CoCalc -- twistedlseries-timing.sagews

Project: Harvard Workshop: Distribution of modular symbols and L-values

Path: code / alex / psage / twistedlseries-timing.sagews

Views: ¹⁸⁴⁶⁰⁷

attach("twistedlseries.sage")

psage/modform/hilbert/sqrt5/sqrt5.py:852: DeprecationWarning: python.pxi is deprecated, use "from cpython cimport *" instead
See http://trac.sagemath.org/20158 for details.
  from tables import primes_of_bounded_norm
psage/number_fields/__init__.py:1: DeprecationWarning: import "cysignals/signals.pxi" instead of "sage/ext/interrupt.pxi"
See http://trac.sagemath.org/20002 for details.
  import sqrt5

E = EllipticCurve(F, [1, a + 1, a, a, 0])
E
L = LSeriesEllipticCurveSqrt5(E)
#L = LSeriesEllipticCurve(E)

Elliptic Curve defined by y^2 + x*y + a*y = x^3 + (a+1)*x^2 + a*x over Number Field in a with defining polynomial x^2 - x - 1

E.torsion_order()

8

import cProfile
t = cputime()
cProfile.runctx("vals,nvals,chis = value_search(E,3,1000)",None, locals(), filename="timing_data/profile_test1", sort='cumulative')
print cputime(t)

