def newforms(N, recompute=False):
if N <= 10:
return []
p = "%s/%s"%(PATH,N)
if os.path.exists(p + ".bz2") and not recompute:
return db.load(p,bzip2=True)
c = conv(N)
db.save(c,p, bzip2=True)
return c
def newforms(N, recompute=False):
if N <= 10:
return []
p = "%s/%s" % (PATH, N)
if os.path.exists(p + ".bz2") and not recompute:
return db.load(p, bzip2=True)
c = conv(N)
db.save(c, p, bzip2=True)
return c
def zeta_zeros():
r"""
List of the imaginary parts of the first 100,000 nontrivial zeros
of the Riemann zeta function. Andrew Odlyzko computed these to
precision within `3\cdot 10^{-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/
EXAMPLES:
The following example prints the imaginary part of the 13th
nontrivial zero of the Riemann zeta function. Note that only the
first 9 digits after the decimal come from the database. Subsequent
digits are the result of the inherent imprecision of a binary
representation of decimal numbers.
::
sage: zz = zeta_zeros() # optional - database_odlyzko_zeta
sage: zz[12] # optional - database_odlyzko_zeta
59.347044003...
"""
path = os.path.join(misc.SAGE_SHARE, 'odlyzko')
file = os.path.join(path, 'zeros1')
if os.path.exists(file + ".pickle"):
misc.verbose("Loading Odlyzko database from " + file + ".pickle")
return db.load(file + ".pickle")
misc.verbose("Creating Odlyzko Database.")
F = [eval(x) for x in open(file).read().split()]
db.save(F, file + ".pickle")
return F
def zeta_zeros():
r"""
List of the imaginary parts of the first 100,000 nontrivial zeros
of the Riemann zeta function. Andrew Odlyzko computed these to
precision within `3\cdot 10^{-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/
EXAMPLES:
The following example prints the imaginary part of the 13th
nontrivial zero of the Riemann zeta function. Note that only the
first 9 digits after the decimal come from the database. Subsequent
digits are the result of the inherent imprecision of a binary
representation of decimal numbers.
::
sage: zz = zeta_zeros() # optional
sage: zz[12] # optional
59.347044003000001
"""
path = "%s/odlyzko" % PATH
file = "%s/zeros1" % path
if os.path.exists(file + ".pickle"):
misc.verbose("Loading Odlyzko database from " + file + ".pickle")
return db.load(file + ".pickle")
misc.verbose("Creating Odlyzko Database.")
F = [eval(x) for x in open(file).read().split()]
db.save(F, file + ".pickle")
return F