def search_src(string,
extra1='',
extra2='',
extra3='',
extra4='',
extra5='',
interact=True):
r"""
Search \Sage library source code for lines containing \code{string}.
The search is not case sensitive.
INPUT:
-- string: a string to find in the \Sage source code.
-- extra1, ..., extra5: additional strings to require.
NOTE:
The extraN parameters are present only because
search_src(string, *extras, interact=None)
is not parsed correctly by Python 2.6; see http://bugs.python.org/issue1909.
EXAMPLES:
sage: print search_src(" fetch(", "def", interact=False) # random # long
matrix/matrix0.pyx: cdef fetch(self, key):
matrix/matrix0.pxd: cdef fetch(self, key)
sage: print search_src(" fetch(", "def", interact=False) # random # long
matrix/matrix0.pyx: cdef fetch(self, key):
matrix/matrix0.pxd: cdef fetch(self, key)
sage: print search_src(" fetch(", "def", "pyx", interact=False) # random # long
matrix/matrix0.pyx: cdef fetch(self, key):
"""
cmd = 'sage -grep "%s"' % string
for extra in [extra1, extra2, extra3, extra4, extra5]:
if not extra:
continue
cmd += '| grep "%s"' % extra
old_banner = os.environ.has_key('SAGE_BANNER')
if old_banner:
old_banner = os.environ['SAGE_BANNER']
os.environ['SAGE_BANNER'] = "no"
r = os.popen(cmd).read()
if old_banner == False:
del os.environ['SAGE_BANNER']
else:
os.environ['SAGE_BANNER'] = old_banner
if not interact:
return r
from sage.server.support import EMBEDDED_MODE
if EMBEDDED_MODE: # I.e., running from the notebook
print format_search_as_html('Source Code', r, string + extra)
else:
from sage.misc.all import pager
pager()(r)
def help(self):
try:
h = self.__help
except AttributeError:
h = "-" * 70 + '\n'
h += " Call lcalc with one argument, e.g., \n"
h += " sage: lcalc('--tau -z 1000')\n"
h += " is translated into the command line\n"
h += " $ lcalc --tau -z 1000\n"
h += "-" * 70 + '\n'
h += '\n' + self('--help')
self.__help = h
pager()(h)
def help(self):
try:
h = self.__help
except AttributeError:
h = "-"*70 + '\n'
h += " Call lcalc with one argument, e.g., \n"
h += " sage: lcalc('--tau -z 1000')\n"
h += " is translated into the command line\n"
h += " $ lcalc --tau -z 1000\n"
h += "-"*70 + '\n'
h += '\n' + self('--help')
self.__help = h
pager()(h)
def search_src(string, extra1='', extra2='', extra3='', extra4='', extra5='', interact=True):
r"""
Search \Sage library source code for lines containing \code{string}.
The search is not case sensitive.
INPUT:
-- string: a string to find in the \Sage source code.
-- extra1, ..., extra5: additional strings to require.
NOTE:
The extraN parameters are present only because
search_src(string, *extras, interact=None)
is not parsed correctly by Python 2.6; see http://bugs.python.org/issue1909.
EXAMPLES:
sage: print search_src(" fetch(", "def", interact=False) # random # long
matrix/matrix0.pyx: cdef fetch(self, key):
matrix/matrix0.pxd: cdef fetch(self, key)
sage: print search_src(" fetch(", "def", interact=False) # random # long
matrix/matrix0.pyx: cdef fetch(self, key):
matrix/matrix0.pxd: cdef fetch(self, key)
sage: print search_src(" fetch(", "def", "pyx", interact=False) # random # long
matrix/matrix0.pyx: cdef fetch(self, key):
"""
cmd = 'sage -grep "%s"' % string
for extra in [ extra1, extra2, extra3, extra4, extra5 ]:
if not extra:
continue
cmd += '| grep "%s"' % extra
old_banner = os.environ.has_key('SAGE_BANNER')
if old_banner:
old_banner = os.environ['SAGE_BANNER']
os.environ['SAGE_BANNER'] = "no"
r = os.popen(cmd).read()
if old_banner == False:
del os.environ['SAGE_BANNER']
else:
os.environ['SAGE_BANNER'] = old_banner
if not interact:
return r
from sage.server.support import EMBEDDED_MODE
if EMBEDDED_MODE: # I.e., running from the notebook
print format_search_as_html('Source Code', r, string + extra)
else:
from sage.misc.all import pager
pager()(r)
def search_doc(s, extra=''):
"""
Full text search of the SAGE HTML documentation for lines
containing s. The search is not case sensitive.