Fractional ideal (7) 49 Fractional ideal (7) [1]
raw value 4.23997384119518e-16 + 4.63884971589829e-16*I
normalised 6.83594740282864e-17 - 3.75785568287707e-16*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (-8*a + 2) 76 (Fractional ideal (2)) * (Fractional ideal (-4*a + 1)) [1, 2]
raw value 1.77476876452315 - 1.95759988981642*I
normalised 1.00000000000000 + 1.73205080756888*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (8*a - 6) 76 (Fractional ideal (2)) * (Fractional ideal (4*a - 3)) [1, 1]
raw value 5.19285520077821e-17 - 5.43601270621147e-17*I
normalised -5.11928948197067e-17 - 2.48414402630533e-17*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (2*a + 11) 139 Fractional ideal (2*a + 11) [1]
raw value 1.94848534487254 - 0.144575522568633*I
normalised 0.999999999999995 + 1.73205080756887*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-2*a + 13) 139 Fractional ideal (-2*a + 13) [1]
raw value -1.09944874774612 - 1.61515004627698*I
normalised 0.999999999999997 - 1.73205080756887*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (11*a - 6) 151 Fractional ideal (11*a - 6) [1]
raw value 1.28139749191622 - 1.36826182656356*I
normalised -1.99999999999999 - 1.54228076864596e-16*I
algdeprts [(-2.00000000000000, 1)]
Fractional ideal (11*a - 5) 151 Fractional ideal (11*a - 5) [1]
raw value 3.84419247574867 - 4.10478547969069*I
normalised -5.99999999999998 - 4.31838615220870e-15*I
algdeprts [(-6.00000000000000, 1)]
Fractional ideal (13) 169 Fractional ideal (13) [1]
raw value 1.54579562381928 + 0.866227961755149*I
normalised 2.00000000000000 - 1.85073692237516e-15*I
algdeprts [(2.00000000000000, 1)]
Fractional ideal (3*a + 13) 199 Fractional ideal (3*a + 13) [1]
raw value 1.29290702755217 + 0.997438946405499*I
normalised 2.00000000000001 - 6.94026345890684e-15*I
algdeprts [(2.00000000000000, 1)]
Fractional ideal (-3*a + 16) 199 Fractional ideal (-3*a + 16) [1]
raw value 1.51026098008723 - 0.620970857388854*I
normalised 0.999999999999999 - 1.73205080756889*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (14*a - 8) 244 (Fractional ideal (2)) * (Fractional ideal (7*a - 4)) [1, 2]
raw value 0.0314883405142133 + 1.47435757599598*I
normalised -2.00000000000000 + 1.00248249961988e-15*I
algdeprts [(-2.00000000000000, 1)]
Fractional ideal (14*a - 6) 244 (Fractional ideal (2)) * (Fractional ideal (7*a - 3)) [1, 1]
raw value 1.29257528533167 - 0.709909085189666*I
normalised -0.999999999999999 - 1.73205080756887*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-16*a + 4) 304 (Fractional ideal (2))^2 * (Fractional ideal (-4*a + 1)) [1, 1]
raw value 1.77476876452316 + 1.95759988981642*I
normalised 0.999999999999998 - 1.73205080756888*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (16*a - 12) 304 (Fractional ideal (2))^2 * (Fractional ideal (4*a - 3)) [1, 1]
raw value 5.19285520077821e-17 - 5.43601270621147e-17*I
normalised -5.11928948197067e-17 - 2.48414402630533e-17*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (-16*a + 6) 316 (Fractional ideal (2)) * (Fractional ideal (-8*a + 3)) [1, 2]
raw value 1.28951584857673 - 0.127923516106711*I
normalised 1.00000000000000 - 1.73205080756887*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-16*a + 10) 316 (Fractional ideal (2)) * (Fractional ideal (-8*a + 5)) [1, 2]
raw value 0.533972909598524 - 1.18071524150345*I
normalised -0.999999999999997 - 1.73205080756887*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (3*a - 20) 331 Fractional ideal (3*a - 20) [1]
