def main():
if argv.code == "RM14":
s = """
1111111111111111
.1.1.1.1.1.1.1.1
..11..11..11..11
....1111....1111
........11111111
"""
else:
s = argv.get("G")
if s is None:
G = parse("111")
#G = parse("1. .1")
#G = parse("11. .11")
#G = parse("1.. .11")
else:
G = parse(s)
print(G)
w1 = genus_enum1(G)
w2 = genus_enum2(G)
#print(w1)
print("w1 =")
print(w1.flatstr())
#print(w2)
print("w2 =")
print(w2.flatstr())
items = get_phi_2(w2)
#for w in items:
# print("\t", w.flatstr())
w = sum(items)
print("sum(items) =")
print(w.flatstr())
print("diff:")
print((w2 - w).flatstr())
w3 = genus_enum3(G)
print("w3 =")
print(w3.flatstr())
#for w in items:
# print("\t", w.flatstr(), w.flatstr()==w2.flatstr())
items = get_phi_3(w3, w2)
#w = sum(items)
#print("diff:")
#print((w3 - w).flatstr())
if 0:
w4 = genus_enum4(G)
print("w4 =")
print(w4.flatstr())
#for w in items:
# print("\t", w.flatstr(), w.flatstr()==w2.flatstr())
items = get_phi_4(w4, w3)
def test_hamming():
G = parse("""
1....111
.1..1.11
..1.11.1
...1111.
""")
assert strong_morthogonal(G, 2)
def test():
G = parse("11 ..")
test_enum(G)
G = parse("11. .11")
#test_enum(G, verbose=True)
#print(p.flatstr())
#return
#G = parse("11.. .11. 1..1")
#test_enum(G)
for m in range(1, 5):
for n in range(m, 6):
for G in all_codes(m, n):
test_enum(G)
print("OK")
def parse(self, decl):
A = solve.parse(decl)
decl = decl.replace('.', '0')
rows = decl.split()
rows = [l.strip() for l in rows if l.strip()]
promote = self.ring.promote
rows = [list(promote(int(c)) for c in l) for l in rows]
assert rows
n = len(rows[0])
for row in rows:
assert len(row) == n, "rows have varying lengths"
A = numpy.array(rows, dtype=object)
m, n = A.shape
src = Space(self.ring, n)
tgt = Space(self.ring, m)
return Lin(tgt, src, A)
def main_torus():
n = 8
# ZZZZZZZZ|XXXXXXXX
# 12345678|12345678
H = parse("""
111..1..|........
1..1....|1.1.....
........|11.11...
.1..1...|.1...1..
..1...1.|...1..1.
...11.11|........
.....1.1|....1..1
........|..1..111
""".replace("|", ""))
print()
print("H=")
print(shortstr(H))
F = symplectic(n)
C = dot2(H, dot2(F, H.transpose()))
for i in range(n):
for j in range(i + 1, n):
if C[i, j]:
print("fail:", i + 1, j + 1)
print(rank(H))
H = linear_independent(H)
print("H=")
print(shortstr(H))
HF = dot2(H, F)
K = array2(find_kernel(HF))
print("K=")
print(shortstr(K))
HK = numpy.concatenate((H, K))
L = linear_independent(HK)
print()
print(shortstr(L))
def test_main():
for ring in [element.Q, element.FiniteField(2), element.FiniteField(7)]:
#for ring in [element.FiniteField(2)]:
cx = Assembly.build_tetrahedron(ring)
chain = cx.get_chain()
#chain.dump()
test_chain(chain)
M = parse("""
1.1..1
11.1..
.11.1.
...111
""")
chain = Chain.from_array(M, ring)
test_chain(chain)
#cx = Assembly.build_torus(ring, 2, 2)
cx = Assembly.build_surface(ring, (0, 0), (2, 2))
chain = cx.get_chain()
test_chain(chain)
continue
x, y = layout[key]
cvs.stroke(path.circle(x, y, r), st_thick + [orange])
# ---------------------------------------------------------
ring = element.FiniteField(2)
if 0:
# ------------------------------------
M = parse("""
11.....
1.1....
.1.11..
..11.1.
