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Refactor Schottky and Theta classes for improved functionality and pe…
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…rformance
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@mmasdeu
mmasdeu committed Dec 11, 2024
1 parent 3b6e5fe commit e6f1c03
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Showing 2 changed files with 64 additions and 71 deletions.
83 changes: 41 additions & 42 deletions darmonpoints/schottky.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -27,7 +27,7 @@
from .divisors import Divisors, DivisorsElement
from .meromorphic import *
from .theta import *
from .util import muted
from .util import muted, our_sqrt

infinity = Infinity

Expand Down Expand Up @@ -100,17 +100,20 @@ def uniq(lst):


@muted
@cached_function
def find_eigenvector_matrix(g):
K = g.parent().base_ring()
t = g.trace()
n = g.determinant()
delta = (t * t - 4 * n).sqrt()
vaps = sorted([(t + delta) / 2, (t - delta) / 2], key=lambda o: o.valuation())
veps = sum(((g - l).right_kernel().basis() for l in vaps), [])
delta = (t * t - K(4) * n).sqrt()
vaps = sorted([(t + delta) / K(2), (t - delta) / K(2)], key=lambda o: o.valuation())
assert len(vaps) == 2
veps = []
for l in vaps:
B = g - l
veps.append((B[0,1], -B[0,0])) # The right kernel of a rank-1 2x2 matrix
return g.matrix_space()(veps).transpose()


@cached_function
def find_parameter(g, ball, pi=None, check=True):
if pi is None:
pi = g.parent().base_ring().uniformizer()
Expand Down Expand Up @@ -210,6 +213,8 @@ def theta_naive(self, m, a=ZZ(0), b=ZZ(1), z=None, gamma=None, **kwargs):
K = self.K
if z is Infinity:
return K(1)
if isinstance(z, Divisors): # z is a divisor!
return prod(self.theta_naive(m, a, b, P, gamma, **kwargs)**n for P, n in z)
if gamma is not None:
if b != ZZ(1):
raise ValueError("If gamma is specified, then b should not")
Expand All @@ -225,9 +230,9 @@ def theta_naive(self, m, a=ZZ(0), b=ZZ(1), z=None, gamma=None, **kwargs):
can_stop = True
for _, g in self.enumerate_group_elements(i):
ga = act(g, a)
tmp1 = K(1) if ga is Infinity else z - ga
tmp1 = K(1) if ga is Infinity or z == ga else z - ga
gb = act(g, b)
tmp2 = K(1) if gb is Infinity else z - gb
tmp2 = K(1) if gb is Infinity or z == gb else z - gb
new_num *= tmp1
new_den *= tmp2
try:
Expand Down Expand Up @@ -353,7 +358,7 @@ def construct_tree(self, level):
return self.NJtree

@cached_method
@muted
# @muted # DEBUG
def fundamental_domain(self, level=1, check=True):
while True:
level += 1
Expand All @@ -364,7 +369,7 @@ def fundamental_domain(self, level=1, check=True):
except ValueError as e:
verbose(str(e))

@muted
# @muted # DEBUG
def _fundamental_domain(self, i0=None, check=True):
tree = self.NJtree
if i0 is None:
Expand Down Expand Up @@ -546,13 +551,14 @@ def test_fundamental_domain(self):
gens = self._generators
test_fundamental_domain(gens, balls)

def balls(self):
def balls(self, generators=None):
try:
return self._balls
except AttributeError:
pass
K = self.base_ring()
generators = self._generators
if generators is None:
generators = self._generators
G = PreSchottkyGroup(K, generators)
gp = G.group()
good_gens, good_balls, _ = G.fundamental_domain()
Expand Down Expand Up @@ -608,22 +614,18 @@ def a_point(self):
return x0
raise RuntimeError("Reached maximum iterations (100)")