raw value 5.51133057385612 - 3.11499430386439*I
normalised 9.99999999999998 - 1.85073692237516e-15*I
algdeprts [(10.0000000000000, 1)]
Fractional ideal (-3*a - 17) 331 Fractional ideal (-3*a - 17) [1]
raw value 0.0116002174275343 - 1.26608988750909*I
normalised 0.999999999999996 - 1.73205080756887*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (19) 361 (Fractional ideal (4*a - 3)) * (Fractional ideal (-4*a + 1)) [1, 1]
raw value 3.31254869309870 - 1.50202417497642*I
normalised -2.99999999999999 + 5.19615242270663*I
algdeprts [(-3.00000000000000 - 5.19615242270663*I, 1), (-3.00000000000000 + 5.19615242270663*I, 1)]
Fractional ideal (2*a - 22) 436 (Fractional ideal (2)) * (Fractional ideal (a - 11)) [1, 1]
raw value 0.105811424643225 + 3.30790252782655*I
normalised 6.00000000000002 - 9.71636884246957e-15*I
algdeprts [(6.00000000000000, 1)]
Fractional ideal (2*a + 20) 436 (Fractional ideal (2)) * (Fractional ideal (a + 10)) [1, 2]
raw value 0.937273970006314 + 0.581862215221642*I
normalised -0.999999999999999 + 1.73205080756888*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (3*a + 22) 541 Fractional ideal (3*a + 22) [1]
raw value 0.220342943690387 - 0.965548904601734*I
normalised -0.999999999999960 - 1.73205080756884*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-3*a + 25) 541 Fractional ideal (-3*a + 25) [1]
raw value 5.67816811095919 - 1.75171119312209*I
normalised 5.99999999999994 - 10.3923048454130*I
algdeprts [(6.00000000000000 - 10.3923048454133*I, 1), (6.00000000000000 + 10.3923048454133*I, 1)]
Fractional ideal (-5*a - 23) 619 Fractional ideal (-5*a - 23) [1]
raw value 2.97938352704803e-17 + 3.43681605226057e-16*I
normalised 7.44849374231626e-16 + 2.21641516343011e-17*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (-5*a + 28) 619 Fractional ideal (-5*a + 28) [1]
raw value 0.850102587652341 + 0.366833047835574*I
normalised 0.999999999999995 - 1.73205080756885*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (23*a - 12) 661 Fractional ideal (23*a - 12) [1]
raw value -1.05030706605215 - 1.45187533489213*I
normalised -1.99999999999996 - 3.46410161513771*I
algdeprts [(-2.00000000000000 - 3.46410161513775*I, 1), (-2.00000000000000 + 3.46410161513775*I, 1)]
Fractional ideal (23*a - 11) 661 Fractional ideal (23*a - 11) [1]
raw value 2.67377168425605 - 0.275482400294101*I
normalised 5.99999999999991 + 2.15919307610435e-14*I
algdeprts [(6.00000000000000, 1)]
Fractional ideal (4*a + 25) 709 Fractional ideal (4*a + 25) [1]
raw value 0.407925749775957 + 0.762902270422673*I
normalised -0.999999999999962 - 1.73205080756885*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-4*a + 29) 709 Fractional ideal (-4*a + 29) [1]
raw value 3.65383897522305 - 5.87780157900103*I
normalised -7.99999999999996 + 13.8564064605506*I
algdeprts [(-8.00000000000000 - 13.8564064605510*I, 1), (-8.00000000000000 + 13.8564064605510*I, 1)]
Fractional ideal (2*a - 28) 724 (Fractional ideal (2)) * (Fractional ideal (a - 14)) [1, 1]
raw value 0.0750071924253409 - 0.852813699004227*I
normalised 1.00000000000000 - 1.73205080756888*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (2*a + 26) 724 (Fractional ideal (2)) * (Fractional ideal (a + 13)) [1, 1]
raw value 2.10316419546110 + 1.47409495082702*I
normalised 3.00000000000001 + 5.19615242270664*I
algdeprts [(3.00000000000000 - 5.19615242270663*I, 1), (3.00000000000000 + 5.19615242270663*I, 1)]
Fractional ideal (a - 29) 811 Fractional ideal (a - 29) [1]