....1.1
.....11
""")
#print(M)
M = numpy.array([[1, 1, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0],
[0, 1, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 1, 0],
[0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 1, 1]])
chain = Chain.fromnumpy(M, ring)
verts = chain.cells[0]
for i, v in enumerate(verts):
x = (i // 2)
y = -(i % 2)
v.pos = x, y
def parse(self, decl):
ring = self.ring
A = solve.parse(decl)
B = self.zeros(*A.shape)
B = B + A
return B
def test_dual():
from vec import Space, Hom, Map
import element
ring = element.Z
#ring = element.Q
one = ring.one
space = Space(2, ring)
hom = Hom(space, space)
I = Map.from_array([[1, 0], [0, 1]], hom)
X = Map.from_array([[0, 1], [1, 0]], hom)
Z = Map.from_array([[1, 0], [0, -1]], hom)
assert X+X == (2*X)
assert X*Z == -Z*X
assert (X@X) * (Z@Z) == (Z@Z) * (X@X)
assert (I@X@X) * (I@Z@Z) == (I@Z@Z) * (I@X@X)
if argv.code == "repitition":
G = parse("111")
H = parse("""
11.
.11""")
elif argv.code == "steane":
G = parse("""
1111...
.1.11.1
..11.11
""")
else:
return
code = Code(G)
if argv.dual:
code = code.get_dual()
dual = code.get_dual()
code.dump()
#W = lambda A, B : (A@A@A + B@B@B)
#WD = lambda A, B : (A@A@A + B@B@A + B@A@B + A@B@B)
W = code.tensor_enum
WD = dual.tensor_enum
a = 2**len(code.G)
b = 2**len(dual.G)
A = WD(I, X)
B = W(I, Z)
assert A*B == B*A
AA = W(I+X, I-X)
BB = WD(I+Z, I-Z)
assert AA == a*A
assert BB == b*B
assert AA*BB == a*b*A*B
#print(W(I+X, I-X))
#print(WD(I, X))
#print(W(I, Z))
src = Space(2, ring)
tgt = Space(3, ring)
hom = Hom(src, tgt)
A = Map.from_array([
[1, 2],
[5, 6],
[7, 8]], hom)
B = Map.from_array([
[7, 2],
[6, 3],
[5, 4]], hom)
assert W(A+B, A-B) == a*WD(A, B)
assert WD(A+B, A-B) == b*W(A, B)
def get_code():
name = argv.get("code")
code = None
if name == "toric":
G = parse("""
1.1.....
.1...1..
11.11...
.111..1.
1...11.1
""") # l=2 toric code X logops + X stabs
elif name == "toric3":
G = parse("""
.....1.....1.....1
............1.1.1.
.111..........1...
...111..........1.
1.....11...1......
..1....111........
....1....111......
......1.....11...1
........1....111..
..........1....111
""") # l=3 toric code X logops + X stabs
elif name == "steane":
G = parse("""
1111111
1111...
.1.11.1
..11.11
""")
elif name == "haah":
# triorthogonal matrix
G = parse("""
1111111.......
.......1111111
1.1.1.11.1.1.1
.11..11.11..11
...1111...1111
""")
G = parse("""
1.1.1.11.1.1.1
.11..11.11..11
...1111...1111
""")
G = parse("""
..............1111111111111111
......11111111........11111111
..1111....1111....1111....1111
.1..11..11..11..11..11..11..11
11.1.1.1.1.1.1.1.1.1.1.1.1.1.1
""")
elif name == "rm":
r = argv.get("r", 1)
m = argv.get("m", 3)
code = reed_muller(r, m)
if argv.puncture:
code = code.puncture(0)
elif name == "rand":
n = argv.get("n", 8)
m = argv.get("m", 4)
G = rand2(m, n)
code = Code(G)
else:
assert 0, "no code chosen"
if code is None:
code = Code(G)
if argv.dual:
code = code.get_dual()
return code
def search_extend():
# Extend the checks of a random code to make it triorthogonal.
# Based on the search function above.
verbose = argv.get("verbose")
m = argv.get("m", 6)
n = argv.get("n", m+2)
k = argv.get("k") # odd _numbered rows ( logical operators)
code = argv.get("code", "rand")
if code == "rand":
while 1:
G0 = rand2(m, n)
counts = G0.sum(0)
if min(counts)==2 and rank(G0) == m:
cols = set()
for i in range(n):
cols.add(tuple(G0[:, i]))
if len(cols) == n: # no repeated cols
break
elif code == "toric":
G0 = parse("""
11.11...
