def R_mon(*args):
R"""Return the monomial $\prod R_{ij}$.
args is i1, j1, i2, j2, ..."""
result = DualSteenrodDense.unit()
for i in range(len(args) // 2):
s, t = args[2 * i], args[2 * i + 1]
result *= DualSteenrodDense.gen(t - s, 2**s)
for m in result.data:
return m
def basis_mon(s, t, u):
"""Return a basis of degree s, t and weight <= u."""
for d in orderedpartition(s, t):
iters = (DualSteenrodDense.basis_mons(d[i]) for i in range(s))
for mon in itertools.product(*iters):
if CobarSteenrod.weight_mon(mon) <= u:
yield mon
def d0(self):
"""Return the d_0 differential."""
data = set()
for mon in self.data:
for i in range(len(mon)):
m = mon[i]
coprod = DualSteenrodDense(m).coprod_E0()
for m1, m2 in coprod.data:
if m1 and m2:
data ^= {mon[:i] + (m1, m2) + mon[i + 1:]}
return type(self)(data)
def d0_inv_data(cls, data: set):
"""Find a cycle $c$ such that $d_0c = data$."""
data = data.copy()
result = set()
while data:
mon = max(data, key=cls.key_mon)
i = cls._get_i(mon)
if i is None:
raise BA.MyValueError("Not d0 invertible")
m_d0_inv = mon[:i] + (DualSteenrodDense.mul_mons(
mon[i + 1], mon[i]), ) + mon[i + 2:]
assert m_d0_inv not in result
result ^= {m_d0_inv}
data ^= cls(m_d0_inv).d0().data
BA.Monitor.print(len(data))
return result
def _get_i(mon):
"""$R_{ij}<R_{kl}$ if (j-i, i)<(l-k,k)"""
for i in range(len(mon)):
if DualSteenrodDense.is_gen_E0(mon[i]):
if i > 0 and (len(mon[i]), mon[i][-1]) < (len(
mon[i - 1]), mon[i - 1][-1]):
return i - 1
else:
if i > 0 and all(
(g + 1, 1 << s) < (len(mon[i - 1]), mon[i - 1][-1])
for g, e in enumerate(mon[i]) if e > 0
for s in two_expansion(e)):
return i - 1
else:
break
return None
def R(i, j):
"""Return $R_{ij}$"""
return DualSteenrodDense.gen(j - i, 2**i)
def deg_mon(mon: tuple):
return Vector(
(len(mon), sum(DualSteenrodDense.deg_mon(m) for m in mon)))
def key_mon(mon):
return [(DualSteenrodDense.is_gen_E0(m), len(m), m[-1]) for m in mon]
def weight_mon(mon: tuple):
return sum(DualSteenrodDense.weight_mon(m) for m in mon)