N=14 #butterfly big
R=PolynomialRing(ZZ,['x%s'%(p+1) for p in range(N)],N,order='lex')
R.inject_variables()
F=[x1*x7+x1*x5*x8+x3*x6*x8-1,x2*x7+x2*x5*x8+x4*x6*x8]
F+=[x1*x9+x1*x5*x10+x3*x6*x10,x2*x9+x2*x5*x10+x4*x6*x10-1]
F+=[x1*x5*x11+x3*x5*x11+x3*x12-1,x2*x5*x11+x4*x6*x11+x4*x12]
F+=[x1*x5*x13+x3*x6*x13+x3*x14,x2*x5*x13+x4*x6*x13+x4*x14-1]
Defining x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14 Defining x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14 |
g=Ideal(F).groebner_basis(algorithm='singular:std')
lcm([x.lc() for x in g])
2 2 |
if sum([x.is_constant() for x in g])>1:
print "potrebno je uraditi gcd svih"
if sum([x.is_constant() for x in g])>0:
if 1 in g:
print "no solution"
else:
k=[x for x in g if x.is_constant()][0]
char=prime_factors(k)
print "karakteristike su",char
else:
k=lcm([x.lc() for x in g])
g1=Ideal(g+[k]).groebner_basis(algorithm='singular:std')
k1=[x for x in g1 if x.is_constant()][0]
char=[x for x in primes(10) if x not in prime_factors(k) or x in prime_factors(k1)]
print "karakterisike su char=",char, " a lose karakteristike su",[x for x in primes(10) if x not in char]
karakterisike su char= [2, 3, 5, 7] a lose karakteristike su [] karakterisike su char= [2, 3, 5, 7] a lose karakteristike su [] |
field_extension=1
char_iter=0
min_field=infinity
while char_iter<len(char):
print "da li u polju GF(",char[char_iter],"^",field_extension,") postoji resenje"
if char[char_iter]^field_extension > min_field:
print "ne vredi povecavati"
field_extension=1
char_iter+=1
continue
field_equations=[]
for v in R.gens():
field_equations += [v^(char[char_iter]^field_extension)-v]
I=Ideal(F+field_equations).change_ring(R.change_ring(GF(char[char_iter]^field_extension, name='alpha')))
g=I.groebner_basis()
if 1 not in g:
print "imamo resenje u polju velicine min_field=",char[char_iter]^field_extension
min_field=char[char_iter]^field_extension
char_iter+=1
field_extension=1
else:
print "nema resenje za polje velicine ",char[char_iter]^field_extension
field_extension+=1
da li u polju GF( 2 ^ 1 ) postoji resenje imamo resenje u polju velicine min_field= 2 da li u polju GF( 3 ^ 1 ) postoji resenje ne vredi povecavati da li u polju GF( 5 ^ 1 ) postoji resenje ne vredi povecavati da li u polju GF( 7 ^ 1 ) postoji resenje ne vredi povecavati da li u polju GF( 2 ^ 1 ) postoji resenje imamo resenje u polju velicine min_field= 2 da li u polju GF( 3 ^ 1 ) postoji resenje ne vredi povecavati da li u polju GF( 5 ^ 1 ) postoji resenje ne vredi povecavati da li u polju GF( 7 ^ 1 ) postoji resenje ne vredi povecavati |
import networkx
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K=networkx.complete_graph(3)
K.adj
{0: {1: {}, 2: {}}, 1: {0: {}, 2: {}}, 2: {0: {}, 1: {}}}
{0: {1: {}, 2: {}}, 1: {0: {}, 2: {}}, 2: {0: {}, 1: {}}}
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K.cho
<networkx.classes.graph.Graph object at 0x622ba10> <networkx.classes.graph.Graph object at 0x622ba10> |
D=DiGraph(K)
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D
Digraph on 3 vertices Digraph on 3 vertices |
G=Graph(networkx.complete_graph(10))
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G.delete_edge(9,3)
Traceback (click to the left of this block for traceback) ... NameError: name 'G' is not defined Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "_sage_input_3.py", line 10, in <module>
exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("Ry5kZWxldGVfZWRnZSg5LDMp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
File "", line 1, in <module>
File "/tmp/tmpo43OXa/___code___.py", line 3, in <module>
exec compile(u'G.delete_edge(_sage_const_9 ,_sage_const_3 )
File "", line 1, in <module>
NameError: name 'G' is not defined
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G.chromatic_number()
3 3 |
G.show()
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