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I want to construct a dictionary where the keys are the subsets of the vertex set $V$ of a randomly generated graph and the values are the maximal indipendent sets (denoted MI in the code) for which the function:

$$w(A,B)=\sum\limits_{i\in A\triangle B}2^i \quad \text{where} \quad A\triangle B=(A\setminus B) \cup (B\setminus A) $$

is minimized, for $A\subset V$ and $B\subset MI$. I am having difficulties on encoding the information in a dictionary. I have spent quite some time and I can not figure out how to do it. Here is the code:

sage: from sage.graphs.independent_sets import IndependentSets
sage: def generate(n):
...       n_0=randint(1,n)
...       G=graphs.RandomGNP(n_0,0.4)
...       V=set(G.vertices())
...       MI=list(IndependentSets(G, maximal = True))
...       d={}
...       
...       for i in Subsets(V):
...           alpha_i=[]

...           print(i)
...           for j in MI:

...               delta_ij=set(i).symmetric_difference(set(j))
...               print(delta_ij)
...               
...               alpha_ij=0
...               for k in delta_ij:
...                   alpha_ij=alpha_ij+2^k
...               print(alpha_ij) 
...               alpha_i.append(alpha_ij)

...           print(alpha_i)

...          
...           ll=MI[alpha_i.index(min(alpha_i))]
...           d.update(tupple(i):ll)
...           print('*******')
...       
...       print("dictionary",d)

When I compile it I get

Traceback (most recent call last):
...
SyntaxError: invalid syntax

Basically it wont let me use MI[alpha_i.index(min(alpha_i))] as a value. In other cases I tried to use lists as values and it seemed to work.

I want to construct a dictionary where the keys are the subsets of the vertex set $V$ of a randomly generated graph and the values are the maximal indipendent sets (denoted MI in the code) for which the function:

$$w(A,B)=\sum\limits_{i\in $$\omega (A,B)=\sum\limits_{i\in A\triangle B}2^i \quad \text{where} \quad A\triangle B=(A\setminus B) \cup (B\setminus A) $$

is minimized, for $A\subset V$ and $B\subset MI$. I am having difficulties on encoding the information in a dictionary. I have spent quite some time and I can not figure out how to do it. Here is the code:

sage: from sage.graphs.independent_sets import IndependentSets
sage: def generate(n):
...       n_0=randint(1,n)
...       G=graphs.RandomGNP(n_0,0.4)
...       V=set(G.vertices())
...       MI=list(IndependentSets(G, maximal = True))
...       d={}
...       
...       for i A in Subsets(V):
...           alpha_i=[]

...           print(i)
...           omega_A=[]         #omega_A will contain  the values ω(A,B) for j B⊂MI

...           print(A)
...           for B in MI:

...               delta_ij=set(i).symmetric_difference(set(j))
...               print(delta_ij)
...               
...               alpha_ij=0
delta_AB=set(A).symmetric_difference(set(B))
...               print(delta_AB)
...               
...               omega_AB=0         #we initialize ω(A,B) for a pair (A,B)
...               for k in delta_ij:
...                   alpha_ij=alpha_ij+2^k
...               print(alpha_ij) 
...               alpha_i.append(alpha_ij)

...           print(alpha_i)

...          
...           ll=MI[alpha_i.index(min(alpha_i))]
...           d.update(tupple(i):ll)
delta_AB:
...                   omega_AB=omega_AB+2^k      #calculate the function ω 
...               print(omega_AB) 
...               omega_A.append(omega_AB)      #add the found value to omega_A

...           print(omega_A)

...          
...           ll=MI[omega_A.index(min(omega_A))]      #find the max. ind. set which minimizes ω(A,B
...           d.update(tuple(A):ll)                       #add the found element to the dictionary d 
...           print('*******')
...       
...       print("dictionary",d)

When I compile it I get

Traceback (most recent call last):
...
SyntaxError: invalid syntax

Basically it wont let me use MI[alpha_i.index(min(alpha_i))] as a value. In other cases I tried to use lists as values and it seemed to work.

