def tensor_get_an_no_deg1(L1, L2, d1, d2, BadPrimeInfo):
"""
Same as the above in the case no dimension is 1
"""
if d1 == 1 or d2 == 1:
raise ValueError('min(d1,d2) should not be 1, use direct method then')
s1 = len(L1)
s2 = len(L2)
if s1 < s2:
S = s1
if s2 <= s1:
S = s2
BadPrimes = []
for bpi in BadPrimeInfo:
BadPrimes.append(bpi[0])
P = prime_range(S + 1)
Z = S * [1]
S = RealField()(S)
for p in P:
f = S.log(base=p).floor()
q = 1
E1 = []
E2 = []
if not p in BadPrimes:
for i in range(f):
q = q * p
E1.append(L1[q - 1])
E2.append(L2[q - 1])
e1 = list_to_euler_factor(E1, f + 1)
e2 = list_to_euler_factor(E2, f + 1)
# ld1 = d1 # not used
# ld2 = d2 # not used
else: # either convolve, or have one input be the answer and other 1-t
i = BadPrimes.index(p)
e1 = BadPrimeInfo[i][1]
e2 = BadPrimeInfo[i][2]
# ld1 = e1.degree() # not used
# ld2 = e2.degree() # not used
F = e1.list()[0].parent().fraction_field()
R = PowerSeriesRing(F, "T", default_prec=f + 1)
e1 = R(e1)
e2 = R(e2)
E = tensor_local_factors(e1, e2, f)
A = euler_factor_to_list(E, f)
while len(A) < f:
A.append(0)
q = 1
for i in range(f):
q = q * p
Z[q - 1] = A[i]
all_an_from_prime_powers(Z)
return Z
def tensor_get_an_no_deg1(L1, L2, d1, d2, BadPrimeInfo):
"""
Same as the above in the case no dimension is 1
"""
if d1==1 or d2==1:
raise ValueError('min(d1,d2) should not be 1, use direct method then')
s1 = len(L1)
s2 = len(L2)
if s1 < s2:
S = s1
if s2 <= s1:
S = s2
BadPrimes = []
for bpi in BadPrimeInfo:
BadPrimes.append(bpi[0])
P = prime_range(S+1)
Z = S * [1]
S = RealField()(S)
for p in P:
f = S.log(base=p).floor()
q = 1
E1 = []
E2 = []
if not p in BadPrimes:
for i in range(f):
q=q*p
E1.append(L1[q-1])
E2.append(L2[q-1])
e1 = list_to_euler_factor(E1,f+1)
e2 = list_to_euler_factor(E2,f+1)
# ld1 = d1 # not used
# ld2 = d2 # not used
else: # either convolve, or have one input be the answer and other 1-t
i = BadPrimes.index(p)
e1 = BadPrimeInfo[i][1]
e2 = BadPrimeInfo[i][2]
# ld1 = e1.degree() # not used
# ld2 = e2.degree() # not used
F = e1.list()[0].parent().fraction_field()
R = PowerSeriesRing(F, "T", default_prec=f+1)
e1 = R(e1)
e2 = R(e2)
E = tensor_local_factors(e1,e2,f)
A = euler_factor_to_list(E,f)
while len(A) < f:
A.append(0)
q = 1
for i in range(f):
q = q*p
Z[q-1]=A[i]
all_an_from_prime_powers(Z)
return Z
def get_euler_factor(L, p):
"""
takes L list of all ans and p is a prime
it returns the euler factor at p
# utility function to get an Euler factor, unused
"""
S = RealField()(len(L))
f = S.log(base=p).floor()
E = []
q = 1
for i in range(f):
q = q * p
E.append(L[q - 1])
return list_to_euler_factor(E, f)
def get_euler_factor(L,p):
"""
takes L list of all ans and p is a prime
it returns the euler factor at p
# utility function to get an Euler factor, unused
"""
S = RealField()(len(L))
f = S.log(base=p).floor()
E = []
q = 1
for i in range(f):
q = q*p
E.append(L[q-1])
return list_to_euler_factor(E,f)
def all_an_from_prime_powers(L):
"""
L is a list of an such that the terms
are correct for all n which are prime powers
and all others are equal to 1;
this function changes the list in place to make
the correct ans for all n
"""
S = ZZ(len(L))
for p in prime_range(S + 1):
q = 1
Sr = RealField()(len(L))
f = Sr.log(base=p).floor()
for k in range(f):
q = q * p
for m in range(2, 1 + (S // q)):
if (m % p) != 0:
L[m * q - 1] = L[m * q - 1] * L[q - 1]
def all_an_from_prime_powers(L):
"""
L is a list of an such that the terms
are correct for all n which are prime powers
and all others are equal to 1;
this function changes the list in place to make
the correct ans for all n
"""
S = ZZ(len(L))
for p in prime_range(S+1):
q = 1
Sr = RealField()(len(L))
f = Sr.log(base=p).floor()
for k in range(f):
q = q*p
for m in range(2, 1+(S//q)):
if (m%p) != 0:
L[m*q-1] = L[m*q-1] * L[q-1]
def tensor_get_an_deg1(L, D, BadPrimeInfo):
"""
Same as above, except that the BadPrimeInfo
is now a list of lists of the form
[p,f] where f is a polynomial.
"""
s1 = len(L)
s2 = len(D)
if s1 < s2:
S = s1
if s2 <= s1:
S = s2
BadPrimes = []
for bpi in BadPrimeInfo:
BadPrimes.append(bpi[0])
P = prime_range(S + 1)
Z = S * [1]
S = RealField()(S) # fix bug
for p in P:
f = S.log(base=p).floor()
q = 1
u = 1
e = D[p - 1]
if not p in BadPrimes:
for i in range(f):
q = q * p
u = u * e
Z[q - 1] = u * L[q - 1]
else:
i = BadPrimes.index(p)
e = BadPrimeInfo[i][1]
F = e.list()[0].parent().fraction_field()
R = PowerSeriesRing(F, "T", default_prec=f + 1)
e = R(e)
A = euler_factor_to_list(e, f)
for i in range(f):
q = q * p
Z[q - 1] = A[i]
all_an_from_prime_powers(Z)
return Z
def tensor_get_an_deg1(L, D, BadPrimeInfo):
"""
Same as above, except that the BadPrimeInfo
is now a list of lists of the form
[p,f] where f is a polynomial.
"""
s1 = len(L)
s2 = len(D)
if s1 < s2:
S = s1
if s2 <= s1:
S = s2
BadPrimes = []
for bpi in BadPrimeInfo:
BadPrimes.append(bpi[0])
P = prime_range(S+1)
Z = S * [1]
S = RealField()(S) # fix bug
for p in P:
f = S.log(base=p).floor()
q = 1
u = 1
e = D[p-1]
if not p in BadPrimes:
for i in range(f):
q = q*p
u = u*e
Z[q-1] = u*L[q-1]
else:
i = BadPrimes.index(p)
e = BadPrimeInfo[i][1]
F = e.list()[0].parent().fraction_field()
R = PowerSeriesRing(F, "T", default_prec=f+1)
e = R(e)
A = euler_factor_to_list(e,f)
for i in range(f):
q = q*p
Z[q-1] = A[i]
all_an_from_prime_powers(Z)
return Z
