#----------------------SPACE WASTING SNAKE------------------------------------------
###infinite snake in n-dim room which includes all existing vectors
###in an enumerable-infinity-order, useful for autoproving n-dimensional expressions
###by Patrick Hammer. Email: patrick.hammer@student.tugraz.at
def existing_vectors_positive(dim, upper_limit=-1): #can be infinite too
    r=1; inv=1; rev=false; step=0
    while upper_limit==-1 or step<upper_limit:
        V=[0 for x in range(dim)]; V[0]=r
        for x in range(1,len(V)):
            Break=false
            for y in range(r):
                W=list(reversed(V)) if rev else V
                yield W; V[x]+=1*inv
        inv=inv*(-1);
        for x in range(0,len(V)):
            Break=false
            for y in range(r+1):
                W=list(reversed(V)) if rev else V
                yield W; V[x]+=1*inv
                if(V[x]==0): Break=true
            if Break: break
        r=r+1; inv=inv*(-1); step+=1; rev=not rev
#------------------------------------------------------------------------------------