.111..1.
1...11.1
""") # l=2 toric code X logops + X stabs
l = argv.get("l", 3)
G0 = build_toric(l)
m, n = G0.shape
else:
return
code = Code(G0, check=False)
print(shortstr(G0))
print("is_triorthogonal:", code.is_triorthogonal())
# these are the variables N_x
xs = list(cross([(0, 1)]*m))
N = len(xs)
lookup = {}
for i, x in enumerate(xs):
lookup[x] = i
lhs = []
rhs = []
taken = set()
for i in range(n):
x = G0[:, i]
idx = lookup[tuple(x)]
assert idx not in taken
taken.add(idx)
if verbose:
for idx in range(N):
print(idx, xs[idx], "*" if idx in taken else "")
for idx in taken:
v = zeros2(N)
v[idx] = 1
lhs.append(v)
rhs.append(1)
# bi-orthogonality
for a in range(m):
for b in range(a+1, m):
v = zeros2(N)
for i, x in enumerate(xs):
if x[a] == x[b] == 1:
v[i] += 1
assert v.sum()
lhs.append(v)
rhs.append(0)
# tri-orthogonality
for a in range(m):
for b in range(a+1, m):
for c in range(b+1, m):
v = zeros2(N)
for i, x in enumerate(xs):
if x[a] == x[b] == x[c] == 1:
v[i] += 1
assert v.sum()
lhs.append(v)
rhs.append(0)
# dissallow columns with weight <= 1
for i, x in enumerate(xs):
if sum(x)<=1:
v = zeros2(N)
v[i] = 1
lhs.append(v)
rhs.append(0)
if k is not None:
# constrain to k _number of odd-weight rows
assert 0<=k<m
for a in range(m):
v = zeros2(N)
for i, x in enumerate(xs):
if x[a] == 1:
v[i] = 1
lhs.append(v)
if a<k:
rhs.append(1)
else:
rhs.append(0)
A = array2(lhs)
rhs = array2(rhs)
if verbose:
print("lhs:")
print(shortstr(A))
print("rhs:")
print(shortstr(rhs))
B = pseudo_inverse(A)
soln = dot2(B, rhs)
if not eq2(dot2(A, soln), rhs):
print("no solution")
return
if verbose:
print("soln:")
print(shortstr(soln))
soln.shape = (N, 1)
rhs.shape = A.shape[0], 1
K = array2(list(find_kernel(A)))
best = None
density = 1.0
size = 9999*n
trials = argv.get("trials", 1024)
count = 0
for trial in range(trials):
u = rand2(len(K), 1)
v = dot2(K.transpose(), u)
#print(v)
assert dot2(A, v).sum()==0
#if v.sum() != n:
# continue
assert v[0]==0
v = (v+soln)%2
assert eq2(dot2(A, v), rhs)
Gt = list(G0.transpose())
for i, x in enumerate(xs):
if v[i] and not i in taken:
Gt.append(x)
if not Gt:
continue
Gt = array2(Gt)
G = Gt.transpose()
if verbose:
print("G0")
print(shortstr(G0))
print("solution:")
print(shortstr(G))
assert is_morthogonal(G, 3)
if G.shape[1]<m:
continue
if 0 in G.sum(1):
continue
#print(shortstr(G))
# for g in G:
# print(shortstr(g), g.sum())
# print()
_density = float(G.sum()) / (G.shape[0]*G.shape[1])
#if best is None or _density < density:
if best is None or G.shape[1] < size:
best = G
density = _density
size = G.shape[1]
if 0:
#sols.append(G)
Gx = even_rows(G)
assert is_morthogonal(Gx, 3)
if len(Gx)==0:
continue
GGx = array2(list(span(Gx)))
assert is_morthogonal(GGx, 3)
count += 1
print("found %d solutions" % count)
G = best
#print(shortstr(G))
for g in G:
print(shortstr(g), g.sum())
print()
print("density:", density)
def test_matrix(ring):
one = ring.one
zero = ring.zero
rows = cols = [Cell(0, i) for i in [0, 1]]
I = Matrix.from_array([[1, 0], [0, 1]], ring, rows, cols)
X = Matrix.from_array([[0, 1], [1, 0]], ring, rows, cols)
Z = Matrix.from_array([[1, 0], [0, -1]], ring, rows, cols)
assert I * X == X
assert X * X == I
assert Z * Z == I
assert ring.one == -ring.one or X * Z != Z * X
assert X * Z == -Z * X
assert (-1) * I == -I
assert (I + -I).is_zero()
II = I @ I
XI = X @ I
IZ = I @ Z
assert XI * XI == II
assert XI * IZ == X @ Z
M = parse("""
1.1..1
11.1..
