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I want to define all functions from a finite subset (which is closed under addition) of \mathbb{N} to another finite subset of \mathbb{N}( target set is {0,1} in my case) with some special properties e.g. f is in my collection if and only if f is additive. I came across this type of problem as a part of my research. (e.g. the set of ways we can color a finite graph with finite set of colors where is the set of vertices we have a binary operation). Of course theoretically we can do it by considering power sets ( considering all elements which are mapped to 1) which is not helpful while programming is Sage. Later I have to run my program over this collection to reach the destination.

I tried with the following code which isn't helpful when the number of vertices is little large.

def Lab_Funs(M):
P=list(powerset(M))
l=len(P)
F=list(var('F_%d' % i) for i in range(l))

for i in range(l):
    Q=P[i];
    F[i]=[];
    for s in range(len(M)):
        if M[s] in Q:
            F[i]=F[i]+[(M[s],1)];
        else:
            F[i]=F[i]+[(M[s],0)]
return([F[i] for i in range(l)])

def Req_Lab_Funs(M,y):
RLF=[];
for f in Lab_Funs(M):
    k=1;
    for s in range(len(M)):
        for p in range(len(M)):
            if plus(f[s][0],f[p][0])[1]==1:
                N=plus(f[s][0],f[p][0])[0];
                r=M.index(N);
                if f[s][1]+f[p][1]!=f[r][1]:
                    k=0;
    if k>0:
        L=[f[r][0] for r in range(len(M))];
        t=L.index(y);
        if f[t][1]==1:
            RLF=RLF+[f]
return(RLF)

Lab_Funs: Labeling functions Req_Lab_Funs: Required Labeling functions.

Any suggestion or help is highly appreciated.

Thank you for your help in advance.

I want to define all functions from a finite subset (which is closed under addition) of \mathbb{N} to another finite subset of \mathbb{N}( target set is {0,1} in my case) with some special properties e.g. f is in my collection if and only if f is additive. I came across this type of problem as a part of my research. (e.g. the set of ways we can color a finite graph with finite set of colors where is the set of vertices we have a binary operation). Of course theoretically we can do it by considering power sets ( considering all elements which are mapped to 1) which is not helpful while programming is Sage. Later I have to run my program over this collection to reach the destination.

I tried with the following code which isn't helpful when the number of vertices is little large.

def Lab_Funs(M):
P=list(powerset(M))
l=len(P)
F=list(var('F_%d' % i) for i in range(l))

for i in range(l):
    Q=P[i];
    F[i]=[];
    for s in range(len(M)):
        if M[s] in Q:
            F[i]=F[i]+[(M[s],1)];
        else:
            F[i]=F[i]+[(M[s],0)]
return([F[i] for i in range(l)])

def Req_Lab_Funs(M,y):
RLF=[];
for f in Lab_Funs(M):
    k=1;
    for s in range(len(M)):
        for p in range(len(M)):
            if plus(f[s][0],f[p][0])[1]==1:
                N=plus(f[s][0],f[p][0])[0];
                r=M.index(N);
                if f[s][1]+f[p][1]!=f[r][1]:
                    k=0;
    if k>0:
        L=[f[r][0] for r in range(len(M))];
        t=L.index(y);
        if f[t][1]==1:
            RLF=RLF+[f]
return(RLF)

Lab_Funs: Labeling functions Req_Lab_Funs: Required Labeling functions.

Any suggestion or help is highly appreciated.

Thank you for your help in advance.

I want to define all functions from a finite subset (which is closed under addition) of \mathbb{N} $\mathbb{N}$ to another finite subset of \mathbb{N}( target $\mathbb{N}$ (target set is {0,1} in my case) with some special properties e.g. f is in my collection if and only if f is additive. I came across this type of problem as a part of my research. (e.g. the set of ways we can color a finite graph with finite set of colors where is the set of vertices we have a binary operation). Of course theoretically we can do it by considering power sets ( considering (considering all elements which are mapped to 1) which is not helpful while programming is Sage. Later I have to run my program over this collection to reach the destination.

I tried with the following code which isn't helpful when the number of vertices is little large.

def Lab_Funs(M):
P=list(powerset(M))
l=len(P)
F=list(var('F_%d'     P = list(powerset(M))
    l = len(P)
    F = list(var('F_%d' % i) for i in range(l))
  for i in range(l):
    Q=P[i];
    F[i]=[];
    Q = P[i]
        F[i] = []
        for s in range(len(M)):
         if M[s] in Q:
            F[i]=F[i]+[(M[s],1)];
    F[i] = F[i] + [(M[s], 1)]
            else:
            F[i]=F[i]+[(M[s],0)]
return([F[i]     F[i] = F[i] + [(M[s], 0)]
    return [F[i] for i in range(l)])
range(l)]

def Req_Lab_Funs(M,y):
RLF=[];
Req_Lab_Funs(M, y):
    RLF = []
    for f in Lab_Funs(M):
    k=1;
    k = 1
        for s in range(len(M)):
         for p in range(len(M)):
             if plus(f[s][0],f[p][0])[1]==1:
                N=plus(f[s][0],f[p][0])[0];
                r=M.index(N);
plus(f[s][0], f[p][0])[1] == 1:
                    N = plus(f[s][0], f[p][0])[0]
                    r = M.index(N)
                    if f[s][1]+f[p][1]!=f[r][1]:
                    k=0;
f[s][1] + f[p][1] != f[r][1]:
                        k = 0
        if k>0:
        L=[f[r][0] k > 0:
            L = [f[r][0] for r in range(len(M))];
        t=L.index(y);
range(len(M))]
            t = L.index(y)
            if f[t][1]==1:
            RLF=RLF+[f]
return(RLF)
f[t][1] == 1:
                RLF = RLF + [f]
    return RLF

Lab_Funs: Labeling functions Req_Lab_Funs: Required Labeling functions.

Any suggestion or help is highly appreciated.

Thank you for your help in advance.

I want to define all functions from a finite subset (which is closed under addition) of $\mathbb{N}$ to another finite subset of $\mathbb{N}$ (target set is {0,1} in my case) with some special properties e.g. f is in my collection if and only if f is additive. I came across this type of problem as a part of my research. (e.g. the set of ways we can color a finite graph with finite set of colors where is the set of vertices we have a binary operation). Of course theoretically we can do it by considering power sets (considering all elements which are mapped to 1) which is not helpful while programming is Sage. Later I have to run my program over this collection to reach the destination.

I tried with the following code which isn't helpful when the number of vertices is little large.

def Lab_Funs(M):
    P = list(powerset(M))
    l = len(P)
    F = list(var('F_%d' % i) for i in range(l))
    for i in range(l):
        Q = P[i]
        F[i] = []
        for s in range(len(M)):
            if M[s] in Q:
                F[i] = F[i] + [(M[s], 1)]
            else:
                F[i] = F[i] + [(M[s], 0)]
    return [F[i] for i in range(l)]

def Req_Lab_Funs(M, y):
    RLF = []
    for f in Lab_Funs(M):
        k = 1
        for s in range(len(M)):
            for p in range(len(M)):
                if plus(f[s][0], f[p][0])[1] == 1:
                    N = plus(f[s][0], f[p][0])[0]
                    r = M.index(N)
                    if f[s][1] + f[p][1] != f[r][1]:
                        k = 0
        if k > 0:
            L = [f[r][0] for r in range(len(M))]
            t = L.index(y)
            if f[t][1] == 1:
                RLF = RLF + [f]
    return RLF

Lab_Funs: Labeling functions Req_Lab_Funs: Required Labeling functions.

Any suggestion or help is highly appreciated.

Thank you for your help in advance.