301, 253, 234, 84, 155, 201, 278, 230, 283, 310, 26, 174, 79, 143, 221, 86, 121, 52, 281, 303, 60, 272, 78, 68, 295, 302], 216: [292, 268, 116, 304, 246, 236, 36, 142, 79, 71, 308, 242, 109, 148, 218, 75, 306, 90, 255, 166, 295, 302, 124, 299, 20, 289, 261], 217: [293, 264, 126, 301, 181, 233, 34, 99, 149, 88, 279, 227, 283, 310, 26, 300, 48, 79, 212, 39, 86, 251, 131, 303, 61, 272, 84, 69, 83], 218: [293, 264, 126, 301, 181, 233, 34, 99, 149, 88, 279, 227, 283, 310, 26, 300, 48, 79, 212, 39, 86, 251, 172, 281, 303, 61, 272, 84, 69, 83], 219: [77, 264, 257, 301, 252, 234, 34, 99, 137, 278, 226, 283, 310, 26, 300, 48, 79, 211, 39, 86, 250, 52, 281, 303, 61, 272, 78, 154, 55, 295, 302], 220: [119, 190, 309, 257, 170, 147, 305, 92, 84, 44], 221: [119, 190, 309, 257, 170, 147, 305, 92, 183], 222: [123, 228, 148, 172, 35, 45, 75, 272, 78, 157, 28, 302], 223: [123, 228, 148, 172, 35, 45, 75, 272, 78, 157, 54, 295, 302], 224: [294, 203, 308, 16, 287, 304, 96, 148, 112, 35, 43, 15, 306, 90, 125, 167, 280, 302], 225: [294, 203, 308, 16, 287, 304, 96, 148, 112, 35, 43, 85, 90, 125, 167, 280, 302], 226: [294, 203, 308, 244, 304, 96, 148, 112, 35, 43, 15, 306, 90, 125, 167, 280, 302], 227: [294, 203, 308, 244, 304, 96, 148, 112, 35, 43, 85, 90, 125, 167, 280, 302], 228: [79, 204, 308, 243, 164, 148, 259, 97, 75, 273, 125, 166, 295, 302], 229: [79, 204, 308, 243, 164, 148, 259, 97, 75, 273, 125, 188, 302], 230: [294, 203, 308, 244, 110, 148, 200, 43, 15, 306, 90, 125, 167, 280, 302], 231: [79, 203, 308, 243, 110, 148, 200, 43, 75, 232, 125, 167, 280, 302], 232: [292, 216, 116, 304, 246, 175, 283, 310, 29, 108, 79, 71, 308], 233: [292, 210, 116, 304, 249, 175, 36, 21, 31, 79, 158, 163, 282, 308], 234: [292, 210, 116, 304, 249, 175, 36, 21, 37, 108, 79, 158, 163, 282, 308], 235: [292, 210, 116, 304, 249, 175, 36, 21, 38, 87, 79, 158, 163, 282, 308], 236: [294, 262, 220, 287, 304, 96, 148, 112, 35, 43, 15, 306, 90, 125, 167, 280, 302], 237: [294, 262, 220, 287, 304, 96, 148, 112, 35, 43, 15, 232, 125, 167, 280, 302], 238: [178, 195, 131, 303, 18, 75, 273, 84, 101, 9, 295, 302, 248, 106, 298, 310, 59, 275], 239: [178, 195, 131, 303, 18, 75, 273, 84, 101, 25, 302, 248, 106, 298, 310, 59, 275], 240: [178, 195, 130, 303, 89, 75, 306, 152, 84, 101, 8, 295, 284, 247, 224, 283, 310, 59, 274], 241: [178, 195, 130, 303, 89, 75, 273, 84, 101, 8, 295, 284, 247, 224, 283, 310, 59, 274], 242: [119, 135, 257, 170, 147, 305, 92, 84, 44, 8, 295, 284, 247, 225, 283, 310, 57, 277], 243: [119, 135, 257, 170, 147, 305, 92, 84, 44, 118, 284, 247, 225, 283, 310, 57, 277], 244: [119, 135, 257, 170, 147, 305, 92, 84, 44, 201, 247, 225, 283, 310, 57, 277], 245: [243, 194, 258, 18, 75, 273, 78, 101, 168, 295, 302, 238, 107, 298, 310, 197, 102], 246: [243, 194, 258, 18, 75, 273, 78, 101, 187, 302, 238, 107, 298, 310, 197, 102], 247: [178, 195, 258, 18, 75, 273, 84, 101, 9, 295, 302, 248, 106, 298, 310, 197, 102], 248: [178, 195, 258, 18, 75, 273, 84, 101, 9, 295, 302, 248, 106, 298, 310, 214], 249: [243, 229, 148, 258, 18, 75, 273, 78, 101, 187, 302, 238, 107, 298, 310, 197, 102], 250: [243, 164, 148, 259, 97, 75, 273, 125, 166, 295, 302, 238, 107, 298, 310, 136, 50], 251: [243, 164, 148, 259, 97, 75, 273, 125, 166, 295, 302, 238, 107, 289, 215], 252: [123, 228, 148, 172, 281, 303, 45, 75, 272, 78, 157, 28, 302, 241, 105, 289, 196, 49], 253: [123, 228, 148, 172, 281, 303, 45, 75, 272, 78, 157, 28, 302, 241, 105, 289, 213], 254: [242, 109, 288, 199, 160, 75, 273, 182, 166, 295, 302, 124, 107, 298, 310, 67, 81], 255: [242, 109, 288, 199, 160, 75, 273, 182, 166, 295, 302, 124, 107, 298, 310, 207], 256: [293, 264, 257, 301, 222, 147, 305, 91, 34, 99, 137, 279, 227, 283, 310, 26, 174], 257: [293, 74, 