def decomposition_display(self):
factors = self.decomp
if len(factors) == 1 and factors[0][1] == 1:
return 'simple'
ans = ''
for factor in factors:
if ans != '':
ans += '$\\times$ '
if factor[1] == 1:
ans += av_display_knowl(factor[0]) + ' '
else:
ans += av_display_knowl(factor[0]) + '<sup> {0} </sup> '.format(factor[1])
return ans
def decomposition_display(self):
factors = self.decomp
if len(factors) == 1 and factors[0][1] == 1:
return 'simple'
ans = ''
for factor in factors:
if ans != '':
ans += '$\\times$ '
if factor[1] == 1:
ans += av_display_knowl(factor[0]) + ' '
else:
ans += av_display_knowl(factor[0]) + '<sup> {0} </sup> '.format(factor[1])
return ans
def decomposition_display(factors):
if len(factors) == 1 and factors[0][1] == 1:
return "simple"
factor_str = ""
for factor in factors:
if factor_str != "":
factor_str += " $\\times$ "
factor_str += av_display_knowl(factor[0])
if factor[1] > 1:
factor_str += "<sup> {0} </sup>".format(factor[1])
return factor_str
def twist_display(self, show_all):
if not self.twists:
return "This isogeny class has no twists."
if show_all:
ans = "Below is a list of all twists of this isogeny class."
else:
ans = "Below are some of the twists of this isogeny class."
ans += '<table class = "ntdata">\n'
ans += "<tr><td>Twist</td><td>Extension Degree</td><td>Common base change</td></tr>\n"
i = 0
for twist in self.twists:
if twist[2] <= 3 or show_all or i < 3:
if self.q**twist[2] <= maxq(self.g, self.p):
bc = av_display_knowl(twist[1])
else:
bc = "(not in LMFDB)"
ans += "<tr><td>%s</td><td>$%s$</td><td>%s</td></tr>\n" % (
av_display_knowl(twist[0]), str(twist[2]), bc)
i += 1
ans += "</table>\n"
return ans
def basechange_display(self):
models = self.prim_models
if len(models) == 0:
return 'primitive'
ans = '<table class = "ntdata">\n'
ans += '<tr><td>Subfield</td><td>Primitive Model</td></tr>\n'
for model in models:
ans += ' <tr><td class="center">$%s$</td><td>'%(self.field(model.split('.')[1]))
ans += av_display_knowl(model) + ' '
ans += '</td></tr>\n'
ans += '</table>\n'
return ans
def basechange_display(self):
models = self.prim_models
if len(models) == 0:
return 'primitive'
ans = '<table class = "ntdata">\n'
ans += '<tr><td>Subfield</td><td>Primitive Model</td></tr>\n'
for model in models:
ans += ' <tr><td class="center">$%s$</td><td>'%(self.field(model.split('.')[1]))
ans += av_display_knowl(model) + ' '
ans += '</td></tr>\n'
ans += '</table>\n'
return ans
def basechange_display(self):
if self.is_primitive:
return "primitive"
else:
models = self.primitive_models
ans = '<table class = "ntdata">\n'
ans += "<tr><td>Subfield</td><td>Primitive Model</td></tr>\n"
for model in models:
ans += ' <tr><td class="center">${0}$</td><td>'.format(self.field(model.split(".")[1]))
ans += av_display_knowl(model) + " "
ans += "</td></tr>\n"
ans += "</table>\n"
return ans
def non_simple_loop(p, factors):
ans = '<ul style="margin-top: 5px;margin-bottom: 8px;">\n'
for factor in factors:
ans += "<li>"
ans += av_display_knowl(factor[0])
if factor[1] > 1:
ans += "<sup> {0} </sup>".format(factor[1])
ans += " : "
end_alg = describe_end_algebra(p, factor[0])
if end_alg is None:
ans += no_endo_data()
elif factor[1] == 1:
ans += end_alg[1]
else:
ans += matrix_display(factor, end_alg)
ans += "</li>\n"
ans += "</ul>\n"
return ans
def display_endo_info(self, degree, do_describe=True):
# When degree > 1 we find the factorization by looking at the extension database
if degree > 1:
factors = self.endo_extension_by_deg(degree)
if not factors:
return "The data at degree %s is missing." % degree, do_describe
ans = "The base change of $A$ to ${0}$ is ".format(
self.ext_field(degree))
else:
factors = list(
zip(self.simple_distinct, self.simple_multiplicities))
if self.is_simple:
ans = "The endomorphism algebra of this simple isogeny class is "
else:
ans = "The isogeny class factors as "
dec_display = decomposition_display(factors)
if dec_display == "simple":
end_alg = describe_end_algebra(self.p, factors[0][0])
if end_alg is None:
return no_endo_data(), do_describe
if degree > 1:
ans += "the simple isogeny class "
ans += av_display_knowl(factors[0][0])
ans += " and its endomorphism algebra is "
ans += end_alg[1]
elif len(factors) == 1:
end_alg = describe_end_algebra(self.p, factors[0][0])
if end_alg is None:
return no_endo_data(), do_describe
ans += dec_display + " and its endomorphism algebra is "
ans += matrix_display(factors[0], end_alg)
else:
ans += dec_display
if do_describe:
ans += " and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor"
do_describe = False
ans += ". The endomorphism algebra for each factor is: \n"
ans += non_simple_loop(self.p, factors)
return ans, do_describe