"""
cmd = 'sage -grepdoc "%s" | grep "%s"'%(s,extra)
old_banner = os.environ.has_key('SAGE_BANNER')
if old_banner:
old_banner = os.environ['SAGE_BANNER']
os.environ['SAGE_BANNER'] = "no"
r = os.popen(cmd).read()
if old_banner == False:
del os.environ['SAGE_BANNER']
else:
os.environ['SAGE_BANNER'] = old_banner
from sage.server.support import EMBEDDED_MODE
if EMBEDDED_MODE: # I.e., running from the notebook
print format_search_as_html('Documentation', r, s + extra)
else:
from sage.misc.all import pager
pager()(r)
def search_doc(s, extra=''):
"""
Full text search of the SAGE HTML documentation for lines
containing s. The search is not case sensitive.
"""
cmd = 'sage -grepdoc "%s" | grep "%s"' % (s, extra)
old_banner = os.environ.has_key('SAGE_BANNER')
if old_banner:
old_banner = os.environ['SAGE_BANNER']
os.environ['SAGE_BANNER'] = "no"
r = os.popen(cmd).read()
if old_banner == False:
del os.environ['SAGE_BANNER']
else:
os.environ['SAGE_BANNER'] = old_banner
from sage.server.support import EMBEDDED_MODE
if EMBEDDED_MODE: # I.e., running from the notebook
print format_search_as_html('Documentation', r, s + extra)
else:
from sage.misc.all import pager
pager()(r)
def help(self):
h = """
sympow('-sp 2p16 -curve "[1,2,3,4,5]"')
will compute L(Sym^2 E,edge) for E=[1,2,3,4,5] to 16 digits of precision
The result
2n0: 8.370510845377639E-01
2w0: 8.370510845377586E-01
consists of two calculations using different parameters to test the
functional equation (to see if these are sufficiently close).
sympow('-sp 3p12d2,4p8 -curve "[1,2,3,4,5]"')
will compute the 0th-2nd derivatives of L(Sym^3 E,center) to 12 digits
and L(Sym^4 E,edge) to 8 digits
Special cases: When a curve has CM, Hecke power can be used instead
sympow('-sp 7p12d1 -hecke -curve "[0,0,1,-16758,835805]"')
will compute the 0th-1st derivatives of L(Sym^7 psi,special) to 12 digits.
Bloch-Kato numbers can be obtained for powers not congruent to 0 mod 4:
sympow('-sp 2bp16 -curve "[1,2,3,4,5]"')
should return
2n0: 4.640000000000006E+02
2w0: 4.639999999999976E+02
which can be seen to be very close to the integer 464.
Modular degrees can be computed with the -moddeg option.
sympow('-curve "[1,2,3,4,5]" -moddeg')
should return
Modular Degree is 464
Analytic ranks can be computed with the -analrank option.
sympow('-curve "[1,2,3,4,5]" -analrank')
should return
Analytic Rank is 1 : L'-value 3.51873e+00
and (if the mesh file for the fifth derivative is present)
sympow('-curve "[0,0,1,-79,342]" -analrank')
should return
Analytic Rank is 5 : leading L-term 3.02857e+01
========================================================================
Adding new symmetric powers:
SYMPOW keeps data for symmetric powers in the directory datafiles
If a pre-computed mesh of inverse Mellin transform values is not
available for a given symmetric power, SYMPOW will fail. The command
sympow('-new_data 2')
will add the data the 2nd symmetric power, while
sympow('-new_data 3d2')
will add the data for the 2nd derivative and 3rd symmetric power,
sympow('-new_data 6d0h')
will add the data for the 0th derivative of the 6th Hecke power, and
sympow('-new_data 4c')
will add data for the 4th symmetric power for curves with CM
(these need to be done separately for powers divisible by 4).
The mesh files are stored in binary form, and thus endian-ness is a
worry when moving from one platform to another.
To enable modular degree computations, the 2nd symmetric power must
be extant, and analytic rank requires derivatives of the 1st power.
===================================================================
Output of "!sympow -help":
-bound # an upper BOUND for how many ap to compute
-help print the help message and exit
-info [] [] only report local information for primes/sympows
1st argument is prime range, 2nd is sympow range
-local only report local information (bad primes)
-curve [] input a curve in [a1,a2,a3,a4,a6] form
-label [] label the given curve
-quiet turn off some messages
-verbose turn on some messages
-rootno # compute the root number of the #th symmetric power
-moddeg compute the modular degree
-analrank compute the analytic rank
-sloppy [] for use with -analrank; have X sloppy digits
-nocm abort if curve has complex multiplication
-noqt ignore even powers of non-minimal quad twists
-hecke compute Hecke symmetric powers for a CM curve
-maxtable set the max size of factor tables: 2^27 default
-sp [] argument to specify which powers
this is a comma separated list
in each entry, the 1st datum is the sympow
then could come b which turns Bloch-Kato on
then could come w# which specifies how many tests
then could come s# which says # sloppy digits
then must come p# which specifies the precision
or P# which says ignore BOUND for this power
then must come d# which says the derivative bound
or D# which says do only this derivative
(neither need be indicated for even powers)
default is 2w3s1p32,3bp16d1,4p8
-new_data [] will compute inverse Mellin transform mesh for
the given data: the format is [sp]d[dv]{h,c}
sp is the symmetric power, dv is the derivative,
h indicates Hecke powers, and c indicates CM case
d[dv] is given only for odd or Hecke powers
Examples: 1d3 2 2d1h 3d2 4 4c 5d0 6 7d0h 11d1 12c
NOTE: new_data runs a shell script that uses GP
Other options are used internally/recursively by -new_data
"""
pager()(h)
def help(self):
h = """
sympow('-sp 2p16 -curve "[1,2,3,4,5]"')
will compute L(Sym^2 E,edge) for E=[1,2,3,4,5] to 16 digits of precision
The result
2n0: 8.370510845377639E-01
2w0: 8.370510845377586E-01
consists of two calculations using different parameters to test the
functional equation (to see if these are sufficiently close).
