def test_yang_baxter():
from huygens.box import Box, HBox
from huygens.diagram import VWire, Braid
Box.DEBUG = False
Id = VWire
scale = 2.0
w = 1.5 * scale
h = 0.5 * scale
s12 = lambda: Braid(min_width=w, min_height=h) @ Id(min_height=h,
min_width=h)
s23 = lambda: Id(min_height=h, min_width=h) @ Braid(min_width=w,
min_height=h)
lhs = s12() * s23() * s12()
#lhs = lhs @ Braid()
rhs = s23() * s12() * s23()
box = HBox([lhs, "$=$", rhs], align="center")
yield box, "yang-baxter"
def test_braid_3():
from huygens.box import Box, HBox
from huygens.diagram import VWire, Braid
Box.DEBUG = False
Id = VWire
scale = 1.0
w = 0.8 * scale
h = 0.5 * scale
s1 = lambda: Braid(min_width=w, min_height=h) @ Id(min_height=h,
min_width=h)
s2 = lambda: Id(min_height=h, min_width=h) @ Braid(min_width=w,
min_height=h)
from operator import mul
from functools import reduce
word = [[s1, s2][i % 2]() for i in range(6)]
box = reduce(mul, word)
box = HBox(["$Z =$", box], align="center")
yield box, "braid-Z"
def XXXtest_braid():
from random import shuffle, seed, randint
from operator import matmul
from functools import reduce
seed(1)
scale = 0.5
w = 1.4 * scale
h = 1.8 * scale
Id = lambda: VWire(min_height=0.5, min_width=0.5)
Swap = lambda inverse: Braid(
inverse=inverse, min_width=w, min_height=h, space=0.7)
box = None
m, n = 4, 4
k = 2 * m + n
for count in range(6):
items = [Swap(randint(0, 1))
for k in range(m)] + [Id() for k in range(n)]
shuffle(items)
row = reduce(matmul, items)
if box is None:
box = row
else:
box = box * row
#box = Id() @ box
lhs = reduce(matmul, [Id() for i in range(k)])
box = lhs @ box
rels = [(i, 2 * k - i - 1) for i in range(k)]
#rels = [(i, i+k) for i in range(k)]
rel = Relation(0, 2 * k, botbot=rels, weight=200.0)
box = rel * box
rels = [(i, 2 * k - i - 1) for i in range(k)]
rel = Relation(2 * k, 0, toptop=rels, weight=200.0)
box = box * rel
#rect = RectBox(box, bg=color.rgb(0.9, 0.9, 0.3, 0.6))
Box.DEBUG = False
cvs = canvas.canvas()
#cvs.append(trafo.rotate(pi/2))
system = box.layout(cvs)
def rectbox(box):
x = system[box.llx]
y = system[box.lly]
width = system[box.width]
height = system[box.height]
return x, y, width, height
def fillbox(box, st):
rect = rectbox(box)
p = path.rect(*rect)
cvs.fill(p, st)
#fillbox(box, [color.rgb(0.9, 0.8, 0.5)])
sub = box[0][1][1]
x = 0.5 * (system[box.llx] + system[box.urx])
y = system[sub.lly]
width = system[box.urx] - x
height = system[sub.ury] - y
p = path.rect(x, y, width, height)
cvs.fill(p, [color.rgb(0.9, 0.9, 0.6)])
cvs.stroke(p, [style.linewidth.thick])
cvs.append(style.linewidth.THICk)
#cvs.append(color.rgb(0.2,0.5,0.2))
box.render(cvs)
cvs.append(style.linewidth.thick)
cvs.append(color.rgb(0.9, 0.9, 0.9))
box.render(cvs)
#cvs.writePDFfile("test_diagram.pdf")
yield cvs
def test_braid():
from random import shuffle, seed, randint
from operator import matmul
from functools import reduce
from huygens import canvas, color, style, path
from huygens.box import Box, HBox
from huygens.diagram import VWire, Braid, Relation
seed(1)
scale = 0.3
w = 1.4 * scale
h = 1.8 * scale
Id = lambda: VWire(min_height=scale, min_width=scale)
Swap = lambda inverse: Braid(
inverse=inverse, min_width=w, min_height=h, space=0.5)
box = None
m, n = 3, 3
k = 2 * m + n
for count in range(3):
items = [Swap(randint(0, 1))
for k in range(m)] + [Id() for k in range(n)]
shuffle(items)
row = reduce(matmul, items)
if box is None:
box = row
else:
box = box * row
# This is what the `box` looks like now:
yield box, "braid-strands"
# Now we take the closure of this braid:
#box = Id() @ box
lhs = reduce(matmul, [Id() for i in range(k)])
box = lhs @ box
rels = [(i, 2 * k - i - 1) for i in range(k)]
#rels = [(i, i+k) for i in range(k)]
rel = Relation(0, 2 * k, botbot=rels, weight=200.0)
box = rel * box
rels = [(i, 2 * k - i - 1) for i in range(k)]
rel = Relation(2 * k, 0, toptop=rels, weight=200.0)
box = box * rel
yield box
# Draw this now with some more fancy tricks.
cvs = canvas.canvas()
system = box.layout(cvs)
sub = box[0][1][1]
x = 0.5 * (box.llx + box.urx)
y = sub.lly
width = box.urx - x
height = sub.ury - y
p = path.rect(x, y, width, height)
cvs.fill(p, [color.rgb(0.9, 0.9, 0.6)])
cvs.stroke(p, [style.linewidth.thick])
system.refresh() # refresh for a new render
cvs.append(style.linewidth.THICk)
#cvs.append(color.rgb(0.2,0.5,0.2))
box.render(cvs)
cvs.append(style.linewidth.thick)
cvs.append(color.rgb(0.9, 0.0, 0.0))
box.render(cvs)
#cvs.writePDFfile("test_diagram.pdf")
yield cvs