.11.1.
...111
""")
A = Matrix.from_array(M, ring)
#print(A)
A.check()
if 0:
print("kernel:")
print(A.kernel())
print("image:")
print(A.image())
print("cokernel:")
print(A.cokernel())
At = A.dual()
#print(A*At)
At.check()
M = [[1, 0, 1], [1, 1, 0]]
C = Chain.from_array(M, ring)
Ct = C.dual()
#Ct.dump()
#print(Ct.cells)
#print(Ct.get_cells(-1))
#M = Ct.get_bdymap(-1)
#print(M.cols, M.rows)
Ct.check()
#C.dump()
#Ct.dump()
A = C @ Ct
#test_chain(A)
A.check()
def main():
ring = element.Q
#ring = element.FiniteField(2)
# tetra-hedron face map:
M = parse("""
1.1..1
11.1..
.11.1.
...111
""")
chain = Chain.from_array(M, ring)
chain.check()
M = chain.get_bdymap(1)
print(M)
rows, cols = M.rows, M.cols
flow = Flow(chain)
#flow.build()
# match goes from src:grade-1 --> tgt:grade
# rows are faces, cols are edges
assert flow.accept(rows[1], cols[0])
flow.add(rows[1], cols[0])
assert flow.accept(rows[2], cols[1])
flow.add(rows[2], cols[1])
assert flow.accept(rows[3], cols[4])
flow.add(rows[3], cols[4])
print(flow)
A = flow.get_bdymap(2) # 2 --> 1
B = flow.get_bdymap(1) # 1 --> 0
print(A, A.shape)
print(B, B.shape)
print(B.cols, B.rows)
C = B * A
assert C.is_zero()
f0 = flow.get_f(0)
f1 = flow.get_f(1)
f2 = flow.get_f(2)
assert f0 * chain.get_bdymap(1) == B * f1
assert f1 * chain.get_bdymap(2) == A * f2
g0 = flow.get_g(0)
g1 = flow.get_g(1)
g2 = flow.get_g(2)
assert chain.get_bdymap(1) * g1 == g0 * B
assert chain.get_bdymap(2) * g2 == g1 * A
fs = [f0, f1, f2]
gs = [g0, g1, g2]
chi0 = flow.get_homotopy(0)
chi1 = flow.get_homotopy(1)
chi2 = flow.get_homotopy(2)
chis = [chi0, chi1, chi2]
for i in [1, 2]:
cells = chain.get_cells(i)
I = Matrix.identity(cells, ring)
lhs = gs[i] * fs[i] - I
rhs = chain.get_bdymap(i + 1) * chis[i] + chis[i -
1] * chain.get_bdymap(i)
assert lhs == rhs
#print(lhs)
cells = flow.get_critical(i)
I = Matrix.identity(cells, ring)
lhs = fs[i] * gs[i]
#print(lhs)
#print(I)
assert lhs == I
print()
for grade in range(2):
print("grade =", grade)
print("f =")
print(fs[grade])
print("g =")
print(gs[grade])
print("chi =")
print(chis[grade])
#print("rows:", chis[grade].rows)
#print("cols:", chis[grade].cols)
print("fg =")
print(fs[grade] * gs[grade])
print("gf =")
print(gs[grade] * fs[grade])
print()
print(flow.get_bdymap(1))