257, 301, 223, 147, 305, 91, 34, 156, 137, 278, 225, 283, 310, 56, 174], 258: [293, 264, 126, 301, 222, 147, 233, 34, 99, 137, 279, 227, 283, 310, 26, 300, 48, 79, 212], 259: [293, 264, 126, 301, 222, 147, 233, 34, 99, 149, 88, 279, 227, 283, 310, 26, 300, 48, 79, 212], 260: [77, 4, 33, 114, 296, 301, 253, 234, 84, 155, 201, 278, 191, 310, 26, 174, 79, 143, 221, 86, 121, 52, 281, 303, 60, 272, 78, 68, 295, 302], 261: [77, 4, 33, 114, 296, 301, 253, 234, 84, 155, 201, 278, 191, 310, 26, 174, 79, 143, 221, 86, 121, 52, 281, 303, 60, 272, 78, 70, 302], 262: [292, 307, 206, 24, 304, 246, 237, 289, 30, 1, 80, 79, 71, 308, 244, 304, 153, 148, 217, 15, 306, 90, 255, 166, 295, 302, 124, 299, 20, 289, 73], 263: [292, 307, 206, 24, 304, 246, 237, 289, 30, 1, 80, 79, 71, 308, 244, 304, 153, 148, 217, 85, 90, 255, 166, 295, 302, 124, 299, 20, 289, 73], 264: [292, 307, 205, 116, 285, 245, 51, 36, 27, 274, 79, 71, 308, 243, 109, 148, 200, 161, 75, 306, 90, 254, 166, 295, 302, 124, 107, 289, 260], 265: [292, 307, 205, 116, 285, 245, 51, 36, 27, 274, 79, 71, 308, 243, 109, 148, 200, 161, 75, 232, 254, 166, 295, 302, 124, 107, 289, 260], 266: [77, 265, 114, 296, 301, 253, 234, 84, 155, 201, 278, 191, 310, 26, 300, 48, 79, 143, 221, 86, 121, 58, 303, 60, 272, 78, 68, 295, 302], 267: [77, 265, 114, 296, 301, 253, 234, 84, 155, 201, 278, 191, 310, 26, 174, 79, 143, 221, 86, 121, 58, 303, 60, 272, 78, 68, 295, 302], 268: [292, 268, 116, 304, 246, 236, 36, 27, 108, 79, 71, 308, 242, 109, 148, 218, 75, 306, 90, 255, 166, 295, 302, 124, 299, 20, 289, 261], 269: [292, 268, 116, 304, 246, 236, 36, 27, 108, 79, 71, 308, 242, 109, 148, 218, 75, 232, 255, 166, 295, 302, 124, 107, 289, 261], 270: [77, 264, 257, 301, 252, 305, 92, 34, 99, 137, 278, 226, 283, 310, 26, 300, 48, 79, 211, 39, 6, 285, 250, 52, 281, 303, 46, 75, 272, 78, 154, 55, 295, 302], 271: [77, 264, 257, 301, 252, 305, 92, 34, 99, 137, 278, 226, 283, 310, 26, 174, 79, 211, 39, 6, 285, 250, 52, 281, 303, 46, 75, 272, 78, 154, 55, 295, 302], 272: [292, 216, 116, 304, 246, 175, 36, 21, 37, 108, 79, 32, 282, 308], 273: [292, 216, 116, 304, 246, 175, 36, 29, 108, 79, 71, 308], 274: [79, 143, 221, 6, 285, 121, 52, 281, 303, 47, 75, 272, 78, 68, 295, 302], 275: [79, 143, 221, 6, 285, 121, 52, 281, 303, 60, 272, 78, 68, 295, 302], 276: [79, 143, 221, 6, 285, 121, 52, 35, 47, 75, 272, 78, 68, 295, 302], 277: [79, 143, 221, 6, 285, 121, 52, 35, 47, 75, 272, 78, 154, 169, 295, 302], 278: [178, 229, 288, 258, 18, 75, 273, 184, 9, 295, 302, 248, 106, 298, 310, 197, 102], 279: [178, 229, 288, 258, 18, 75, 273, 184, 25, 302, 248, 106, 298, 310, 197, 102], 280: [23, 300, 103], 281: [26, 300, 48], 282: [124, 299, 20], 283: [239, 299, 20], 284: [79, 138, 308], 285: [79, 204, 308], 286: [137, 278, 225, 283, 310, 56, 174], 287: [201, 247, 225, 283, 310, 57, 277], 288: [238, 107, 289, 215], 289: [239, 107, 289, 266], 290: [241, 105, 289, 213], 291: [120, 231, 289, 271], 292: [240, 231, 289, 270], 293: [176, 231, 289, 146], 294: [176, 231, 289, 219], 295: [23, 277], 296: [56, 174], 297: [124, 107], 298: [239, 107], 299: [294, 262], 300: [79, 143], 301: [79, 208], 302: [79, 209], 303: [79, 212], 304: [79, 263], 305: [292, 210], 306: [292, 216], 307: [292, 268], 308: [289, 73], 309: [289, 260], 310: [289, 266]}
In [29]:
# plot the Rauzy fractal
mg.plot_list([a for a,t in la], nprec=7)
Out[29]:
In [30]:
# plot it from the substitution
s = WordMorphism(d)
s.rauzy_fractal_plot(exchange=True)
Out[30]:
In [ ]:
In [31]:
#######################################
# Rauzy fractal approximating an oval #
#######################################
mo = m.approx(15, lambda x: (pm(x).real())^2 + 2*(pm(x).imag())^2 < .4 )
mo
Out[31]:
