def download_full_space(self, label, lang='text'):
try:
space = WebGamma1Space.by_label(label)
except ValueError:
return abort(404, "Label not found: %s"%label)
data = {}
for attr in ['level', 'weight', 'label', 'oldspaces']:
data[attr] = getattr(space, attr)
data['newspaces'] = [spc['label'] for spc, forms in space.decomp]
data['newforms'] = sum([[form['label'] for form in forms] for spc, forms in space.decomp], [])
data['dimgrid'] = space.dim_grid._grid
return self._wrap(Json.dumps(data),
label,
lang=lang,
title='Stored data for newspace %s,'%(label))
def download_full_space(self, label, lang='text'):
try:
space = WebGamma1Space.by_label(label)
except ValueError:
return abort(404, "Label not found: %s"%label)
data = {}
for attr in ['level', 'weight', 'label', 'oldspaces']:
data[attr] = getattr(space, attr)
data['newspaces'] = [spc['label'] for spc, forms in space.decomp]
data['newforms'] = sum([[form['label'] for form in forms] for spc, forms in space.decomp], [])
data['dimgrid'] = space.dim_grid._grid
return self._wrap(Json.dumps(data),
label,
lang=lang,
title='Stored data for newspace %s,'%(label))
def render_full_gamma1_space_webpage(label):
try:
space = WebGamma1Space.by_label(label)
except (TypeError, KeyError, ValueError) as err:
return abort(404, err.args)
info = {}
set_info_funcs(info)
return render_template("cmf_full_gamma1_space.html",
info=info,
space=space,
properties2=space.properties,
downloads=space.downloads,
credit=credit(),
bread=space.bread,
learnmore=learnmore_list(),
title=space.title,
friends=space.friends)
def paintSvgHoloGeneral(Nmin, Nmax, kmin, kmax, imagewidth, imageheight):
# the import must be here to avoid circular import
from lmfdb.classical_modular_forms.web_newform import WebNewform
from lmfdb.classical_modular_forms.web_space import WebGamma1Space
xfactor = 90
yfactor = 30
extraSpace = 20
ticlength = 4
radius = 3.3
xdotspacing = 0.30 # horizontal spacing of dots
ydotspacing = 0.11 # vertical spacing of dots
# colourplus = signtocolour(1) # not used
# colourminus = signtocolour(-1) # not used
maxdots = 5 # max number of dots to display
ans = svgBegin()
xMax = int(Nmax)
yMax = int(kmax)
width = xfactor * xMax + extraSpace
height = yfactor * yMax + extraSpace
# make the coordinate system
ans += paintCSHoloTMP(width, height, xMax, yMax, xfactor, yfactor,
ticlength)
alphabet = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j']
# create appearanceinfo, common to all points
appearanceinfo = []
# loop over levels and weights, using plotsector to put the appropriate dots at each lattice point
for x in range(int(Nmin), int(Nmax) + 1): # x is the level
for y in range(int(kmin), int(kmax) + 1, 2): # y is the weight
# lid = "(" + str(x) + "," + str(y) + ")" # not used
# linkurl = "/L/ModularForm/GL2/Q/holomorphic/" + str(y) + "/" + str(x) + "/1/" # not used
WS = WebGamma1Space(
level=x,
weight=y) # space of modular forms of weight y, level x
galois_orbits = WS.decomp # make a list of Galois orbits
numlabels = len(galois_orbits) # one label per Galois orbit
thelabels = alphabet[
0:
numlabels] # list of labels for the Galois orbits for weight y, level x
# countplus = 0 # count how many Galois orbits have sign Plus (+ 1) (not used)
# countminus = 0 # count how many Galois orbits have sign Minus (- 1) (not used)
# ybaseplus = y # baseline y-coord for plus cases (not used)
# ybaseminus = y # baseline y-coord for minus cases (not used)
# numpluslabels = 0 # not used
# numminuslabels = 0 # not used
# plotsector requires three dictionaries: dimensioninfo, appearanceinfo, and urlinfo
# create dimensioninfo
dimensioninfo = {}