def find_point(self, gamma, eps=1, idx=None):
def find_point(self, gamma, eps=1, idx=None, check=True):
balls = self.balls()
gens = self.gens_extended()
if idx is not None:
B = balls[-idx]
if idx > 0:
if self._generators[idx - 1] != gamma:
B1 = next(balls[-i] for i, g in gens if g == gamma)
# print(f'!! {B = } but {B1 = }')
# print(balls)
B = B1
else:
if self._generators[-idx - 1] ** -1 != gamma:
B1 = next(balls[-i] for i, g in gens if g == gamma)
# print(f'!! {B = } but {B1 = }')
# print(balls)
B = B1
else:
B = next(balls[-i] for i, g in gens if g == gamma)
Expand All @@ -632,11 +634,10 @@ def find_point(self, gamma, eps=1, idx=None):
except TypeError:
raise RuntimeError(
"Fundamental domain has balls with fractional radius. \
Try with a quadratic (ramified) extension."
Try with a quadratic (ramified) extension."
)
test = lambda x: self.in_fundamental_domain(x, strict=False)

try:
if check:
test = lambda x: self.in_fundamental_domain(x, strict=False)
if not test(ans):
raise RuntimeError(
f"{ans = } should be in fundamental domain, but it is not."
Expand All @@ -646,11 +647,6 @@ def find_point(self, gamma, eps=1, idx=None):
raise RuntimeError(
f"gamma * ans = {ga} should be in fundamental domain, but it is not."
)
except RuntimeError:
new_idx = -idx if idx is not None else None
ginv = gamma**-1
ans = self.find_point(ginv, eps, new_idx)
return act(ginv, ans)
return ans

def to_fundamental_domain(self, x):
Expand Down Expand Up @@ -731,7 +727,7 @@ def find_equivalent_divisor(self, D):
if e == 0:
continue
zz = self.find_point(g, idx=i + 1)
ans -= Div([(e, zz), (-e, act(g, zz))])
ans += Div([(-e, zz), (e, act(g, zz))])
return ans

def theta(self, prec, a, b=None, **kwargs):
Expand Down Expand Up @@ -767,9 +763,7 @@ def theta(self, prec, a, b=None, **kwargs):
s = kwargs.pop("s", None)
if s is not None:
D0 += s * D0
recursive = kwargs.get("recursive", True)
if recursive:
D0 = self.find_equivalent_divisor(D0)
D0 = self.find_equivalent_divisor(D0)
ans = ThetaOC(self, a=D0, b=None, prec=prec, base_ring=K, **kwargs)
z = kwargs.pop("z", None)
improve = kwargs.pop("improve", True)
Expand All @@ -788,32 +782,37 @@ def u_function(self, gamma, prec, a=None, **kwargs):
if z is None:
kwargs.pop("z", None)
return lambda z: prod(
self._u_function(gens[abs(i) - 1], prec, a=a)(z) ** ZZ(sgn(i))
self._u_function(abs(i) - 1, prec, a=a)(z) ** ZZ(sgn(i))
for i in wd
)
return prod(
self._u_function(gens[abs(i) - 1], prec, a=a)(z) ** ZZ(sgn(i))
self._u_function(abs(i) - 1, prec, a=a)(z) ** ZZ(sgn(i))
for i in wd
)
naive = kwargs.get('naive', None)
if z is None:
return lambda z: self._u_function(gens[wd[0] - 1], prec, a=a)(z)
return lambda z: self._u_function(wd[0] - 1, prec, a=a, naive=naive)(z)
else:
return self._u_function(gens[wd[0] - 1], prec, a=a)(z)
return self._u_function(wd[0] - 1, prec, a=a, naive=naive)(z)

@cached_method
def _u_function(self, gamma, prec, a):
def _u_function(self, i, prec, a, naive=False):
r"""
Compute u_gamma
"""
(i,) = self.word_problem(gamma)
assert i > 0
gamma = self._generators[i]
if a is None:
a = self.a_point() # self.find_point(gamma, idx=g)
a = self.base_ring()(1) * a
K = a.parent()
a = self.find_point(gamma, idx=i) # self.a_point()
K = a.parent()
else:
a = self.base_ring()(1) * a
K = a.parent()
D = self.find_equivalent_divisor(Divisors(K)([(1, a), (-1, act(gamma, a))]))
ans = ThetaOC(self, a=D, b=None, prec=prec, base_ring=K)
ans = ans.improve(prec)
if naive:
return lambda z : self.theta_naive(prec, z=z, a=a, gamma=gamma)
else:
ans = ThetaOC(self, a=D, b=None, prec=prec, base_ring=K)
ans = ans.improve(prec)
return ans