b-adic set with b root of x^3 - x^2 - x - 1, and an automaton of 297 states and 2 letters
In [32]:
m.plot_list([mo])
Out[32]:
In [33]:
d, la = mo.substitution(get_aut=True)
print(d)
{1: [371, 340], 2: [155, 160, 162, 470], 3: [164, 464, 121], 4: [241, 18], 5: [241, 3], 6: [171, 242, 225], 7: [323, 245], 8: [313, 4], 9: [313, 5], 10: [142, 159, 7], 11: [324, 62, 212], 12: [132, 169, 422, 54], 13: [102, 155, 168, 470], 14: [333, 235, 73], 15: [248, 446, 64, 339], 16: [426, 74], 17: [299, 74], 18: [46, 464, 121], 19: [48, 157, 179], 20: [47, 157, 72], 21: [419, 313, 5], 22: [115, 464, 180], 23: [115, 464, 71], 24: [94, 66, 37], 25: [94, 66, 33], 26: [101, 156, 277, 6, 471], 27: [425, 277, 6, 471], 28: [142, 159, 114, 444], 29: [142, 159, 7, 444], 30: [299, 277, 61], 31: [302, 241, 3], 32: [302, 241, 18], 33: [397, 464, 19], 34: [439, 447, 20], 35: [395, 240, 22], 36: [396, 240, 23], 37: [223, 115, 464, 180], 38: [223, 115, 464, 71], 39: [94, 66, 240, 22], 40: [66], 41: [8], 42: [450], 43: [21], 44: [12], 45: [13], 46: [14], 47: [16], 48: [17], 49: [26], 50: [27], 51: [28], 52: [29], 53: [30], 54: [31], 55: [32], 56: [33], 57: [34], 58: [36], 59: [37], 60: [171, 242, 225, 469], 61: [171, 242, 225, 57], 62: [422, 55], 63: [1, 434], 64: [49, 404], 65: [351, 434], 66: [318, 104], 67: [238, 278, 321], 68: [208, 287, 322], 69: [48, 79], 70: [324, 244, 212], 71: [116, 35], 72: [66, 33], 73: [132, 172, 368, 422, 54], 74: [274, 171, 242, 225, 57], 75: [15, 435, 136], 76: [357, 435, 136], 77: [197, 435, 136], 78: [67, 463, 429], 79: [395, 37], 80: [396, 38], 81: [337, 243, 44], 82: [337, 243, 99], 83: [132, 186, 368, 422, 54], 84: [133, 185, 464, 95, 58], 85: [391, 277, 61], 86: [326, 158, 11], 87: [239, 158, 11], 88: [239, 158, 377], 89: [188, 368, 451], 90: [216, 464, 120], 91: [68, 465, 382], 92: [215, 465, 382], 93: [205], 94: [408], 95: [53], 96: [54], 97: [212], 98: [55], 99: [73], 100: [74], 101: [409], 102: [78], 103: [83], 104: [84], 105: [85], 106: [86], 107: [87], 108: [88], 109: [89], 110: [90], 111: [91], 112: [92], 113: [323, 42], 114: [323, 43], 115: [317, 99], 116: [312, 100], 117: [76, 283], 118: [77, 283], 119: [360, 154], 120: [53, 35], 121: [53, 36], 122: [53, 79], 123: [53, 80], 124: [236, 170, 211], 125: [236, 170, 56], 126: [364, 134, 278, 203], 127: [425, 277, 60], 128: [397, 464, 69], 129: [144, 464, 121], 130: [144, 464, 123], 131: [126, 463, 429], 132: [102], 133: [227], 134: [229], 135: [111], 136: [112], 137: [127], 138: [128], 139: [129], 140: [130], 141: [131], 142: [357, 259], 143: [366, 201, 243, 204], 144: [227, 337, 243, 44], 145: [143, 465, 382], 146: [141], 147: [145], 148: [367, 156, 279, 204], 149: [367, 156, 279, 44], 150: [148, 340, 309], 151: [149, 340, 432], 152: [147], 153: [150], 154: [151], 155: [153], 156: [154], 157: [94], 158: [135], 159: [136], 160: [152], 161: [166, 96], 162: [167, 225], 163: [166, 98], 164: [288, 99], 165: [288, 103], 166: [132, 169, 422], 167: [146, 169, 422], 168: [152, 167, 225], 169: [155, 168, 470], 170: [94, 66], 171: [132, 169], 172: [155, 168], 173: [45, 449], 174: [171, 449], 175: [15, 435], 176: [197, 435], 177: [75, 336], 178: [357, 435], 179: [66, 37], 180: [116, 39], 181: [338, 2, 421, 54], 182: [132, 2, 422, 54], 183: [28, 453], 184: [258, 432], 185: [337, 243, 161], 186: [155, 160, 162], 187: [365, 156, 279, 161], 188: [102, 155, 160, 162], 189: [367, 156, 279, 161], 190: [132, 186, 368, 451], 191: [334, 155, 160, 162, 470], 192: [102, 155, 160, 162, 470], 193: [239, 158, 247, 97], 194: [117, 446, 428], 195: [118, 446, 453], 196: [142, 159, 379], 197: [177, 446, 427], 198: [397, 464, 291], 199: [439, 447, 290], 200: [302, 241, 295], 201: [63], 202: [65], 203: [181], 204: [182], 205: [184], 206: [190], 207: [193], 208: [194], 209: [195], 210: [196], 211: [198], 212: [199], 213: [200], 214: [176, 159, 283], 215: [208, 287, 103], 216: [209, 288, 103], 217: [214, 446, 453], 218: [208, 93, 243, 204], 219: [390, 277, 375], 220: [187, 369, 432], 221: [189, 340, 432], 222: [218, 465, 382], 223: [353], 224: [209], 225: [213], 226: [263], 227: [217], 228: [219], 229: [220], 230: [221], 231: [222], 232: [409, 230], 233: [426, 277, 61], 234: [232, 277, 61], 235: [231], 236: [233], 237: [234], 238: [357, 229], 239: [264, 230], 240: [223], 241: [224], 242: [422], 243: [235], 244: [422, 8], 245: [421, 9], 246: [323, 448], 247: [324, 62], 248: [286, 159, 336], 249: [142, 159, 113], 250: [142, 159, 114], 251: [345, 432], 252: [196, 453], 253: [197, 378], 254: [133, 81, 464, 121], 255: [133, 82, 464, 121], 256: [133, 185, 464, 121], 257: [119, 279, 173, 332], 258: [119, 279, 174, 332], 259: [251], 260: [254], 261: [255], 262: [256], 263: [249, 446, 453], 264: [250, 446, 453], 265: [208, 202, 243, 322], 266: [208, 202, 243, 103], 267: [208, 202, 243, 204], 268: [265, 465, 382], 269: [266, 465, 382], 270: [267, 465, 382], 271: [268], 272: [269], 273: [270], 274: [271], 275: [272], 276: [273], 277: [274], 278: [275], 279: [276], 280: [248, 446, 64], 281: [191, 308], 282: [191, 21], 283: [281], 284: [282], 285: [285, 416, 436], 286: [280, 415, 435], 287: [65, 235], 288: [333, 235], 289: [238, 278, 246], 290: [47, 25], 291: [48, 24], 292: [133, 164, 464, 121], 293: [191, 421, 54], 294: [192, 422, 54], 295: [46, 464, 95, 58], 296: [47, 157, 40, 56], 297: [236, 157, 40, 56], 298: [51, 311, 230], 299: [52, 316, 154], 300: [53, 401, 59], 301: [105, 402, 138], 302: [106, 315, 139], 303: [107, 315, 139], 304: [108, 315, 140], 305: [350, 433, 231], 306: [207, 315, 140], 307: [210, 311, 230], 308: [419, 313, 386], 309: [237, 384, 387], 310: [439, 447, 125], 311: [453], 312: [299], 313: [302], 314: [303], 315: [304], 316: [430], 317: [305], 318: [306], 319: [308], 320: [292], 321: [293], 322: [294], 323: [191], 324: [192], 325: [310], 326: [183, 230], 327: [252, 230], 328: [253, 283], 329: [370, 340, 431], 330: [289, 463, 452], 331: [437, 464, 300], 332: [325], 333: [329], 334: [330], 335: [331], 336: [323, 319], 337: [333], 338: [334], 339: [335], 340: [332], 341: [175, 159, 336], 342: [178, 159, 114], 343: [29, 453], 344: [29, 430], 345: [365, 156, 279, 161, 363], 346: [226, 156, 277, 163, 470], 347: [328, 446, 428], 348: [328, 446, 453], 349: [439, 447, 297], 350: [257], 351: [258], 352: [347], 353: [348], 354: [349], 355: [178, 159, 283], 356: [178, 159, 284], 357: [341, 446, 427], 358: [342, 446, 453], 359: [355, 446, 428], 360: [356, 446, 453], 361: [326, 158, 374], 362: [326, 158, 376], 363: [354], 364: [357], 365: [358], 366: [359], 367: [360], 368: [470], 369: [363], 370: [119, 279, 173], 371: [119, 279, 174], 372: [224, 164, 464, 121], 373: [224, 165, 464, 120], 374: [45, 242, 98, 57], 375: [45, 242, 225, 57], 376: [324, 242, 41, 57], 377: [324, 242, 98, 212], 378: [388, 434, 112], 379: [323, 43, 442], 380: [407, 315, 260], 381: [423, 313, 386], 382: [236, 402, 414], 383: [236, 401, 211], 384: [380], 385: [381], 386: [372], 387: [373], 388: [345], 389: [346], 390: [343, 230], 391: [344, 154], 392: [437, 447, 301], 393: [392], 394: [393], 395: [408, 318, 104], 396: [408, 318, 262], 397: [353, 317, 99], 398: [353, 317, 103], 399: [424, 314, 261], 400: [424, 314, 320], 401: [395], 402: [396], 403: [399], 404: [400], 405: [326, 158, 70], 406: [327, 158, 70], 407: [405], 408: [406], 409: [10, 446, 453], 410: [10, 446, 430], 411: [437, 464, 122], 412: [398, 464, 122], 413: [411], 414: [412], 415: [339], 416: [394], 417: [298, 158, 374], 418: [307, 158, 374], 419: [417], 420: [418], 