Improved ozman sieve

helper_scripts/bash_sage_init.sh

@@ -7,5 +7,8 @@ if [ ! -f ${SAGE_BIN_DIR}/sage-env-config ]; then
     SAGE_BIN_DIR=$(sage -sh -c 'echo $SAGE_VENV')/bin
 fi
 source ${SAGE_BIN_DIR}/sage-env-config
+if [ ! -f ${SAGE_BIN_DIR}/sage-env ]; then
+    SAGE_BIN_DIR=$(sage -sh -c 'echo $SAGE_VENV')/bin
+fi
 source ${SAGE_BIN_DIR}/sage-env
 export PATH=$(dirname -- ${HELPER_DIR})/venv/bin:$SAGE_BIN_DIR:${PATH}

isogeny_primes.py

@@ -61,7 +61,7 @@ def DLMV(K):
     delta_K = log(2) / (r_K + 1)
     C_1_K = r_K ** (r_K + 1) * delta_K ** (-(r_K - 1)) / 2
     C_2_K = exp(24 * C_1_K * R_K)
-    CHEB_DEN_BOUND = (4 * log(Delta_K ** h_K) + 5 * h_K + 5) ** 2
+    CHEB_DEN_BOUND = (4 * log(Delta_K**h_K) + 5 * h_K + 5) ** 2
     C_0 = ((CHEB_DEN_BOUND ** (12 * h_K)) * C_2_K + CHEB_DEN_BOUND ** (6 * h_K)) ** 4
 
     # Now the Type 1 and 2 bounds

latex_helper.py

@@ -176,7 +176,7 @@ def type_2_bounds(self):
             log_type_2_bound = type_2_bound.log10()
             exp_at_10 = int(log_type_2_bound)
             rem = log_type_2_bound - exp_at_10
-            rem = 10 ** rem
+            rem = 10**rem
             rem = rem.numerical_approx(digits=3)
             lmfdb_link = LMFDB_NF_URL_TRUNK.format(label)
             lmfdb_link_latex = r"\href{{{the_link}}}{{{my_text}}}".format(

requirements-dev.txt

@@ -1,5 +1,5 @@
 #
-# This file is autogenerated by pip-compile with python 3.9
+# This file is autogenerated by pip-compile with python 3.10
 # To update, run:
 #
 #    pip-compile requirements-dev.in
@@ -73,7 +73,7 @@ pyflakes==2.5.0
     #   flake8
 pylint==2.15.5
     # via -r requirements-dev.in
-pyparsing==3.0.6
+pyparsing==3.0.9
     # via
     #   -c requirements.txt
     #   packaging
@@ -100,16 +100,13 @@ tomli==2.0.1
     #   pytest
 tomlkit==0.11.6
     # via pylint
-typing-extensions==4.0.1
+typing-extensions==4.4.0
     # via
     #   -c requirements.txt
-    #   astroid
-    #   black
     #   mypy
-    #   pylint
 vulture==2.6
     # via -r requirements-dev.in
-wrapt==1.13.3
+wrapt==1.14.1
     # via
     #   -c requirements.txt
     #   astroid

requirements.txt

@@ -1,5 +1,5 @@
 #
-# This file is autogenerated by pip-compile with python 3.9
+# This file is autogenerated by pip-compile with python 3.10
 # To update, run:
 #
 #    pip-compile requirements.in

sage_code/character_enumeration.py

@@ -45,15 +45,15 @@
 def filter_possible_values(possible_values_list, q, residue_class_degree, prime_field):
 
     output = []
-    fq = q ** residue_class_degree
+    fq = q**residue_class_degree
     for c in possible_values_list:
-        if c ** 2 == prime_field(1):
+        if c**2 == prime_field(1):
             output.append(c)
-        elif c ** 2 == prime_field(fq ** 2):
+        elif c**2 == prime_field(fq**2):
             output.append(c)
         else:
             possible_mid_coeffs = lifts_in_hasse_range(fq, c + prime_field(fq) / c)
-            possible_weil_polys = [x ** 2 + a * x + fq for a in possible_mid_coeffs]
+            possible_weil_polys = [x**2 + a * x + fq for a in possible_mid_coeffs]
 
             elliptic_weil_polys = [
                 f
@@ -87,13 +87,13 @@ def get_possible_vals_at_gens(gens_info, eps, embeddings, residue_field, prime_f
         q = class_gp_gen.smallest_integer()
         e = class_gp_gen.residue_class_degree()
         filtered_values = filter_possible_values(possible_values, q, e, prime_field)
-        output[class_gp_gen] = list({x ** 12 for x in filtered_values})
+        output[class_gp_gen] = list({x**12 for x in filtered_values})
 
     return output
 
 
 def tuple_exp(tup, exp_tup):
-    return tuple((t ** e for t, e in zip(tup, exp_tup)))
+    return tuple((t**e for t, e in zip(tup, exp_tup)))
 
 
 def lifts_in_hasse_range(fq, res_class):
@@ -114,13 +114,13 @@ def lifts_in_hasse_range(fq, res_class):
 
     low_run = centered_lift
 
-    while low_run ** 2 <= fq4:
+    while low_run**2 <= fq4:
         output.append(low_run)
         low_run = low_run - p
 
     high_run = centered_lift + p
 
-    while high_run ** 2 <= fq4:
+    while high_run**2 <= fq4:
         output.append(high_run)
         high_run = high_run + p
 