I want to construct a dictionary where the keys are the subsets of the vertex set $V$ of a randomly generated graph and the values are the maximal indipendent sets (denoted MI in the code) for which the function:

$$\omega (A,B)=\sum\limits_{i\in A\triangle B}2^i \quad \text{where} \quad A\triangle B=(A\setminus B) \cup (B\setminus A) $$

is minimized, for $A\subset V$ and $B\subset MI$. I am having difficulties on encoding the information in a dictionary. I have spent quite some time and I can not figure out how to do it. Here is the code:

sage: from sage.graphs.independent_sets import IndependentSets
sage: def generate(n):
...       n_0=randint(1,n)
...       G=graphs.RandomGNP(n_0,0.4)
...       V=set(G.vertices())
...       MI=list(IndependentSets(G, maximal = True))
...       d={}
...       
...       for A in Subsets(V):
...           omega_A=[]         #omega_A will contain  the values ω(A,B) for B⊂MI

...           print(A)
...           for B in MI:

...               delta_AB=set(A).symmetric_difference(set(B))
...               print(delta_AB)
...               
...               omega_AB=0         #we initialize ω(A,B) for a pair (A,B)
...               for k in delta_AB:
...                   omega_AB=omega_AB+2^k      #calculate the function ω 
...               print(omega_AB) 
...               omega_A.append(omega_AB)      #add the found value to omega_A

...           print(omega_A)

...          
...           ll=MI[omega_A.index(min(omega_A))]    #find the max. ind. set which minimizes ω(A,B
ω(A,B)
...           d.update(tuple(A):ll)                       #add the found element to the dictionary d 
...           print('*******')
...       
...       print("dictionary",d)

When I compile it I get

Traceback (most recent call last):
...
SyntaxError: invalid syntax

Basically it wont let me use MI[alpha_i.index(min(alpha_i))] as a value. In other cases I tried to use lists as values and it seemed to work.

I want to construct a dictionary where the keys are the subsets of the vertex set $V$ of a randomly generated graph and the values are the maximal indipendent sets (denoted MI in the code) for which the function:

$$\omega (A,B)=\sum\limits_{i\in A\triangle B}2^i \quad \text{where} \quad A\triangle B=(A\setminus B) \cup (B\setminus A) $$

is minimized, for $A\subset V$ and $B\subset MI$. I am having difficulties on encoding the information in a dictionary. I have spent quite some time and I can not figure out how to do it. Here is the code:

sage: from sage.graphs.independent_sets import IndependentSets
sage: def generate(n):
...       n_0=randint(1,n)
...       G=graphs.RandomGNP(n_0,0.4)
...       V=set(G.vertices())
...       MI=list(IndependentSets(G, maximal = True))
...       d={}
...       
...       for A in Subsets(V):
...           omega_A=[]         #omega_A will contain  the values ω(A,B) for B⊂MI

...           print(A)
...           for B in MI:

...               delta_AB=set(A).symmetric_difference(set(B))
...               print(delta_AB)
...               
...               omega_AB=0         #we initialize ω(A,B) for a pair (A,B)
...               for k in delta_AB:
...                   omega_AB=omega_AB+2^k      #calculate the function ω 
...               print(omega_AB) 
...               omega_A.append(omega_AB)      #add the found value to omega_A

...           print(omega_A)

...          
...           ll=MI[omega_A.index(min(omega_A))]  #find the max. ind. set which minimizes ω(A,B)
...           d.update(tuple(A):ll)                       #add the found element to the dictionary d 
...           print('*******')
...       
...       print("dictionary",d)

When I compile it I get

Traceback (most recent call last):
...
SyntaxError: invalid syntax

Basically it wont let me use MI[alpha_i.index(min(alpha_i))] as a value. In other cases I tried to use lists as values and it seemed to work.

I want to construct a dictionary where the keys are the subsets of the vertex set $V$ of a randomly generated graph and the values are the maximal indipendent sets (denoted MI in the code) for which the function:

$$\omega (A,B)=\sum\limits_{i\in A\triangle B}2^i \quad \text{where} \quad A\triangle B=(A\setminus B) \cup (B\setminus A) $$

is minimized, for $A\subset V$ and $B\subset MI$. I am having difficulties on encoding the information in a dictionary. I have spent quite some time and I can not figure out how to do it. Here is the code:

sage: from sage.graphs.independent_sets import IndependentSets
sage: def generate(n):
...       n_0=randint(1,n)
...       G=graphs.RandomGNP(n_0,0.4)
...       V=set(G.vertices())
...       MI=list(IndependentSets(G, maximal = True))
...       d={}
...       
...       for A in Subsets(V):
...           omega_A=[]         #omega_A will contain  the values ω(A,B) for B⊂MI

...           print(A)
...           for B in MI:

...               delta_AB=set(A).symmetric_difference(set(B))
...               print(delta_AB)
...               
...               omega_AB=0         #we initialize ω(A,B) for a pair (A,B)
...               for k in delta_AB:
...                   omega_AB=omega_AB+2^k      #calculate the function ω 
...               print(omega_AB) 
...               omega_A.append(omega_AB)      #add the found value to omega_A

