def render_zeroesLfunction(request, arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9):
''' Renders the first few zeroes of the L-function with the given arguments.
'''
L = generateLfunctionFromUrl(arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9, to_dict(request.args))
if hasattr(L,"lfunc_data"):
website_zeros = p2sage(L.lfunc_data['zeros'])
else:
# This depends on mathematical information, all below is formatting
# More semantic this way
# Allow 10 seconds
website_zeros = L.compute_web_zeros(time_allowed = 10)
positiveZeros = []
negativeZeros = []
for zero in website_zeros:
if zero.abs() < 1e-10:
zero = 0
if zero < 0:
negativeZeros.append(zero)
else:
positiveZeros.append(zero)
# Format the html string to render
positiveZeros = str(positiveZeros)
negativeZeros = str(negativeZeros)
if len(positiveZeros) > 2 and len(negativeZeros) > 2: # Add comma and empty space between negative and positive
negativeZeros = negativeZeros.replace("]", ", ]")
return "<span class='redhighlight'>{0}</span><span class='bluehighlight'>{1}</span>".format(
negativeZeros[1:len(negativeZeros) - 1], positiveZeros[1:len(positiveZeros) - 1])
def getLfunctionPlot(request, arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9):
pythonL = generateLfunctionFromUrl(
arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9, to_dict(request.args))
if not pythonL:
return ""
plotrange = 30
if hasattr(pythonL, 'plotpoints'):
F = p2sage(pythonL.plotpoints)
plotrange = min(plotrange, F[-1][0]) # F[-1][0] is the highest t-coordinated that we have a value for L
else:
# obsolete, because lfunc_data comes from DB?
L = pythonL.sageLfunction
if not hasattr(L, "hardy_z_function"):
return None
plotStep = .1
if pythonL._Ltype not in ["riemann", "maass", "ellipticmodularform", "ellipticcurve"]:
plotrange = 12
F = [(i, L.hardy_z_function(i).real()) for i in srange(-1*plotrange, plotrange, plotStep)]
interpolation = spline(F)
F_interp = [(i, interpolation(i)) for i in srange(-1*plotrange, plotrange, 0.05)]
p = line(F_interp)
# p = line(F) # temporary hack while the correct interpolation is being implemented
styleLfunctionPlot(p, 10)
fn = tempfile.mktemp(suffix=".png")
p.save(filename=fn)
data = file(fn).read()
os.remove(fn)
return data
def getLfunctionPlot(request, arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9):
pythonL = generateLfunctionFromUrl(
arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9, to_dict(request.args))
if hasattr(pythonL,"lfunc_data"):
F = p2sage(pythonL.lfunc_data['plot'])
else:
L = pythonL.sageLfunction
# HSY: I got exceptions that "L.hardy_z_function" doesn't exist
# SL: Reason, it's not in the distribution of Sage
if not hasattr(L, "hardy_z_function"):
return None
# FIXME there could be a filename collission
#F = [(i, L.hardy_z_function(CC(.5, i)).real()) for i in srange(-30, 30, .1)]
plotStep = .1
F = [(i, L.hardy_z_function(i).real()) for i in srange(-30, 30, plotStep)]
p = line(F)
styleLfunctionPlot(p, 10)
fn = tempfile.mktemp(suffix=".png")
p.save(filename=fn)
data = file(fn).read()
os.remove(fn)
return data
def parse_complex_number(z):
zs = p2sage(z)
z_parsed = "(" + str(real_part(zs)) + "," + str(imag_part(zs)) + ")"
return z_parsed
def getGenus2Ldata(label,label_type="url"):
connection = base.getDBConnection()
# g2 = connection.genus2_curves
db = connection.Lfunctions
try:
# Ldata = g2.Lfunctions.find_one({'hash': hash})
# Lpointer = db.instances.find_one({'url': label})
if label_type == "url":
Lpointer = db.instances.find_one({'url': label})
Lhash = Lpointer['Lhash']
Ldata = db.Lfunctions.find_one({'Lhash': Lhash})
elif label_type == "Lhash":
Ldata = db.Lfunctions.find_one({'Lhash': label})
# just return what we have, because
# we are just filling in the dual data
return Ldata
if Ldata['order_of_vanishing']:
central_value = [0.5 + 0.5*Ldata['motivic_weight'], 0]
else:
central_value = [0.5 + 0.5*Ldata['motivic_weight'],Ldata['leading_term']]
if 'values' not in Ldata:
Ldata['values'] = [ central_value ]
else:
Ldata['values'] += [ central_value ]
pos_plot = [
[j * Ldata['plot_delta'], Ldata['plot_values'][j]]
for j in range(min(200, len(Ldata['plot_values'])))]
if Ldata['self_dual']:
neg_zeros = ["-" + str(pos_zero) for pos_zero in Ldata['positive_zeros']]
root_number = p2sage(Ldata['root_number'])
neg_plot = [ [-1*pt[0], root_number * pt[1]] for pt in pos_plot ][1:]
else: # can't happen for genus 2 curves
dual_L_label = Ldata['conjugate']
dual_L_data = getGenus2Ldata(dual_L_label, label_type="Lhash")
neg_zeros = ["-" + str(pos_zero) for pos_zero in dual_L_data['positive_zeros']]
neg_plot = [
[-1 * j * dual_L_data['plot_delta'], dual_L_data['plot_values'][j]]
for j in range(1,min(200,len(dual_L_data['plot_values'])))]
# if label.startswith('Character'): # because those temporarily are missing the plot
# Ldata['plot'] = ""
# else:
# pos_plot = [
# [j * Ldata['plot_delta'], Ldata['plot_values'][j]]
# for j in range(len(Ldata['plot_values']))]
# if Ldata['self_dual']:
# neg_plot = [ [-1*pt[0], Ldata['root_number'] * pt[1]] for pt in pos_plot ][1:]
# neg_plot.reverse()
# else:
# pass # need to add this case
# Ldata['plot'] = neg_plot[:] + pos_plot[:]
neg_zeros.reverse()
Ldata['zeros'] = neg_zeros[:]
Ldata['zeros'] += [0 for _ in range(Ldata['order_of_vanishing'])]
Ldata['zeros'] += [str(pos_zero) for pos_zero in Ldata['positive_zeros']]
neg_plot.reverse()
Ldata['plot'] = neg_plot[:] + pos_plot[:]
#print "Ldata['plot']",Ldata['plot']
except ValueError:
Ldata = None
return Ldata
def getGenus2Ldata(label,label_type="url"):
connection = base.getDBConnection()
# g2 = connection.genus2_curves
db = connection.Lfunctions
try:
# Ldata = g2.Lfunctions.find_one({'hash': hash})
# Lpointer = db.instances.find_one({'url': label})
if label_type == "url":
Lpointer = db.instances.find_one({'url': label})
Lhash = Lpointer['Lhash']
Ldata = db.Lfunctions.find_one({'Lhash': Lhash})
elif label_type == "Lhash":
Ldata = db.Lfunctions.find_one({'Lhash': label})
# just return what we have, because
# we are just filling in the dual data
return Ldata
if Ldata['order_of_vanishing'] or 'leading_term' not in Ldata.keys():
central_value = [0.5 + 0.5*Ldata['motivic_weight'], 0]
else:
central_value = [0.5 + 0.5*Ldata['motivic_weight'],Ldata['leading_term']]
if 'values' not in Ldata:
Ldata['values'] = [ central_value ]
else:
Ldata['values'] += [ central_value ]
pos_plot = [
[j * Ldata['plot_delta'], Ldata['plot_values'][j]]
for j in range(min(200, len(Ldata['plot_values'])))]
if Ldata['self_dual']:
neg_zeros = ["-" + str(pos_zero) for pos_zero in Ldata['positive_zeros']]
root_number = p2sage(Ldata['root_number'])
neg_plot = [ [-1*pt[0], root_number * pt[1]] for pt in pos_plot ][1:]
else: # can't happen for genus 2 curves
dual_L_label = Ldata['conjugate']
dual_L_data = getGenus2Ldata(dual_L_label, label_type="Lhash")
neg_zeros = ["-" + str(pos_zero) for pos_zero in dual_L_data['positive_zeros']]
neg_plot = [
[-1 * j * dual_L_data['plot_delta'], dual_L_data['plot_values'][j]]
for j in range(1,min(200,len(dual_L_data['plot_values'])))]
# if label.startswith('Character'): # because those temporarily are missing the plot
# Ldata['plot'] = ""
# else:
# pos_plot = [
# [j * Ldata['plot_delta'], Ldata['plot_values'][j]]
# for j in range(len(Ldata['plot_values']))]
# if Ldata['self_dual']:
# neg_plot = [ [-1*pt[0], Ldata['root_number'] * pt[1]] for pt in pos_plot ][1:]
# neg_plot.reverse()
# else:
# pass # need to add this case
# Ldata['plot'] = neg_plot[:] + pos_plot[:]
neg_zeros.reverse()
Ldata['zeros'] = neg_zeros[:]
Ldata['zeros'] += [0 for _ in range(Ldata['order_of_vanishing'])]
Ldata['zeros'] += [str(pos_zero) for pos_zero in Ldata['positive_zeros']]
neg_plot.reverse()
Ldata['plot'] = neg_plot[:] + pos_plot[:]
#print "Ldata['plot']",Ldata['plot']
except ValueError:
Ldata = None
return Ldata
def parse_complex_number(z):
zs = p2sage(z)
z_parsed = "(" + str(real_part(zs)) + "," + str(imag_part(zs)) + ")"
return z_parsed