raw value 2.42211496159430 - 0.148329222983797*I
normalised 3.00000000000004 + 5.19615242270670*I
algdeprts [(3.00000000000000 - 5.19615242270663*I, 1), (3.00000000000000 + 5.19615242270663*I, 1)]
Fractional ideal (a + 28) 811 Fractional ideal (a + 28) [1]
raw value 0.807371653864767 - 0.0494430743279323*I
normalised 1.00000000000001 + 1.73205080756890*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-26*a + 9) 829 Fractional ideal (-26*a + 9) [1]
raw value -0.708540684817226 - 0.371560340655551*I
normalised -2.00000000000000 + 2.00496499923975e-15*I
algdeprts [(-2.00000000000000, 1)]
Fractional ideal (-26*a + 17) 829 Fractional ideal (-26*a + 17) [1]
raw value -0.0649792967242118 - 1.59878880598863*I
normalised -2.00000000000001 - 3.46410161513776*I
algdeprts [(-2.00000000000000 - 3.46410161513775*I, 1), (-2.00000000000000 + 3.46410161513775*I, 1)]
Fractional ideal (26*a - 14) 844 (Fractional ideal (2)) * (Fractional ideal (13*a - 7)) [1, 2]
raw value -4.23663230448205e-17 + 1.61753552578096e-16*I
normalised -2.46810589924953e-16 + 3.42003916777016e-16*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (26*a - 12) 844 (Fractional ideal (2)) * (Fractional ideal (13*a - 6)) [1, 1]
raw value 0.739554891290375 + 0.285953838871922*I
normalised 2.00000000000000 - 5.39798269026087e-16*I
algdeprts [(2.00000000000000, 1)]
Fractional ideal (6*a - 34) 916 (Fractional ideal (2)) * (Fractional ideal (3*a - 17)) [1, 2]
raw value 2.13227688423814 - 2.17303439866661*I
normalised 4.00000000000000 - 6.92820323027548*I
algdeprts [(4.00000000000000 - 6.92820323027551*I, 1), (4.00000000000000 + 6.92820323027551*I, 1)]
Fractional ideal (-6*a - 28) 916 (Fractional ideal (2)) * (Fractional ideal (-3*a - 14)) [1, 2]
raw value 0.407882275211829 + 1.46656157449293*I
normalised 1.99999999999999 + 3.46410161513775*I
algdeprts [(2.00000000000000 - 3.46410161513775*I, 1), (2.00000000000000 + 3.46410161513775*I, 1)]
Fractional ideal (3*a - 32) 919 Fractional ideal (3*a - 32) [1]
raw value 1.47488307737899 - 1.73819870330501*I
normalised 2.99999999999996 + 5.19615242270652*I
algdeprts [(3.00000000000000 - 5.19615242270663*I, 1), (3.00000000000000 + 5.19615242270663*I, 1)]
Fractional ideal (-3*a - 29) 919 Fractional ideal (-3*a - 29) [1]
raw value 0.747588590858935 + 0.136062286989824*I
normalised -0.999999999999973 + 1.73205080756885*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (-28*a + 10) 964 (Fractional ideal (2)) * (Fractional ideal (-14*a + 5)) [1, 1]
raw value 1.14136788920694e-16 + 4.08823369652626e-16*I
normalised -4.92001994552848e-16 + 1.03302898020866e-15*I
algdeprts [(0.000000000000000, 1)]
Fractional ideal (-28*a + 18) 964 (Fractional ideal (2)) * (Fractional ideal (-14*a + 9)) [1, 2]
raw value -0.142403971843641 + 0.728127296244202*I
normalised 1.00000000000001 + 1.73205080756889*I
algdeprts [(1.00000000000000 - 1.73205080756888*I, 1), (1.00000000000000 + 1.73205080756888*I, 1)]
Fractional ideal (28*a - 16) 976 (Fractional ideal (2))^2 * (Fractional ideal (7*a - 4)) [1, 2]
raw value 0.0314883405142133 + 1.47435757599598*I
normalised -2.00000000000000 + 1.00248249961988e-15*I
algdeprts [(-2.00000000000000, 1)]
Fractional ideal (28*a - 12) 976 (Fractional ideal (2))^2 * (Fractional ideal (7*a - 3)) [1, 1]
raw value 1.29257528533167 - 0.709909085189666*I
normalised -0.999999999999999 - 1.73205080756887*I
algdeprts [(-1.00000000000000 - 1.73205080756888*I, 1), (-1.00000000000000 + 1.73205080756888*I, 1)]
2951.984