sympow('-sp 3p12d2,4p8 -curve "[1,2,3,4,5]"')
will compute the 0th-2nd derivatives of L(Sym^3 E,center) to 12 digits
and L(Sym^4 E,edge) to 8 digits
Special cases: When a curve has CM, Hecke power can be used instead
sympow('-sp 7p12d1 -hecke -curve "[0,0,1,-16758,835805]"')
will compute the 0th-1st derivatives of L(Sym^7 psi,special) to 12 digits.
Bloch-Kato numbers can be obtained for powers not congruent to 0 mod 4:
sympow('-sp 2bp16 -curve "[1,2,3,4,5]"')
should return
2n0: 4.640000000000006E+02
2w0: 4.639999999999976E+02
which can be seen to be very close to the integer 464.
Modular degrees can be computed with the -moddeg option.
sympow('-curve "[1,2,3,4,5]" -moddeg')
should return
Modular Degree is 464
Analytic ranks can be computed with the -analrank option.
sympow('-curve "[1,2,3,4,5]" -analrank')
should return
Analytic Rank is 1 : L'-value 3.51873e+00
and (if the mesh file for the fifth derivative is present)
sympow('-curve "[0,0,1,-79,342]" -analrank')
should return
Analytic Rank is 5 : leading L-term 3.02857e+01
========================================================================
Adding new symmetric powers:
SYMPOW keeps data for symmetric powers in the directory datafiles
If a pre-computed mesh of inverse Mellin transform values is not
available for a given symmetric power, SYMPOW will fail. The command
sympow('-new_data 2')
will add the data the 2nd symmetric power, while
sympow('-new_data 3d2')
will add the data for the 2nd derivative and 3rd symmetric power,
sympow('-new_data 6d0h')
will add the data for the 0th derivative of the 6th Hecke power, and
sympow('-new_data 4c')
will add data for the 4th symmetric power for curves with CM
(these need to be done separately for powers divisible by 4).
The mesh files are stored in binary form, and thus endian-ness is a
worry when moving from one platform to another.
To enable modular degree computations, the 2nd symmetric power must
be extant, and analytic rank requires derivatives of the 1st power.
===================================================================
Output of "!sympow -help":
-bound # an upper BOUND for how many ap to compute
-help print the help message and exit
-info [] [] only report local information for primes/sympows
1st argument is prime range, 2nd is sympow range
-local only report local information (bad primes)
-curve [] input a curve in [a1,a2,a3,a4,a6] form
-label [] label the given curve
-quiet turn off some messages
-verbose turn on some messages
-rootno # compute the root number of the #th symmetric power
-moddeg compute the modular degree
-analrank compute the analytic rank
-sloppy [] for use with -analrank; have X sloppy digits
-nocm abort if curve has complex multiplication
-noqt ignore even powers of non-minimal quad twists
-hecke compute Hecke symmetric powers for a CM curve
-maxtable set the max size of factor tables: 2^27 default
-sp [] argument to specify which powers
this is a comma separated list
in each entry, the 1st datum is the sympow
then could come b which turns Bloch-Kato on
then could come w# which specifies how many tests
then could come s# which says # sloppy digits
then must come p# which specifies the precision
or P# which says ignore BOUND for this power
then must come d# which says the derivative bound
or D# which says do only this derivative
(neither need be indicated for even powers)
default is 2w3s1p32,3bp16d1,4p8
-new_data [] will compute inverse Mellin transform mesh for
the given data: the format is [sp]d[dv]{h,c}
sp is the symmetric power, dv is the derivative,
h indicates Hecke powers, and c indicates CM case
d[dv] is given only for odd or Hecke powers
Examples: 1d3 2 2d1h 3d2 4 4c 5d0 6 7d0h 11d1 12c
NOTE: new_data runs a shell script that uses GP
Other options are used internally/recursively by -new_data
"""
pager()(h)