dimensioninfo['offset'] = [0, height]
dimensioninfo['scale'] = [xfactor, -1 * yfactor]
dimensioninfo['vertexlocation'] = [x, y]
dimensioninfo['maxdots'] = maxdots
dimensioninfo['dotspacing'] = [xdotspacing, ydotspacing]
dimensioninfo['edge'] = [[0, 1], [1, 0]
] # unit vectors defining edges of sector
# dimensioninfo['edgelength'] = [float(dimensioninfo['scale'][0])/float(Nmax), float(dimensioninfo['scale'][1])/float(kmax)] #add comment
dimensioninfo['edgelength'] = [0.5, 0.5]
dimensioninfo['dotradius'] = radius
dimensioninfo[
'connectinglinewidth'] = dimensioninfo['dotradius'] / 1.5
dimensioninfo['firstdotoffset'] = [0.0, 0.0]
#
appearanceinfo = {}
# appearanceinfo['edgewidth'] = dimensioninfo['dotspacing'][0]/1.0 #just a guess
appearanceinfo['edgewidth'] = [0, 0] # remove the sector edges
appearanceinfo['edgestyle'] = 'stroke-dasharray:3,3'
appearanceinfo['edgecolor'] = 'rgb(202,202,102)'
appearanceinfo['fontsize'] = 'font-size:11px'
appearanceinfo['fontweight'] = ""
#
urlinfo = {'base': '/L/ModularForm/GL2/Q/holomorphic?'}
urlinfo['space'] = {'weight': y}
urlinfo['space']['level'] = x
urlinfo['space']['character'] = 0
#
# scale = 1 # not used
# Symmetry types: +1 or -1
symmetrytype = [1, -1]
for signtmp in symmetrytype:
# urlinfo['space']['orbits'] = [ [] for label in thelabels ] # initialise
# an empty list for each orbit
urlinfo['space']['orbits'] = []
for label in thelabels: # looping over Galois orbit: one label per orbit
# do '+' case first
MF = WebNewform.by_label(
label=label
) # one of the Galois orbits for weight y, level x
numberwithlabel = MF.degree(
) # number of forms in the Galois orbit
if x == 1: # For level 1, the sign is always plus
signfe = 1
else:
# signfe = -1
frickeeigenvalue = prod(MF.atkin_lehner_eigenvalues(
).values()) # gives Fricke eigenvalue
signfe = frickeeigenvalue * (-1)**float(
y / 2) # sign of functional equation
if signfe == signtmp: # we find an orbit with sign of "signtmp"
if signfe == 1:
dimensioninfo['edge'] = [[0, 1], [1, 0]]
# unit vectors defining edges of sector for signfe positive
else:
# dimensioninfo['edge'] = [[0,1],[-1,0]] # unit vectors defining edges
# of sector for signfe negative
dimensioninfo['edge'] = [[0, -1], [-1, 0]]
# unit vectors defining edges of sector for signfe negative
dimensioninfo['dotspacing'] = [
signfe * xdotspacing, ydotspacing
]
dimensioninfo['firstdotoffset'] = [
0.5 * (dimensioninfo['dotspacing'][0] *
dimensioninfo['edge'][0][0] +
dimensioninfo['dotspacing'][1] *
dimensioninfo['edge'][1][0]), 0
]
signcolour = signtocolour(signfe)
appearanceinfo['edgecolor'] = signcolour
orbitdescriptionlist = []
for n in range(numberwithlabel):
orbitdescriptionlist.append({
'label': label,
'number': n,
'color': signcolour
})
urlinfo['space']['orbits'].append(orbitdescriptionlist)
# urlinfo['space']['orbits'][0][0]['color'] = signtocolour(-1)
# appearanceinfo['orbitcolor'] = 'rgb(102,102,102)'
ans += plotsector(dimensioninfo, appearanceinfo, urlinfo)
ans += svgEnd()
return (ans)
def paintSvgHolo(Nmin, Nmax, kmin, kmax):
# the import must be here to avoid circular import
from lmfdb.classical_modular_forms.web_space import WebGamma1Space
xfactor = 90
yfactor = 30
extraSpace = 20
ticlength = 4
radius = 3.3
xdotspacing = 0.11 # horizontal spacing of dots
ydotspacing = 0.28 # vertical spacing of dots
colourplus = signtocolour(1)
colourminus = signtocolour(-1)
maxdots = 5 # max number of dots to display
ans = svgBegin()
xMax = int(Nmax)
yMax = int(kmax)
width = xfactor * xMax + extraSpace
height = yfactor * yMax + extraSpace
ans += paintCSHolo(width, height, xMax, yMax, xfactor, yfactor, ticlength)