@@ -224,7 +224,7 @@ def final_filter(
             # Check that these exponents correspond to the ideals in
             # my_gens_ideals in the correct order
             sanity_check = prod(
-                [Q ** a for Q, a in zip(my_gens_ideals, exponents_in_class_group)]
+                [Q**a for Q, a in zip(my_gens_ideals, exponents_in_class_group)]
             )
             assert C_K(sanity_check) == C_K(q)
 
@@ -285,7 +285,7 @@ def character_enumeration_filter(
     gens_info = {}
     for q in my_gens_ideals:
         q_order = C_K(q).multiplicative_order()
-        alphas = (q ** q_order).gens_reduced()
+        alphas = (q**q_order).gens_reduced()
         assert len(alphas) == 1
         alpha = alphas[0]
         gens_info[q] = (q_order, alpha)
@@ -314,7 +314,7 @@ def character_enumeration_filter(
                 # stop condition:
                 # 4sqrt(Nm(q)) > 2p
                 # Nm(q) > (p/2)**2
-                stop = (p ** 2 // 4) + 1
+                stop = (p**2 // 4) + 1
                 if enumeration_bound:
                     stop = min(stop, enumeration_bound)
                 aux_primes = primes_iter(K, stop)

sage_code/common_utils.py

@@ -76,12 +76,12 @@ def get_weil_polys(F):
     """
     q = F.characteristic()
     a = F.degree()
-    weil_polys = R.weil_polynomials(2, q ** a)
+    weil_polys = R.weil_polynomials(2, q**a)
     return [f for f in weil_polys if weil_polynomial_is_elliptic(f, q, a)]
 
 
 def get_ordinary_weil_polys_from_values(q, a):
-    weil_polys = R.weil_polynomials(2, q ** a)
+    weil_polys = R.weil_polynomials(2, q**a)
     return [f for f in weil_polys if f[1] % q != 0]
 
 
@@ -129,7 +129,7 @@ def to_A(g):
 
     def from_A(a):
         assert a in A
-        return C_K.prod(gi ** ei for gi, ei in zip(C_K.gens(), a))
+        return C_K.prod(gi**ei for gi, ei in zip(C_K.gens(), a))
 
     return A, to_A, from_A
 

sage_code/frobenius_polynomials.py

@@ -114,7 +114,7 @@ def semi_stable_frobenius_polynomial(
         x = polygen(K)
         u = uniformizer(q)
         e = semistable_ramification(local_data)
-        L = K.extension(x ** e - t * u, "a")
+        L = K.extension(x**e - t * u, "a")
         EL = E.change_ring(L)
         qL = L.primes_above(q)[0]
         Ebar = reduction(EL, qL)
@@ -146,4 +146,4 @@ def isogeny_character_values_12(
     E: EllipticCurve_number_field, p: Integer, q: NumberFieldFractionalIdeal
 ):
     values = isogeny_character_values(E, p, q)
-    return [a ** 12 for a in values]
+    return [a**12 for a in values]

sage_code/generic.py

@@ -210,7 +210,7 @@ def get_aux_primes(K, norm_bound, C_K, h_K, contains_imaginary_quadratic):
 
 
 def alpha_eps_beta_bound(alpha_eps, beta, nm_q_pow_12hq):
-    C_mat = alpha_eps ** 2 - alpha_eps * beta.trace() + nm_q_pow_12hq
+    C_mat = alpha_eps**2 - alpha_eps * beta.trace() + nm_q_pow_12hq
     N = ZZ(C_mat.det())
     return N
 
@@ -248,7 +248,7 @@ def ABC_integers(
         multiplicative_bounds = {}
 
     nm_q = ZZ(frak_q.absolute_norm())
-    alphas = (frak_q ** q_class_group_order).gens_reduced()
+    alphas = (frak_q**q_class_group_order).gens_reduced()
     assert len(alphas) == 1, "q^q_class_group_order not principal, which is very bad"
     alpha = alphas[0]
     output_dict = {}

sage_code/type_one_primes.py

@@ -287,7 +287,7 @@ def apply_formal_immersion_at_2(
 def get_N(frob_poly, nm_q, exponent):
     """Helper method for computing Type 1 primes"""
     beta = Matrix.companion(frob_poly) ** exponent
-    N = ZZ(1 - beta.trace() + nm_q ** exponent)
+    N = ZZ(1 - beta.trace() + nm_q**exponent)
     return N
 
