def wrapped(*args, **kwds):
output = method(*args, **kwds)
assert isinstance(output, HtmlFragment)
if _old_and_deprecated_behavior:
# workaround for the old SageNB interacts
pretty_print(output)
return WarnIfNotPrinted()
else:
return output
def wrapped(*args, **kwds):
output = method(*args, **kwds)
assert isinstance(output, HtmlFragment)
if _old_and_deprecated_behavior:
# workaround for the old SageNB interacts
pretty_print(output)
return WarnIfNotPrinted()
else:
return output
def __init__(self,
parent,
initial_point,
pt0=None,
pr0=None,
pth0=None,
pph0=None,
mu=None,
E=None,
L=None,
Q=None,
r_increase=True,
th_increase=True,
chart=None,
name=None,
latex_name=None,
a_num=None,
m_num=None,
verbose=False):
r"""
Initializes a geodesic in Kerr spacetime.
"""
self._spacetime = parent.codomain()
self._mu = mu
self._E = E
self._L = L
self._Q = Q
self._a = a_num
if self._a is None:
self._a = self._spacetime.spin()
self._m = m_num
if self._m is None:
self._m = self._spacetime.mass()
self._latest_solution = None # to keep track of latest solution key
self._init_vector = self._compute_init_vector(initial_point, pt0, pr0,
pth0, pph0, r_increase,
th_increase, verbose)
if verbose:
print("Initial tangent vector: ")
pretty_print(self._init_vector.display())
metric = self._spacetime.metric()
lamb = SR.var('lamb', latex_name=r'\lambda')
IntegratedGeodesic.__init__(self,
parent,
metric,
lamb,
self._init_vector,
chart=chart,
name=name,
latex_name=latex_name,
verbose=verbose)
def print_data():
if show_seq.value:
pretty_print(html("Mutation sequence: ${}$".format(seq)))
if show_vars.value and kind == 'seed':
pretty_print(html("Cluster variables:"))
table = "$\\begin{align*}\n"
for i in range(self._n):
table += "\tv_{%s} &= " % i + latex(self.cluster_variable(i)) + "\\\\ \\\\\n"
table += "\\end{align*}$"
pretty_print(html(table))
if show_matrix.value:
pretty_print(html("B-Matrix:"))
pretty_print(html(self._M))
def print_data():
if show_seq.value:
pretty_print(html("Mutation sequence: ${}$".format(seq)))
if show_vars.value and kind == 'seed':
pretty_print(html("Cluster variables:"))
table = "$\\begin{align*}\n"
for i in range(self._n):
table += "\tv_{%s} &= " % i + latex(
self.cluster_variable(i)) + "\\\\ \\\\\n"
table += "\\end{align*}$"
pretty_print(html(table))
if show_matrix.value:
pretty_print(html("B-Matrix:"))
pretty_print(html(self._M))
def zon_info(X, variant="central", data={}, spaces="IJPD"):
data = data.copy()
if 'varNames' not in data:
rws = X.nrows()
varstr = "xyzwabcd"
if rws <= len(varstr):
varstr = varstr[:rws]
else:
varstr = varstr[0]
data['varNames'] = varstr
Z = ZonotopalAlgebra(X, variant, data)
tup = zon_spaces(Z, spaces)
# print out central zonotopal spaces
print "X = "
pretty_print(Z.matrix())
print ""
print_zon_info(tup)
return tup
def print_zon_info(tup):
I, J, P, D = tup
if I is not None:
print "I(X) ="
pretty_print(I)
print
if J is not None:
print "J(X) ="
pretty_print(J)
print
if P is not None:
print "P(X) ="
pretty_print(P)
print
if D is not None:
print "D(X) ="
pretty_print(D)
print
def _compute_init_vector(self, point, pt0, pr0, pth0, pph0, r_increase,
th_increase, verbose):
r"""
Computes the initial 4-momentum vector `p` from the constants of motion
"""
BLchart = self._spacetime.boyer_lindquist_coordinates()
basis = BLchart.frame().at(point)
r, th = BLchart(point)[1:3]
a, m = self._a, self._m
r2 = r**2
a2 = a**2
rho2 = r2 + (a * cos(th))**2
Delta = r2 - 2 * m * r + a2
if pt0 is None:
if (self._mu is not None and pr0 is not None and pth0 is not None
and pph0 is not None):
xxx = SR.var('xxx')
v = self._spacetime.tangent_space(point)(
(xxx, pr0, pth0, pph0), basis=basis)
muv2 = -self._spacetime.metric().at(point)(v, v)
muv2 = muv2.substitute(self._numerical_substitutions())
solutions = solve(muv2 == self._mu**2, xxx, solution_dict=True)
if verbose:
print("Solutions for p^t:")
pretty_print(solutions)
for sol in solutions:
if sol[xxx] > 0:
pt0 = sol[xxx]
break
else: # pt0 <= 0 might occur in the ergoregion
pt0 = solutions[0][xxx]
try:
pt0 = RR(pt0)
except TypeError: # pt0 contains some symbolic expression
pass
else:
if self._E is None:
raise ValueError("the constant E must be provided")
if self._L is None:
raise ValueError("the constant L must be provided")
E, L = self._E, self._L
pt0 = ((r2 + a2) / Delta * ((r2 + a2) * E - a * L) + a *
(L - a * E * sin(th)**2)) / rho2
if pph0 is None:
if self._E is None:
raise ValueError("the constant E must be provided")
if self._L is None:
raise ValueError("the constant L must be provided")
E, L = self._E, self._L
pph0 = (L / sin(th)**2 - a * E + a / Delta *
((r2 + a2) * E - a * L)) / rho2
if pr0 is None:
if self._E is None:
raise ValueError("the constant E must be provided")
if self._L is None:
raise ValueError("the constant L must be provided")
if self._mu is None:
raise ValueError("the constant mu must be provided")
if self._Q is None:
raise ValueError("the constant Q must be provided")
E, L, Q = self._E, self._L, self._Q
mu2 = self._mu**2
E2_mu2 = E**2 - mu2
pr0 = sqrt((E2_mu2) * r**4 + 2 * m * mu2 * r**3 +
(a2 * E2_mu2 - L**2 - Q) * r**2 + 2 * m *
(Q + (L - a * E)**2) * r - a2 * Q) / rho2
if not r_increase:
pr0 = -pr0
if pth0 is None:
if self._E is None:
raise ValueError("the constant E must be provided")
if self._L is None:
raise ValueError("the constant L must be provided")
if self._mu is None:
raise ValueError("the constant mu must be provided")
if self._Q is None:
raise ValueError("the constant Q must be provided")
E2 = self._E**2
L2 = self._L**2
mu2 = self._mu**2
Q = self._Q
pth0 = sqrt(Q + cos(th)**2 * (a2 *
(E2 - mu2) - L2 / sin(th)**2)) / rho2
if not th_increase:
pth0 = -pth0
return self._spacetime.tangent_space(point)((pt0, pr0, pth0, pph0),
basis=basis,
name='p')
