def fill_degree_table(self,
update_func,
deg_neg_one,
maxdeg=None,
mindeg=None):
''' Generic function that iterates by increasing degree
from 0 to curve.MAXDEG (usually set to 2g).
At each iteration update_func is called with -P and -Q values
from previous iteration.
Input: update_func, a curve.m list representing the values at -1
degree divisors.
'''
maxdeg = maxdeg if maxdeg else self.MAXDEG
mindeg = mindeg if mindeg else 0
L = [deg_neg_one]
for degA in range(mindeg, maxdeg + 1):
N = []
for Aq in range(self.m):
div = TwoPDivisor(Q=Aq, deg=degA, curve=self)
minus_p_val = L[-1][Aq]
minus_q_val = L[-1][
Aq -
1] # python does the right thing with negative indices
N.append(update_func(div, minus_p_val, minus_q_val))
L.append(N)
return L[1:]
def map_div(self, func, mindeg=None, maxdeg=None):
maxdeg = maxdeg if maxdeg else self.MAXDEG
mindeg = mindeg if mindeg else 0
L = []
for degA in range(mindeg, maxdeg + 1):
N = []
for Aq in range(self.m):
div = TwoPDivisor(Q=Aq, deg=degA, curve=self)
N.append(func(div, self))
L.append(N)
return L
def wrap_table(self, name):
offset_tup = self._data['offset'][name]
offset = TwoPDivisor(P=offset_tup[0], Q=offset_tup[1])
if name.lower()[0] == 'd':
self.__dict__[name.lower()] = DivTable(self._data[name],
self,
start=offset,
min=1)
else:
self.__dict__[name.lower()] = DivTable(self._data[name],
self,
start=offset)
def reduce_table(self, update_func, start, maxdeg=None, mindeg=None):
''' same as fill_degree_table but don't keep the table'''
maxdeg = maxdeg if maxdeg else self.MAXDEG
mindeg = mindeg if mindeg else 0
L = start
for degA in range(mindeg, maxdeg + 1):
N = []
for Aq in range(self.m):
div = TwoPDivisor(Q=Aq, deg=degA, curve=self)
minus_p_val = L[Aq]
minus_q_val = L[
Aq -
1] # python does the right thing with negative indices
N.append(update_func(div, minus_p_val, minus_q_val))
L = N
return L
def fill_degree_table_reverse(self,
update_func,
deg_max,
maxdeg=None,
mindeg=None):
''' Same as fill_degree_table but in reverse degree order (i.e. going
from DEGMAX down to 0, and updating on +P and +Q values'''
maxdeg = maxdeg if maxdeg else self.MAXDEG
mindeg = mindeg if mindeg else 0
L = [deg_max]
for degA in range(maxdeg, mindeg - 1, -1):
N = []
for Aq in range(self.m):
div = TwoPDivisor(Q=Aq, deg=degA, curve=self)
plus_p_val = L[-1][Aq]
plus_q_val = L[-1][
(Aq + 1) % self.
m] # python does the right thing with negative indices
N.append(update_func(div, plus_p_val, plus_q_val))
L.append(N)
L = L[1:]
L.reverse()
return L
def D(self):
'''Two point-divisor equivalent to sum of all rational point minus
P,Q'''
return TwoPDivisor(deg=self.ddeg, Q=self.dq, curve=self)
def Q(self):
return TwoPDivisor(deg=1, Q=1, curve=self)
def P(self):
return TwoPDivisor(deg=1, P=1, curve=self)
def K(self):
return TwoPDivisor(deg=2 * self.g - 2, Q=self.kq, curve=self)
def div(self, **kwds):
return TwoPDivisor(curve=self, **kwds)