%sh
python ../../gprof2dot/gprof2dot.py -n 0.05 -e 0.0001 -f pstats timing_data/profile_test1 | dot -Tpng -o timing_data/profile_value_search_3_1000.png 2> /dev/null

1+2

3

x = E.base_field().ideals_of_bdd_norm(1000)

sum(len(y) for y in x.values() )

864

{1: [Fractional ideal (1)], 2: [], 3: [], 4: [Fractional ideal (2)], 5: [Fractional ideal (-2*a + 1)], 6: [], 7: [], 8: [], 9: [Fractional ideal (3)], 10: [], 11: [Fractional ideal (-3*a + 1), Fractional ideal (-3*a + 2)], 12: [], 13: [], 14: [], 15: [], 16: [Fractional ideal (4)], 17: [], 18: [], 19: [Fractional ideal (-4*a + 1), Fractional ideal (4*a - 3)], 20: [Fractional ideal (-4*a + 2)], 21: [], 22: [], 23: [], 24: [], 25: [Fractional ideal (5)], 26: [], 27: [], 28: [], 29: [Fractional ideal (a - 6), Fractional ideal (a + 5)], 30: [], 31: [Fractional ideal (5*a - 3), Fractional ideal (5*a - 2)], 32: [], 33: [], 34: [], 35: [], 36: [Fractional ideal (6)], 37: [], 38: [], 39: [], 40: [], 41: [Fractional ideal (a - 7), Fractional ideal (a + 6)], 42: [], 43: [], 44: [Fractional ideal (-6*a + 2), Fractional ideal (-6*a + 4)], 45: [Fractional ideal (-6*a + 3)], 46: [], 47: [], 48: [], 49: [Fractional ideal (7)], 50: [], 51: [], 52: [], 53: [], 54: [], 55: [Fractional ideal (a + 7), Fractional ideal (-a + 8)], 56: [], 57: [], 58: [], 59: [Fractional ideal (7*a - 5), Fractional ideal (7*a - 2)], 60: [], 61: [Fractional ideal (7*a - 4), Fractional ideal (7*a - 3)], 62: [], 63: [], 64: [Fractional ideal (8)], 65: [], 66: [], 67: [], 68: [], 69: [], 70: [], 71: [Fractional ideal (a - 9), Fractional ideal (a + 8)], 72: [], 73: [], 74: [], 75: [], 76: [Fractional ideal (-8*a + 2), Fractional ideal (8*a - 6)], 77: [], 78: [], 79: [Fractional ideal (-8*a + 3), Fractional ideal (-8*a + 5)], 80: [Fractional ideal (-8*a + 4)], 81: [Fractional ideal (9)], 82: [], 83: [], 84: [], 85: [], 86: [], 87: [], 88: [], 89: [Fractional ideal (a - 10), Fractional ideal (a + 9)], 90: [], 91: [], 92: [], 93: [], 94: [], 95: [Fractional ideal (2*a + 9), Fractional ideal (-2*a + 11)], 96: [], 97: [], 98: [], 99: [Fractional ideal (-9*a + 3), Fractional ideal (-9*a + 6)], 100: [Fractional ideal (10)], 101: [Fractional ideal (9*a - 5), Fractional ideal (9*a - 4)], 102: [], 103: [], 104: [], 105: [], 106: [], 107: [], 108: [], 109: [Fractional ideal (a - 11), Fractional ideal (a + 10)], 110: [], 111: [], 112: [], 113: [], 114: [], 115: [], 116: [Fractional ideal (2*a - 12), Fractional ideal (2*a + 10)], 117: [], 118: [], 119: [], 120: [], 121: [Fractional ideal (10*a - 7), Fractional ideal (11), Fractional ideal (10*a - 3)], 122: [], 123: [], 124: [Fractional ideal (10*a - 6), Fractional ideal (10*a - 4)], 125: [Fractional ideal (-10*a + 5)], 126: [], 127: [], 128: [], 129: [], 130: [], 131: [Fractional ideal (a - 12), Fractional ideal (a + 11)], 132: [], 133: [], 134: [], 135: [], 136: [], 137: [], 138: [], 139: [Fractional ideal (2*a + 11), Fractional ideal (-2*a + 13)], 140: [], 141: [], 142: [], 143: [], 144: [Fractional ideal (12)], 145: [Fractional ideal (-11*a + 8), Fractional ideal (-11*a + 3)], 146: [], 147: [], 148: [], 149: [Fractional ideal (-11*a + 4), Fractional ideal (-11*a + 7)], 150: [], 151: [Fractional ideal (11*a - 6), Fractional ideal (11*a - 5)], 152: [], 153: [], 154: [], 155: [Fractional ideal (a - 13), Fractional ideal (a + 12)], 156: [], 157: [], 158: [], 159: [], 160: [], 161: [], 162: [], 163: [], 164: [Fractional ideal (2*a - 14), Fractional ideal (2*a + 12)], 165: [], 166: [], 167: [], 168: [], 169: [Fractional ideal (13)], 170: [], 171: [Fractional ideal (-12*a + 3), Fractional ideal (12*a - 9)], 172: [], 173: [], 174: [], 175: [], 176: [Fractional ideal (-12*a + 4), Fractional ideal (-12*a + 8)], 177: [], 178: [], 179: [Fractional ideal (-12*a + 5), Fractional ideal (12*a - 7)], 180: [Fractional ideal (-12*a + 6)], 181: [Fractional ideal (a - 14), Fractional ideal (a + 13)], 182: [], 183: [], 184: [], 185: [], 186: [], 187: [], 188: [], 189: [], 190: [], 191: [Fractional ideal (2*a + 13), Fractional ideal (-2*a + 15)], 192: [], 193: [], 194: [], 195: [], 196: [Fractional ideal (14)], 197: [], 198: [], 199: [Fractional ideal (3*a + 13), Fractional ideal (-3*a + 16)], 200: [], 201: []}