421: [419], 422: [420], 423: [361], 424: [362], 425: [409, 154], 426: [410, 154], 427: [49, 404, 335], 428: [49, 404, 413], 429: [137, 403, 413], 430: [137, 404, 413], 431: [228, 384, 110], 432: [228, 384, 387], 433: [431], 434: [432], 435: [388, 434], 436: [389, 385], 437: [352, 317, 103], 438: [352, 317, 109], 439: [352, 317, 206], 440: [437, 447, 383], 441: [438, 447, 383], 442: [440], 443: [441], 444: [442], 445: [443], 446: [444], 447: [445], 448: [421, 54], 449: [422, 54], 450: [419, 31], 451: [420, 31], 452: [50, 403, 413], 453: [50, 404, 413], 454: [437, 447, 124], 455: [438, 447, 124], 456: [439, 447, 124], 457: [454], 458: [455], 459: [456], 460: [457], 461: [458], 462: [459], 463: [460], 464: [461], 465: [462], 466: [438, 447, 296], 467: [439, 447, 296], 468: [466], 469: [467], 470: [468], 471: [469]}
In [34]:
print(la)
[(DetAutomaton with 30 states and an alphabet of 2 letters, b^2), (DetAutomaton with 35 states and an alphabet of 2 letters, b^2 + 1), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2), (DetAutomaton with 36 states and an alphabet of 2 letters, b^2), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2), (DetAutomaton with 17 states and an alphabet of 2 letters, b^2), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 35 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 31 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 32 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 31 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 33 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 17 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 19 states and an alphabet of 2 letters, b), (DetAutomaton with 19 states and an alphabet of 2 letters, b), (DetAutomaton with 13 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 25 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 34 states and an alphabet of 2 letters, b^2), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2), (DetAutomaton with 16 states and an alphabet of 2 letters, b^2), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2), (DetAutomaton with 33 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 32 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 21 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2), (DetAutomaton with 33 states and an alphabet of 2 letters, b^2), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 14 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 33 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 17 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 13 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 17 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 21 states and an alphabet of 2 letters, b), (DetAutomaton with 29 states and an alphabet of 2 letters, b), (DetAutomaton with 24 states and an alphabet of 2 letters, b), (DetAutomaton with 25 states and an alphabet of 2 letters, b), (DetAutomaton with 16 states and an alphabet of 2 letters, b), (DetAutomaton with 20 states and an alphabet of 2 letters, b), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2), (DetAutomaton with 33 states and an alphabet of 2 letters, b^2), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2), (DetAutomaton with 12 states and an alphabet of 2 letters, b^2), (DetAutomaton with 16 states and an alphabet of 2 letters, b^2), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2), (DetAutomaton with 17 states and an alphabet of 2 letters, b^2), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2), (DetAutomaton with 42 states and an alphabet of 2 letters, b^2), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 13 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 46 states and an alphabet of 2 