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# load the package badic (you can install it with "sage -pip install badic [--user]")
from badic import *
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# union of Rauzy fractals for the same Pisot number
# Tribonnacci and flipped Tribonnacci
s = WordMorphism('1->12,2->13,3->1')
t = WordMorphism('1->12,2->31,3->1')
a = DumontThomas(s).mirror().unshift([0,0])
b = DumontThomas(t).mirror().unshift([1,0,0,0,0])
m = a.union(b)
m.plot()
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# find a substitution whose Rauzy fractal is this beta-adic set
d = m.substitution()
s = WordMorphism(d)
print(s)
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# check
s.rauzy_fractal_plot()
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#intersection of two Rauzy fractals with same Pisot number
m = DumontThomas(WordMorphism('1->12,2->31,3->1')).mirror() # flipped Tribonnacci
m2 = DumontThomas(WordMorphism('1->12,2->13,3->1')).mirror() # Tribonnacci
m3 = m.intersection(m2) # compute the intersection of the two beta-adic set
m3.plot() # plot it
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# compute a substitution whose Rauzy fractal is this beta-adic set
%time d = m3.substitution()
s = WordMorphism(d)
print(s)
s.rauzy_fractal_plot()
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# complementary of Rauzy fractals for the same Pisot number
# Tribonnacci minus flipped Tribonnacci
s = WordMorphism('1->12,2->13,3->1')
t = WordMorphism('1->12,2->31,3->1')
a = DumontThomas(s).mirror()
b = DumontThomas(t).mirror().unshift([1,0,0,0,0])
m = b.complementary(a)
m.plot()
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# compute a substitution whose Rauzy fractal is this beta-adic set
%time d = m.substitution()
s = WordMorphism(d)
print(s)
s.rauzy_fractal_plot()
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# take Tribonnacci
m = DumontThomas(WordMorphism('a->ab,b->ac,c->a')).mirror()
# put a hole
m = m.unshift([1,0,0,0]).complementary(m); m
m.plot()
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# compute a substitution whose Rauzy fractal is this beta-adic set
d = m.substitution()
s = WordMorphism(d)
print(s)
s.rauzy_fractal_plot()
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# countable union of flipped Tribonnacci
s = WordMorphism('a->ab,b->ca,c->a')
m = DumontThomas(s).mirror()
m = BetaAdicSet(x^3-x^2-x-1, dag.AnyWord([0]).concat(dag.Word([1])).concat(dag.AnyWord([0]).concat(dag.Word([1,0,0,0,0]))).concat(m.a))
m.plot()
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# compute a substitution whose Rauzy fractal is this countable union
d = m.substitution()
s = WordMorphism(d)
print(s)
s.rauzy_fractal_plot()
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# Hokkaido
m = DumontThomas(WordMorphism('a->ab,b->c,c->d,d->e,e->a')).mirror()
m.plot()
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# draw something
m = m.user_draw()
m.plot()
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%time d = m.substitution()
s = WordMorphism(d)
print(s)
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s.rauzy_fractal_plot()
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