 

sage_code/type_two_primes.py

@@ -50,7 +50,7 @@
 
 logger = logging.getLogger(__name__)
 
-GENERIC_UPPER_BOUND = 10 ** 30
+GENERIC_UPPER_BOUND = 10**30
 
 
 def LLS(p):
@@ -68,7 +68,7 @@ def get_type_2_uniform_bound(ecdb_type):
     else:
         raise ValueError("argument must be LSS or BS")
 
-    f = BOUND_TERM ** 6 + BOUND_TERM ** 3 + 1 - x
+    f = BOUND_TERM**6 + BOUND_TERM**3 + 1 - x
 
     try:
         bound = find_root(f, 1000, GENERIC_UPPER_BOUND)
@@ -123,8 +123,8 @@ def satisfies_condition_CC(K, p):
     for q in prime_range(p / 4):
         for frak_q in K.primes_above(q):
             f = frak_q.residue_class_degree()
-            if f % 2 == 1 and q ** f < p / 4:
-                if (q ** (2 * f) + q ** f + 1) % p != 0:
+            if f % 2 == 1 and q**f < p / 4:
+                if (q ** (2 * f) + q**f + 1) % p != 0:
                     if legendre_symbol(q, p) == 1:  # i.e. not inert
                         return False
     return True
@@ -141,7 +141,7 @@ def satisfies_condition_CC_uniform(possible_odd_f, p):
         return False
     for q in prime_range((p / 4) ^ (1 / max(possible_odd_f)) + 1):
         if legendre_symbol(q, p) == 1:
-            if all((q ** (2 * f) + q ** f + 1) % p != 0 for f in possible_odd_f):
+            if all((q ** (2 * f) + q**f + 1) % p != 0 for f in possible_odd_f):
                 return False
     return True
 

sage_code/weeding.py

@@ -39,6 +39,7 @@
     QuadraticField,
     companion_matrix,
     gcd,
+    legendre_symbol,
     oo,
     parent,
     prime_range,
@@ -59,16 +60,21 @@
 
 def oezman_sieve(p, N):
     """If p is unramified in Q(sqrt(-N)) this always returns True.
-    Otherwise returns True iff p is in S_N or . Only makes sense if p ramifies in K"""
+    Otherwise returns True iff p is in S_N. Only makes sense if p ramifies in K.
+    Also assumes that N is prime (for the time being).
+    """
+    assert N.is_prime() and N > 2
 
     M = QuadraticField(-N)
     if p.divides(M.discriminant()):
         return True
 
     pp = (M * p).factor()[0][0]
-    C_M = M.class_group()
-    if C_M(pp).order() == 1:
-        return True
+    if pp.is_principal():
+        if N % 4 == 3:
+            return True
+        if legendre_symbol(p, N) == 1:
+            return True
 
     return False
 
@@ -77,10 +83,8 @@ def najman_trbovic_filter(unram_primes, ramified_primes):
     """Return True if a possible isogeny prime can be removed via
     Theorem 2.13 of the paper of Najman-Trbovic"""
 
-    absurd_intersection = set(unram_primes).intersection(
-        set(ramified_primes)
-    )
-    return (len(absurd_intersection) > 0)
+    absurd_intersection = set(unram_primes).intersection(set(ramified_primes))
+    return len(absurd_intersection) > 0
 
 
 def get_dirichlet_character(K):
@@ -119,7 +123,7 @@ def is_torsion_same(p, K, chi, B=30, uniform=False):
     for q, i in frob_poly_data:
         frob_pol_q = J0_min.frobenius_polynomial(q)
         frob_mat = companion_matrix(frob_pol_q)
-        point_counts.append((frob_mat ** i).charpoly()(1))
+        point_counts.append((frob_mat**i).charpoly()(1))
 
