def __pow__(self, other):
if isinstance(other, Integral):
return PLoop(mat24.pow_ploop(self.value, other & 3))
elif isinstance(other, PLoop):
comm = mat24.ploop_comm(self.value, other.value) << 12
return PLoop(self.value ^ comm)
elif isinstance(other, Parity):
if mat24.gcode_weight(self.value) & 1:
raise ValueError("Parker Loop element has order > 2")
return PLoop(mat24.pow_ploop(self.value, other.value))
else:
return NotImplemented
def divide_atom(self, g, tag, data):
"""Auxiliary method for method mul() """
v = g.data
if tag == "d":
mm_group_n_mul_inv_delta_pi(v, data, 0)
elif tag == "p":
mm_group_n_mul_inv_delta_pi(v, 0, data)
elif tag == 'x':
mm_group_n_mul_x(v, pow_ploop(data, 3))
elif tag == 'y':
mm_group_n_mul_y(v, pow_ploop(data, 3))
elif tag == 't':
mm_group_n_mul_t(v, -int(data) % 3)
else:
raise TypeError("Illegal tag %s in group word" % t)
def mul_Xp(tag, d, i, g):
eps, pi, rep = g.cocode, g.perm, g.rep
d1 = m24.op_ploop_autpl(d, rep)
i1 = pi[i]
s = d1 >> 12
if eps & 0x800: # if eps is odd:
s ^= m24.scalar_prod(d, m24.vect_to_cocode(1 << i))
s ^= m24.pow_ploop(d, 2) >> 12
return s, tag, d1 & 0x7ff, i1
def __rtruediv__(self, other):
if isinstance(other, Integral):
if abs(other) == 1:
inv = mat24.pow_ploop(self.value, 3)
return PLoop(inv ^ ((other & 2) << 11))
else:
raise TypeError("Can only divide unit by Parker loop element")
else:
return NotImplemented
def rule_yp(group, word):
global n_rules
n_rules += 1
y, p = word[0], word[1]
pl = mat24.op_ploop_autpl(y.pl, p.rep)
if p.cocode & 0x800:
pl = mat24.pow_ploop(pl, 3)
return [p, xy_Atom('y', pl), xy_Atom('x', pl)]
else:
return [p, xy_Atom('y', pl)]
def rule_yt(group, word):
global n_rules
n_rules += 1
y, t = word[0], word[1]
assert t.exp in [1, 2]
if t.exp == 1:
pl = mat24.pow_ploop(y.pl, 3)
x, y = xy_Atom('x', pl), xy_Atom('y', pl)
return [t, y, x]
else:
x = xy_Atom('x', y.pl)
return [t, x]
def rule_xt(group, word):
global n_rules
n_rules += 1
x, t = word[0], word[1]
assert t.exp in [1, 2]
if t.exp == 2:
pl = mat24.pow_ploop(x.pl, 3)
x, y = xy_Atom('x', pl), xy_Atom('y', pl)
return [t, y, x]
else:
y = xy_Atom('y', x.pl)
return [t, y]
def __truediv__(self, other):
if isinstance(other, PLoop):
return PLoop(
mat24.mul_ploop(self.value, mat24.pow_ploop(other.value, 3)))
elif isinstance(other, Integral):
if abs(other) == 1:
return PLoop(self.value ^ ((other & 2) << 11))
elif abs(other) == 2:
return Parity(0)
elif abs(other) == 4:
return Parity(mat24.gcode_weight(self.value) & 1)
else:
raise TypeError(ERR_DIV4 % type(self))
else:
return NotImplemented
def sign_t_ZX(d, i):
return m24.pow_ploop(d, 2) >> 12
def sign_t_YZ(d, i):
return (m24.scalar_prod(d, m24.vect_to_cocode(1 << i)) ^
(m24.pow_ploop(d, 2)) >> 12)
def mul_Zx(tag, d, i, g):
e = g.pl
ed = m24.mul_ploop(m24.pow_ploop(e, 3), d)
s = m24.scalar_prod(e, m24.vect_to_cocode(1 << i))
s = (ed >> 12)
return s & 1, Z, ed & 0x7ff, i
def iter_inv_xy(group, atom):
global n_inv
n_inv += 1
res = mat24.pow_ploop(atom.pl, 3)
yield xy_Atom(atom.tag, res)
def gen_z(tag, r="r"):
pl = randint(0, 0x1fff) if isinstance(r, str) else r & 0x1fff
pl = mat24.pow_ploop(pl, 3)
yield xy_Atom('y', pl)
yield xy_Atom('x', pl)
def iter_z(tag, r):
pl = pow_ploop(gen_ploop_element(tag, r), 3)
yield tag_dict['x'] + pl
yield tag_dict['y'] + pl