# alphabet = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j']
# loop over levels and weights
for x in range(int(Nmin), int(Nmax) + 1): # x is the level
for y in range(int(kmin), int(kmax) + 1): # y is the weight
# lid = "(" + str(x) + "," + str(y) + ")" # not used
linkurl = "/L/ModularForm/GL2/Q/holomorphic/" + str(x) + "/" + str(
y) + "/1/"
try:
WS = WebGamma1Space(level=x, weight=y)
except ValueError:
continue
newspaces = WS.decomp
# numlabels = len(WS.decomp) # one label per Galois orbit
# thelabels = alphabet[0:numlabels] # list of labels for the Galois orbits for weight y, level x
# countplus = 0 # count how many Galois orbits have sign Plus (+ 1) # not used
# countminus = 0 # count how many Galois orbits have sign Minus (- 1) # not used
ybaseplus = y # baseline y-coord for plus cases
ybaseminus = y # baseline y-coord for minus cases
numpluslabels = 0
numminuslabels = 0
for newsp in newspaces: # looping over Galois orbit
for MF in newsp[1]:
print(MF)
linkurl = "/L/ModularForm/GL2/Q/holomorphic/%d/%d/%s/%s/" % (
x, y, MF['char_orbit_label'],
cremona_letter_code(MF['hecke_orbit'] - 1))
numberwithlabel = MF[
'dim'] # number of forms in the Galois orbit
# frickeeigenvalue = prod(MF.atkin_lehner_eigenvalues().values()) # gives Fricke eigenvalue
self_dual = MF['char_is_real'] * (-1)**float(
y / 2) # sign of functional equation
xbase = x - self_dual * (xdotspacing / 2.0)
if self_dual > 0: # go to right in BLUE if plus
ybase = ybaseplus
ybaseplus += ydotspacing
thiscolour = colourplus
numpluslabels += 1
else: # go to the left in RED of minus
ybase = ybaseminus
ybaseminus += ydotspacing
thiscolour = colourminus
numminuslabels += 1
if numberwithlabel > maxdots: # if more than maxdots in orbit, use number as symbol
xbase += 1.5 * self_dual * xdotspacing
if self_dual < 0: # move over more to position numbers on minus side.
xbase += self_dual * xdotspacing
ybase += -0.5 * ydotspacing
if (self_dual > 0 and numpluslabels > 1) or (
self_dual < 0 and numminuslabels > 1):
ybase += ydotspacing
ans += "<a xlink:href='" + url_for(
'not_yet_implemented') + "' target='_top'>\n"
# TODO: Implement when there is more than maxdots forms
ans += ("<text x='" +
str(float(xbase) * xfactor)[0:7] + "' y='" +
str(height - float(ybase) * yfactor)[0:7] +
"' style='fill:" + thiscolour +
";font-size:14px;font-weight:bold;'>" +
str(numberwithlabel) + "</text>\n")
ans += "</a>\n"
if self_dual < 0:
ybaseminus += 1.5 * ydotspacing
else:
ybaseplus += 1.5 * ydotspacing
else: # otherwise, use one dot per form in orbit, connected with a line
if numberwithlabel > 1: # join dots if there are at least two
# add lines first and then dots to prevent line from hiding link
firstcenterx = xbase + self_dual * xdotspacing
firstcentery = ybase
lastcenterx = xbase + (numberwithlabel *
self_dual * xdotspacing)
lastcentery = ybase
ans += "<line x1='%s' " % str(
float(firstcenterx) * xfactor)[0:7]
ans += "y1='%s' " % str(
float(height - firstcentery * yfactor))[0:7]
ans += "x2='%s' " % str(
float(lastcenterx) * xfactor)[0:7]
ans += "y2='%s' " % str(
float(height - lastcentery * yfactor))[0:7]
ans += "style='stroke:%s;stroke-width:2.4'/>" % thiscolour
for number in range(0, numberwithlabel):
xbase += self_dual * xdotspacing
ans += "<a xlink:href='" + linkurl + str(
number + 1) + "/' target='_top'>\n"
ans += "<circle cx='" + str(
float(xbase) * xfactor)[0:7]
ans += "' cy='" + str(height -
float(ybase) * yfactor)[0:7]
ans += "' r='" + str(radius)
ans += "' style='fill:" + thiscolour + "'>"
ans += "<title>" + str((x, y)).replace(
"u", "").replace("'", "") + "</title>"
ans += "</circle></a>\n"
ans += svgEnd()
return ans