     # Recall that the rational torsion on J0(p) is entirely contained in
     # the minus part (theorem of Mazur), so checking no-growth of torsion

tests/fast_tests/test_character_enumeration.py

@@ -62,10 +62,10 @@ def test_filter_possible_values(possible_values_list, q, e, prime, result):
     [
         (11, GF(3)(0), [0, -3, -6, 3, 6]),
         # make sure we include +/-2sqrt(fq) but not +/-(2sqrt(fq)+1),
-        (145757 ** 2, GF(357686312646216567629137)(2 * 145757), [2 * 145757]),
-        (145757 ** 2, GF(357686312646216567629137)(-2 * 145757), [-2 * 145757]),
-        (145757 ** 2, GF(357686312646216567629137)(2 * 145757 + 1), []),
-        (145757 ** 2, GF(357686312646216567629137)(-2 * 145757 - 1), []),
+        (145757**2, GF(357686312646216567629137)(2 * 145757), [2 * 145757]),
+        (145757**2, GF(357686312646216567629137)(-2 * 145757), [-2 * 145757]),
+        (145757**2, GF(357686312646216567629137)(2 * 145757 + 1), []),
+        (145757**2, GF(357686312646216567629137)(-2 * 145757 - 1), []),
     ],
 )
 def test_lifts_in_hasse_range(fq, res_class, expected_range):
@@ -79,12 +79,12 @@ def test_lifts_in_hasse_range(fq, res_class, expected_range):
 @pytest.mark.parametrize(
     "f, q",
     [
-        (x ** 2 - x + 1007, 13),
-        (x ** 2 - x + 1007, 17),
-        (x ** 2 - x + 1007, 19),
-        (x ** 2 - 11 * 17 * 9011 * 23629, 17),
-        (x ** 2 - 11 * 17 * 9011 * 23629, 47),
-        (x ** 2 - 11 * 17 * 9011 * 23629, 89),
+        (x**2 - x + 1007, 13),
+        (x**2 - x + 1007, 17),
+        (x**2 - x + 1007, 19),
+        (x**2 - 11 * 17 * 9011 * 23629, 17),
+        (x**2 - 11 * 17 * 9011 * 23629, 47),
+        (x**2 - 11 * 17 * 9011 * 23629, 89),
     ],
 )
 @pytest.mark.skip(reason="Only for profiling putative faster solution")
@@ -105,9 +105,9 @@ def test_ideal_log_relation_prime_gens(f, q):
     exponents = C_K(qq).exponents()
 
     t = qq.ideal_log_relation()
-    alpha_new = t * prod([(relation ** e) for relation, e in zip(relations, exponents)])
+    alpha_new = t * prod([(relation**e) for relation, e in zip(relations, exponents)])
 
-    sanity_check = prod([Q ** a for Q, a in zip(prime_gens, exponents)])
+    sanity_check = prod([Q**a for Q, a in zip(prime_gens, exponents)])
     assert C_K(sanity_check) == C_K(qq)
 
     the_principal_ideal = qq * prod([Q ** (-a) for Q, a in zip(prime_gens, exponents)])

tests/fast_tests/test_common_utils.py

@@ -36,8 +36,8 @@
 
 x = polygen(QQ)
 test_cases = [
-    (x ** 5 - x ** 4 + 2 * x ** 3 - 4 * x ** 2 + x - 1, 20),
-    (x ** 6 - 2 * x ** 5 + 6 * x ** 4 + 22 * x ** 3 + 41 * x ** 2 + 48 * x + 36, 6),
+    (x**5 - x**4 + 2 * x**3 - 4 * x**2 + x - 1, 20),
+    (x**6 - 2 * x**5 + 6 * x**4 + 22 * x**3 + 41 * x**2 + 48 * x + 36, 6),
 ]
 
 

tests/fast_tests/test_frobenius_polynomials.py

@@ -39,7 +39,7 @@
 
 K = QuadraticField(-127, "D")
 D = K.gen(0)
-j = 20 * (3 * (-26670989 - 15471309 * D) / 2 ** 26) ** 3
+j = 20 * (3 * (-26670989 - 15471309 * D) / 2**26) ** 3
 # this is one of the curves from the Gonzaléz, Lario, and Quer article
 E = EllipticCurve_from_j(j)
 
@@ -59,8 +59,8 @@ def test_semi_stable_frobenius_polynomial_t():
     x = polygen(QQ)
     K = QQ.extension(x - 1, "one")
     E = EllipticCurve(K, [49, 343])
-    assert E.discriminant() == -(2 ** 4) * 31 * 7 ** 6
-    assert E.j_invariant() == K(2 ** 8 * 3 ** 3) / 31
+    assert E.discriminant() == -(2**4) * 31 * 7**6
+    assert E.j_invariant() == K(2**8 * 3**3) / 31
     f1 = semi_stable_frobenius_polynomial(E, K * 7, 1)
     f2 = semi_stable_frobenius_polynomial(E, K * 7, -1)(x=-x)
     assert f1 == f2
@@ -72,7 +72,7 @@ def test_semi_stable_frobenius_polynomial_t():
         (2, {1, 8}),
         (3, {1}),
         (7, {72}),
-        (11, {13 ** 12 % 73, 57 ** 12 % 73}),
+        (11, {13**12 % 73, 57**12 % 73}),
     ],
 )
 def test_isogeny_character_values_12(p, values):