def test__get_sig__14(self):
pol = MARing.ring('-x0^2+x1^2+x2^2+x3^2+x4^2')
sig = MARing.get_sig(pol)
print(pol)
print(sig)
assert sig == [1, 4]
def test__get_sig__13(self):
pol = MARing.ring('x4^2-x6*x7 + x2^2-x6*x8 - x2*x4+x0*x6')
sig = MARing.get_sig(pol)
print(pol)
print(sig)
assert sig == [1, 3]
def usecase__classification(cache=True):
'''
Prints a classification of quadratic forms
that contain some fixed double Segre surface S
in projective 8-space, such that the quadratic
form is invariant under subgroup of Aut(S).
We consider subgroups equivalent, if they are
real conjugate in Aut(P^1xP^1).
Parameters
----------
cache : bool
If True, then the cached result is used,
otherwise the output is recomputed. The
computation may take about 9 hours.
'''
key = 'usecase__classification'
if cache and key in MATools.get_tool_dct():
MATools.p(MATools.get_tool_dct()[key])
return
out = ''
for involution in ['identity', 'leftright', 'rotate']:
for c_lst_lst in DSegre.get_c_lst_lst_lst():
#
# compute invariant quadratic forms
#
iq_lst = DSegre.get_invariant_qf(c_lst_lst)
iq_lst = DSegre.change_basis(iq_lst, involution)
iq_lst = MARing.replace_conj_pairs(iq_lst)
#
# computes signatures of random quadrics in
# the vector space of invariant quadratic forms.
#
sig_lst = []
if 'I' not in str(iq_lst):
sig_lst = MARing.get_rand_sigs(iq_lst, 10)
tmp = ''
tmp += '\n\t' + 10 * '-'
tmp += '\n\t involution =' + involution
tmp += '\n\t group =' + DSegre.to_str(c_lst_lst)
tmp += '\n\t invariant ideal = <'
for iq in iq_lst:
sig = ''
if 'I' not in str(iq):
sig = MARing.get_sig(iq)
tmp += '\n\t\t' + str(iq) + '\t\t' + str(sig)
tmp += '\n\t\t >'
tmp += '\n\t random signatures ='
tmp += '\n\t\t ' + str(sig_lst)
for sig in sig_lst:
if 1 in sig:
tmp += '\n\t\t' + str(sig)
tmp += '\n\t' + 10 * '-'
# output obtained info to screen
MATools.p(tmp)
# add to output string
out += tmp
# cache output string
MATools.get_tool_dct()[key] = out
MATools.save_tool_dct()