Coverage for local/lib/python2.7/site-packages/sage/databases/odlyzko.py : 63%

""" 

Tables of zeros of the Riemann-Zeta function 

AUTHORS: 

- William Stein: initial version 

- Jeroen Demeyer (2015-01-20): convert ``database_odlyzko_zeta`` to 

new-style package 

""" 

#***************************************************************************** 

# Copyright (C) 2004 William Stein <wstein@gmail.com> 

# Copyright (C) 2015 Jeroen Demeyer <jdemeyer@cage.ugent.be> 

# 

# This program is free software: you can redistribute it and/or modify 

# it under the terms of the GNU General Public License as published by 

# the Free Software Foundation, either version 2 of the License, or 

# (at your option) any later version. 

# http://www.gnu.org/licenses/ 

#***************************************************************************** 

import os 

from sage.structure.sage_object import load 

from sage.env import SAGE_SHARE 

from sage.misc.all import verbose 

def zeta_zeros(): 

r""" 

List of the imaginary parts of the first 2,001,052 zeros of the 

Riemann zeta function, accurate to within 4e-9. 

In order to use ``zeta_zeros()``, you will need to 

install the optional Odlyzko database package:: 

sage -i database_odlyzko_zeta 

You can see a list of all available optional packages with 

``sage --optional``. 

REFERENCES: 

- http://www.dtc.umn.edu/~odlyzko/zeta_tables/index.html 

EXAMPLES: 

The following example prints the imaginary part of the 13th 

nontrivial zero of the Riemann zeta function:: 

sage: zz = zeta_zeros() # optional - database_odlyzko_zeta 

sage: zz[12] # optional - database_odlyzko_zeta 

59.347044003 

sage: len(zz) # optional - database_odlyzko_zeta 

2001052 

""" 

sobj = os.path.join(SAGE_SHARE, 'odlyzko', 'zeros.sobj') 

verbose("Loading Odlyzko database from " + sobj) 

return load(sobj)