...           print(omega_A)

...          
...           ll=MI[omega_A.index(min(omega_A))]  #find the max. ind. set which minimizes 
                                                                         #minimizes ω(A,B)
...           d.update(tuple(A):ll)                       #add the found element to the dictionary d 
...           print('*******')
...       
...       print("dictionary",d)

When I compile it I get

Traceback (most recent call last):
...
SyntaxError: invalid syntax

Basically it wont let me use MI[alpha_i.index(min(alpha_i))] as a value. In other cases I tried to use lists as values and it seemed to work.

I want to construct a dictionary where the keys are the subsets of the vertex set $V$ of a randomly generated graph and the values are the maximal indipendent sets (denoted MI in the code) for which the function:

$$\omega (A,B)=\sum\limits_{i\in A\triangle B}2^i \quad \text{where} \quad A\triangle B=(A\setminus B) \cup (B\setminus A) $$

is minimized, for $A\subset V$ and $B\subset MI$. I am having difficulties on encoding the information in a dictionary. I have spent quite some time and I can not figure out how to do it. Here is the code:

sage: from sage.graphs.independent_sets import IndependentSets
sage: def generate(n):
...       n_0=randint(1,n)
...       G=graphs.RandomGNP(n_0,0.4)
...       V=set(G.vertices())
...       MI=list(IndependentSets(G, maximal = True))
...       d={}
...       
...       for A in Subsets(V):
...           omega_A=[]         #omega_A will contain  the values ω(A,B) for B⊂MI

...           print(A)
...           for B in MI:

...               delta_AB=set(A).symmetric_difference(set(B))
...               print(delta_AB)
...               
...               omega_AB=0         #we initialize ω(A,B) for a pair (A,B)
...               for k in delta_AB:
...                   omega_AB=omega_AB+2^k      #calculate the function ω 
...               print(omega_AB) 
...               omega_A.append(omega_AB)      #add the found value to omega_A

...           print(omega_A)

...          
...           ll=MI[omega_A.index(min(omega_A))]  #find the max. ind. set which 
                                                                        #minimizes ω(A,B)
...           d.update(tuple(A):ll)    #add the found element to the dictionary d 
...           print('*******')
...       
...       print("dictionary",d)

When I compile it I get

Traceback (most recent call last):
...
SyntaxError: invalid syntax

Basically it wont let me use MI[alpha_i.index(min(alpha_i))] as a value. In other cases I tried to use lists as values and it seemed to work.

I want to construct a dictionary where the keys are the subsets of the vertex set $V$ of a randomly generated graph and the values are the maximal indipendent sets (denoted MI in the code) for which the function:

$$\omega (A,B)=\sum\limits_{i\in A\triangle B}2^i \quad \text{where} \quad A\triangle B=(A\setminus B) \cup (B\setminus A) $$

is minimized, for $A\subset V$ and $B\subset $B \in MI$. I am having difficulties on encoding the information in a dictionary. I have spent quite some time and I can not figure out how to do it. Here is the code:

sage: from sage.graphs.independent_sets import IndependentSets
sage: def generate(n):
...       n_0=randint(1,n)
...       G=graphs.RandomGNP(n_0,0.4)
...       V=set(G.vertices())
...       MI=list(IndependentSets(G, maximal = True))
...       d={}
...       
...       for A in Subsets(V):
...           omega_A=[]         #omega_A will contain  the values ω(A,B) for B⊂MI

...           print(A)
...           for B in MI:

...               delta_AB=set(A).symmetric_difference(set(B))
...               print(delta_AB)
...               
...               omega_AB=0         #we initialize ω(A,B) for a pair (A,B)
...               for k in delta_AB:
...                   omega_AB=omega_AB+2^k      #calculate the function ω 
...               print(omega_AB) 
...               omega_A.append(omega_AB)      #add the found value to omega_A

...           print(omega_A)

...          
...           ll=MI[omega_A.index(min(omega_A))]  #find the max. ind. set which 
                                                                       #minimizes ω(A,B)
...           d.update(tuple(A):ll)   #add the found element to the dictionary d 
...           print('*******')
...       
...       print("dictionary",d)

When I compile it I get

Traceback (most recent call last):
...
SyntaxError: invalid syntax

Basically it wont let me use MI[alpha_i.index(min(alpha_i))] as a value. In other cases I tried to use lists as values and it seemed to work.