@cached_method
Expand Down
52 changes: 23 additions & 29 deletions darmonpoints/theta.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -100,8 +100,8 @@ def __init__(self, G, a=None, b=None, prec=None, **kwargs):
self.K = K
self.G = G
self.p = G.pi
generators = G.generators()
balls = G.balls()
_ = G.generators()
_ = G.balls()
if prec is None:
try:
self.prec = K.precision_cap()
Expand All @@ -123,20 +123,21 @@ def __init__(self, G, a=None, b=None, prec=None, **kwargs):
self.b = b
self.m = 1
self.z = K["z"].gen()

self.MM = MeromorphicFunctions(self.K, self.p, self.prec)
params = G.parameters
gens_ext = G.gens_extended()
# self.val will contain the 0 and 1 terms
D1 = sum((g * D for (_, g), _ in zip(gens_ext, params)), self.Div([]))
self.val = D + D1
# self.val = self.z.parent()(1)
# self.val *= prod((self.z - P) ** n for P, n in (D + D1) if P != Infinity)
self.MM = MeromorphicFunctions(self.K, self.p, self.prec)
self.Fnlist = [{}]
D1dict = {i: g * D for (i, g), tau in zip(gens_ext, params)}
for (i, g), tau in zip(gens_ext, params):
gD = sum(g * val for j, val in D1dict.items() if j != -i)
self.Fnlist[0][i] = self.MM(gD, tau)

# Corresponding to words of length exactly 1
D1dict = {i : g * D for i, g in gens_ext}

# Corresponding to words of length exactly 2
# D2dict = {i : sum(g * val) for j, val in D1dict.items() if j != i for i, g in gens_ext }

# self.val will contain the 0, 1 and 2 terms
self.val = sum(D1dict.values(), D)
self.Fnlist = [{ i :
self.MM(sum(g * val for j, val in D1dict.items() if j != -i), tau)
for (i, g), tau in zip(gens_ext, params)}]

def improve(self, m):
gens_ext = self.G.gens_extended()
Expand All @@ -151,12 +152,13 @@ def improve(self, m):
)
for it in range(m):
if self.m >= self.prec:
self.Fnlist = [
if len(self.Fnlist) > 0:
self.Fnlist = [
{
ky: sum((F[ky] for F in self.Fnlist[1:]), self.Fnlist[0][ky])
for ky in self.Fnlist[0]
}
]
]
return self
tmp = {}
for (i, gi), tau in zip(gens_ext, params):
Expand All @@ -177,9 +179,6 @@ def improve(self, m):
]
return self

def improve_one(self):
return self.improve(1)

def _repr_(self):
a, b = self.a, self.b
if b is None:
Expand Down Expand Up @@ -221,23 +220,18 @@ def __call__(self, z, **kwargs):
return self.evaluate(z, **kwargs)

def evaluate(self, z, **kwargs):
# recursive = kwargs.get("recursive", True)
if not isinstance(z, DivisorsElement):
z = self.Div([(1, z)])
if z.degree() != 0:
# inf, wd = self.G.to_fundamental_domain(Infinity)
z -= self.Div([(z.degree(), Infinity)])
z = self.G.find_equivalent_divisor(z)
ans = prod(eval_rat(self.val, P) ** n for P, n in z)
newans = prod(
F(P) ** n for FF in self.Fnlist for ky, F in FF.items() for P, n in z
)
ans *= newans
return ans
ans0 = prod(eval_rat(self.val, P) ** n for P, n in z)
ans1 = prod(F(z) for FF in self.Fnlist for F in FF.values())
return ans0 * ans1

def eval_derivative(self, z, return_value=False):
assert not isinstance(z, DivisorsElement)
# z = self.Div([(1,z)])
if isinstance(z, DivisorsElement):
raise NotImplementedError
z0, wd = self.G.to_fundamental_domain(z)
gens = (
[None]
Expand Down

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