def display_leech_vector(x):
"""Display a vector in the Leech lattice mod 2
Here parameter ``x`` is a vector in the Leech lattice mod 2
in Leech lattice encoding.
"""
gcode = PLoop(x >> 12)
bl = gcode.bit_list
print("GCode:\n", bl)
if len(bl) == 16:
l = [x for x in range(24) if not x in bl]
pos = bl[0]
elif len(gcode):
pos = bl[0]
else:
pos = 0
cocode = Cocode(x) + gcode.theta()
print("Cocode:", cocode.syndrome_list(pos))
def test_Parker_loop():
print("\nTesting operation on Parker loop")
for i in range(200):
# Test power map, inveriosn, sign, theta, and conversion to GCode
n1 = randint(0, 0x1fff)
p1 = PLoop(n1)
assert p1.ord == n1 == p1.gcode + 0x1000 * (1 - p1.sign) / 2
if (i < 2):
print("Testing Parker loop element", p1, ", GCode = ", GCode(p1))
assert len(p1) == mat24.gcode_weight(n1) << 2
assert p1.theta() == Cocode(mat24.ploop_theta(n1))
assert p1 / 4 == p1.theta(p1) == Parity(mat24.ploop_cocycle(n1, n1))
assert p1**2 == PLoopZ(p1 / 4) == (-PLoopZ())**(p1 / 4)
assert p1**(-5) == PLoopZ(p1 / 4) * p1 == (-1)**(p1 / 4) * p1 == 1 / p1
assert (1 / p1).ord ^ n1 == (mat24.gcode_weight(n1) & 1) << 12
assert -1 / p1 == -p1**3 == -(1 / p1)
assert p1 * (-1 / p1) == PLoopZ(1) == -PLoopZ()
assert abs(p1).ord == GCode(p1).ord == p1.ord & 0xfff
assert p1 != GCode(p1)
assert +p1 == 1 * p1 == p1 * 1 == p1
assert p1 != -p1 and p1 != ~p1
assert (-p1).ord == p1.ord ^ 0x1000
assert (~p1).ord == p1.ord ^ 0x800
s, o, p1_pos = p1.split()
assert s == (p1.ord >> 12) & 1
assert o == (p1.ord >> 11) & 1
assert p1.sign == (-1)**s
assert p1_pos.ord == p1.ord & 0x7ff
assert PLoopZ(s, o) * p1_pos == p1
assert PLoopZ(0, o) * p1_pos == abs(p1)
assert PLoopZ(s + 1, o) * p1_pos == -p1
assert -p1 == -1 * p1 == p1 * -1 == p1 / -1 == -1 / p1**-5
assert PLoopZ(s, 1 + o) * p1_pos == ~p1
assert PLoopZ(1 + s, 1 + o) * p1_pos == ~-p1 == -~p1 == ~p1 / -1
assert 2 * p1 == GCode(0) == -2 * GCode(p1)
assert -13 * p1 == GCode(p1) == 7 * GCode(p1)
if len(p1) & 7 == 0:
assert p1**Parity(1) == p1
assert p1**Parity(0) == PLoop(0)
else:
with pytest.raises(ValueError):
p1**Parity(randint(0, 1))
assert p1.bit_list == mat24.gcode_to_bit_list(p1.value & 0xfff)
assert p1.bit_list == GcVector(p1).bit_list
assert p1.bit_list == GCode(p1).bit_list
assert PLoop(GcVector(p1) + 0) == PLoop(GCode(p1) + 0) == abs(p1)
assert p1 + 0 == 0 + p1 == GCode(p1) + 0 == 0 + GCode(p1)
assert Cocode(GcVector(p1)) == Cocode(0)
assert p1 / 2 == Parity(0)
# Test Parker loop multiplication and commutator
n2 = randint(0, 0x1fff)
p2 = PLoop(n2)
coc = Cocode(mat24.ploop_cap(n1, n2))
if (i < 1):
print("Intersection with", p2, "is", coc)
p2inv = p2**-1
assert p1 * p2 == PLoop(mat24.mul_ploop(p1.ord, p2.ord))
assert p1 / p2 == p1 * p2**(-1)
assert p1 + p2 == p1 - p2 == GCode(p1 * p2) == GCode(n1 ^ n2)
assert (p1 * p2) / (p2 * p1) == PLoopZ((p1 & p2) / 2)
assert p1 & p2 == coc
assert p1.theta() == Cocode(mat24.ploop_theta(p1.ord))
assert p1.theta(p2) == Parity(mat24.ploop_cocycle(p1.ord, p2.ord))
assert (p1 & p2) / 2 == p1.theta(p2) + p2.theta(p1)
assert p1 & p2 == p1.theta() + p2.theta() + (p1 + p2).theta()
assert int((p1 & p2) / 2) == mat24.ploop_comm(p1.ord, p2.ord)
assert GcVector(p1 & p2) == GcVector(p1) & GcVector(p2)
assert ~GcVector(p1 & p2) == ~GcVector(p1) | ~GcVector(p2)
assert Cocode(GcVector(p1 & p2)) == p1 & p2
# Test associator
n3 = randint(0, 0x1fff)
p3 = PLoop(n3)
assert p1 * p2 * p3 / (p1 * (p2 * p3)) == PLoopZ(p1 & p2 & p3)
assert int(p1 & p2 & p3) == mat24.ploop_assoc(p1.ord, p2.ord, p3.ord)
i = randint(-1000, 1000)
par = Parity(i)
s3 = ((p3 & p1) & p2) + par
assert s3 == ((p3 & p1) & p2) + par
assert s3 == i + (p1 & (p2 & p3))
assert s3 == par + (p1 & (p2 & p3))
# Test some operations leading to a TypeError
with pytest.raises(TypeError):
p1 & p2 & p3 & p1
with pytest.raises(TypeError):
coc & coc
with pytest.raises(TypeError):
GCode(p1) * GCode(p2)
with pytest.raises(TypeError):
1 / GCode(p2)
with pytest.raises(ValueError):
coc / 4
with pytest.raises(TypeError):
p1 * coc
with pytest.raises(TypeError):
coc * p1
types = [GcVector, GCode, Cocode, PLoop]
for type_ in types:
with pytest.raises(TypeError):
int(type_(0))
print("Parker Loop test passed")
def xsp2xco1_xsp2(v):
pl = PLoop(v >> 12)
coc = Cocode(v)
return Xsp2_Co1([("x", v >> 12), pl.theta(), coc])