letters, b), (DetAutomaton with 18 states and an alphabet of 2 letters, b), (DetAutomaton with 20 states and an alphabet of 2 letters, b), (DetAutomaton with 17 states and an alphabet of 2 letters, b), (DetAutomaton with 28 states and an alphabet of 2 letters, b), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2), (DetAutomaton with 12 states and an alphabet of 2 letters, b^2), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2), (DetAutomaton with 17 states and an alphabet of 2 letters, b^2), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 22 states and an alphabet of 2 letters, b), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 18 states and an alphabet of 2 letters, b), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2), (DetAutomaton with 17 states and an alphabet of 2 letters, b), (DetAutomaton with 34 states and an alphabet of 2 letters, b), (DetAutomaton with 24 states and an alphabet of 2 letters, 1), (DetAutomaton with 16 states and an alphabet of 2 letters, 1), (DetAutomaton with 33 states and an alphabet of 2 letters, 1), (DetAutomaton with 28 states and an alphabet of 2 letters, 1), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2), (DetAutomaton with 31 states and an alphabet of 2 letters, b^2), (DetAutomaton with 12 states and an alphabet of 2 letters, b^2), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2), (DetAutomaton with 31 states and an alphabet of 2 letters, b^2 + 1), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + 1), (DetAutomaton with 31 states and an alphabet of 2 letters, b^2 + 1), (DetAutomaton with 39 states and an alphabet of 2 letters, b^2 + 1), (DetAutomaton with 30 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 36 states and an alphabet of 2 letters, b^2), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2), (DetAutomaton with 37 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 34 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 16 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 33 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 36 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 17 states and an alphabet of 2 letters, b^2), (DetAutomaton with 32 states and an alphabet of 2 letters, b^2), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 33 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 25 states and an alphabet of 2 letters, b), (DetAutomaton with 35 states and an alphabet of 2 letters, b), (DetAutomaton with 32 states and an alphabet of 2 letters, b^2), (DetAutomaton with 35 states and an alphabet of 2 letters, b^2), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2), (DetAutomaton with 17 states and an alphabet of 2 letters, b^2), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 17 states and an alphabet of 2 letters, b), (DetAutomaton with 30 states and an alphabet of 2 letters, b), (DetAutomaton with 17 states and an alphabet of 2 letters, b), (DetAutomaton with 12 states and an alphabet of 2 letters, b^2), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 24 states and an alphabet of 2 letters, b), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2), (DetAutomaton with 31 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 25 states and an alphabet of 2 letters, 1), (DetAutomaton with 23 states and an alphabet of 2 letters, 1), (DetAutomaton with 20 states and an alphabet of 2 letters, 1), (DetAutomaton with 28 states and an alphabet of 2 letters, 1), (DetAutomaton with 20 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 20 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 32 states and an alphabet of 2 letters, b^2), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 14 