I asked this thing because a friend of mine made code for this but it is very time taking. For 2nd order matrices output comes out instantly. For 3rd order , output starts coming but it is taking a lot of time. For 4th order , no output is shown even after hours. Since for 2nd order, number of elements in V.List is 2^4, for 3rd order it is 2^9 and for 4th order it is 2^16 so it is time taking. Can any change be made to make this code run faster?

Program to get all the combinations of 0,1 and 0,-1 matrices which when added up, give the required matrix.

Write your matrix

H = matrix(2,2, [1, 1,1, -1])

H=matrix(3,3,[1,0,1,-1,1,0,0,-1,1])

H=matrix(4,4,[1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1])

show("H=",H)

n = int(input("Enter the order of the matrix H : "))

V = GF(2)^(n^2)

show("V.List=", V.list())

R1=V.list()[1:] #We are removing the all-zero list because not needed for our purpose

show("R1=", R1)

R2=R1[:-1] #We are removing the all-ones list because not needed for our purpose

show("R2=", R2)

A = [] for v in R2: A.append(matrix(ZZ,n,n,v)) #Here we are forming n by n matrices from list in R2

show("A=",A) #This contains all 0,1 matrices

B=[] for a in A: b=-a B.append(b)

show("B=",B) #Here we are forming n by n matrices from A

                                           #by taking their negative.
                                          #This contains all 0,-1 matrices

C = [] for a in A: C.append(a) for b in B: C.append(b)

show("C=",C) #Here we are taking the union of A and B

test_sum = int(input("Into how many matrices you want to break H :"))

test_comb = Combinations(C,test_sum) # Here we are forming all "test_sum"-set combinations from C". That is if #test_sum =3, then test_comb, gives all 3 set combinations from C"

for t in test_comb: if (sum(t)==H): #Checking which combinations in test_sum give the sum = H and printing those

    print("A combination is: ")    
    show(t)                     
    print("\n")

I asked this thing because a friend of mine made code for this but it is very time taking. For 2nd order matrices output comes out instantly. For 3rd order , output starts coming but it is taking a lot of time. For 4th order , no output is shown even after hours. Since for 2nd order, number of elements in V.List is 2^4, for 3rd order it is 2^9 and for 4th order it is 2^16 so it is time taking. Can any change be made to make this code run faster?

Program to get all the combinations of 0,1 and 0,-1 matrices which when added up, give the required matrix.

Write your matrix

H = matrix(2,2, [1, 1,1, -1])

show("H=",H)

n = int(input("Enter the order of the matrix H : "))

V = GF(2)^(n^2)

R1=V.list()[1:] #We are removing the all-zero list because not needed for our purpose

R2=R1[:-1] #We are removing the all-ones list because not needed for our purpose

A = [] for v in R2: A.append(matrix(ZZ,n,n,v)) # Forming n by n matrices from list in R2. Contains all 0,1 matrices

B=[] for a in A: b=-a B.append(b)
#Here we are forming n by n matrices from list in R2

show("A=",A) #This contains all 0,1 matrices

B=[] for a in A: b=-a B.append(b)

show("B=",B) #Here we are forming n A by n matrices from A

                                           #by taking their negative.
                                          #This negative. his contains all 0,-1 matrices

C = [] for a in A: C.append(a) for b in B: C.append(b)

show("C=",C) C.append(b) #Here we are taking the union of A and B

test_sum = int(input("Into how many matrices you want to break H :"))

test_comb = Combinations(C,test_sum) # Here we are forming all "test_sum"-set combinations from C". That is if #test_sum =3, then test_comb, gives all 3 set combinations from C"

for t in test_comb: if (sum(t)==H): #Checking which combinations in test_sum give the sum = H and printing those

    print("A combination is: ")    
    show(t)                     
    print("\n")

I asked this thing because a friend of mine made code for this but it is very time taking. For 2nd order matrices output comes out instantly. For 3rd order , output starts coming but it is taking a lot of time. For 4th order , no output is shown even after hours. Since for 2nd order, number of elements in V.List is 2^4, for 3rd order it is 2^9 and for 4th order it is 2^16 so it is time taking. Can any change be made to make this code run faster?

Write your matrix

H = matrix(2,2, [1, 1,1, -1])

show("H=",H)

n = int(input("Enter the order of the matrix H : "))

V = GF(2)^(n^2)

R1=V.list()[1:]
#We are removing the all-zero list because not needed for our purpose

R2=R1[:-1]
#We are removing the all-ones list because not needed for our purpose

A = [] for v in R2: A.append(matrix(ZZ,n,n,v))
# Forming n by n matrices from list in R2. Contains all 0,1 matricesmatrices.

B=[] for a in A: b=-a B.append(b)
#Here we are forming # Forming n by n matrices from A by taking their negative. his contains Contains all 0,-1 matrices

C = [] for a in A: C.append(a) for b in B: C.append(b) #Here we are taking the C.append(b) #Taking union of A and B

test_sum = int(input("Into how many matrices you want to break H :"))

test_comb = Combinations(C,test_sum)
# Here we are forming all "test_sum"-set combinations from C".
# That is is, if #test_sum test_sum =3, then test_comb, gives all 3 set combinations from C"

for t in test_comb: if (sum(t)==H):
#Checking which combinations in test_sum give the sum = H and printing those

    print("A combination is: ")    
    show(t)                     
    print("\n")

I asked this thing because a friend of mine made code for this but it is very time taking. For 2nd order matrices output comes out instantly. For 3rd order , output starts coming but it is taking a lot of time. For 4th order , no output is shown even after hours. Since for 2nd order, number of elements in V.List is 2^4, for 3rd order it is 2^9 and for 4th order it is 2^16 so it is time taking. Can any change be made to make this code run faster?

those
        print("A combination is: ")    
     show(t)                     
     print("\n")