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2), (DetAutomaton with 13 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2), (DetAutomaton with 20 states and an alphabet of 2 letters, b), (DetAutomaton with 24 states and an alphabet of 2 letters, b), (DetAutomaton with 19 states and an alphabet of 2 letters, b), (DetAutomaton with 23 states and an alphabet of 2 letters, 1), (DetAutomaton with 23 states and an alphabet of 2 letters, 1), (DetAutomaton with 18 states and an alphabet of 2 letters, 1), (DetAutomaton with 33 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 33 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2), (DetAutomaton with 32 states and an alphabet of 2 letters, b^2), (DetAutomaton with 1 state and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 32 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 30 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 30 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 34 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 11 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 15 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 16 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 16 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 17 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 19 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 28 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 16 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 12 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 17 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 20 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 12 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 21 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2), (DetAutomaton with 33 states and an alphabet of 2 letters, b^2), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2), (DetAutomaton with 36 states and an alphabet of 2 letters, b^2), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 20 states and an alphabet of 2 letters, b), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2), (DetAutomaton with 24 states and an alphabet of 2 letters, b), (DetAutomaton with 34 states and an alphabet of 2 letters, b), (DetAutomaton with 25 states and an alphabet of 2 letters, b), (DetAutomaton with 27 states and an alphabet of 2 letters, 1), (DetAutomaton with 33 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 8 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2), (DetAutomaton with 34 states and an alphabet of 2 letters, b^2), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 32 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 29 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 12 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 21 states and an alphabet of 2 letters, b), (DetAutomaton with 32 states and an alphabet of 2 letters, b^2), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2), (DetAutomaton with 15 states and an alphabet of 2 letters, 1), (DetAutomaton with 20 states and an alphabet of 2 letters, 1), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 31 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 10 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 18 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 15 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 6 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 26 states and an alphabet of 2 letters, b^2), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2), (DetAutomaton with 7 states and an alphabet of 2 letters, b^2), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 17 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 10 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 9 states and an alphabet of 2 letters, b^2), (DetAutomaton with 5 states and an alphabet of 2 letters, b), (DetAutomaton with 35 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 17 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 32 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 16 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 20 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 19 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 16 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2), (DetAutomaton with 15 states and an alphabet of 2 letters, b^2), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 22 states and an alphabet of 2 letters, b^2), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2), (DetAutomaton with 18 states and an alphabet of 2 letters, 1), (DetAutomaton with 4 states and an alphabet of 2 letters, 1), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 17 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2), (DetAutomaton with 16 states and an alphabet of 2 letters, b^2), (DetAutomaton with 30 states and an alphabet of 2 letters, b), (DetAutomaton with 22 states and an alphabet of 2 letters, b), (DetAutomaton with 11 states and an alphabet of 2 letters, b^2), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 27 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 22 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 29 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 30 states and an alphabet of 2 letters, b^2), (DetAutomaton with 6 states and an alphabet of 2 letters, b^2), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 17 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 23 states and an alphabet of 2 letters, b^2), (DetAutomaton with 16 states and an alphabet of 2 letters, b^2), (DetAutomaton with 25 states and an alphabet of 2 letters, b), (DetAutomaton with 12 states and an alphabet of 2 letters, b), (DetAutomaton with 27 states and an alphabet of 2 letters, 1), (DetAutomaton with 11 states and an alphabet of 2 letters, 1), (DetAutomaton with 21 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 18 states and an alphabet of 2 letters, b + 1), (DetAutomaton with 17 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 19 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 28 states and an alphabet of 2 letters, b^2 + b), (DetAutomaton with 25 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 17 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 24 states and an alphabet of 2 letters, b^2), (DetAutomaton with 16 states and an alphabet of 2 letters, b^2), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2), (DetAutomaton with 20 states and an alphabet of 2 letters, b), (DetAutomaton with 12 states and an alphabet of 2 letters, b), (DetAutomaton with 16 states and an alphabet of 2 letters, b), (DetAutomaton with 19 states and an alphabet of 2 letters, 1), (DetAutomaton with 11 states and an alphabet of 2 letters, 1), (DetAutomaton with 15 states and an alphabet of 2 letters, 1), (DetAutomaton with 16 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 21 states and an alphabet of 2 letters, b^2 + b + 1), (DetAutomaton with 15 states and an alphabet of 2 letters, b^2), (DetAutomaton with 20 states and an alphabet of 2 letters, b^2), (DetAutomaton with 11 states and an alphabet of 2 letters, b), (DetAutomaton with 22 states and an alphabet of 2 letters, b)]
In [35]:
# plot the Rauzy fractal with min background
m.plot_list([a for a,t in la])
Out[35]:
In [36]:
# plot the Rauzy fractal after exchange with min background
m.plot_list([BetaAdicSet(m.b, a).proj(m, t) for a,t in la])
Out[36]:
In [37]:
# check
s = WordMorphism(d)
s.rauzy_fractal_plot()
Out[37]:
In [ ]: