import copy #treba pre klonovanie zakladnej matice A do B

print("RIESENIE SUSTAVY n-LIN.ROVNIC S n-NEZNAMYMI")
print("KRAMEROVO PRAVIDLO")

#01-podprogram pre determinant rekurzivne
def det(matica):
    n=len(matica) #n je tu aj pocet riadkov matice
    if (n>2):
        i=1
        t=0
        sum=0
        while t<=n-1:
            d={}
            t1=1
            while t1<=n-1:
                m=0
                d[t1]=[]
                while m<=n-1:
                    if (m==t):
                        u=0
                    else:
                        d[t1].append(matica[t1][m])
                    m+=1
                t1+=1
            matica1=[d[x] for x in d]
            sum=sum+i*(matica[0][t])*(det(matica1))
            i=i*(-1)
            t+=1
        return sum
    else:
        return (matica[0][0]*matica[1][1]-matica[0][1]*matica[1][0])

#02-podprogram pre vymenu stlpca za PS
def vymen_PS(A,PS,index_stlpca):
    B=copy.deepcopy(A)
    for i in range(len(PS)):
        B[i][index_stlpca]=PS[i]
    return B

#HLAVNY PROGRAM
#zadanie matice a PS - zatial pracne

A=[[10,2,-1],[5,1,-2],[4,-2,5]]
PS=[11,1,15]

print("A = ",A)
print("PS = ",PS)
"""
#alebo pracne
#Ax=[[11,2,-1],[1,1,-2],[15,-2,5]]
#Ay=[[10,11,-1],[5,1,-2],[4,15,5]]
#Az=[[10,2,11],[5,1,1],[4,-2,15]]
#d=det(A)
#print(d)
#dx=det(Ax)
#print(dx)
#dy=det(Ay)
#print(dy)
#dz=det(Az)
#print(dz)
"""


Ax=vymen_PS(A,PS,0)
#print(Ax)
Ay=vymen_PS(A,PS,1)
#print(Ay)        
Az=vymen_PS(A,PS,2)
#print(Az)        

print("x=",det(Ax)/det(A))
print("y=",det(Ay)/det(A))
print("z=",det(Az)/det(A))

#alebo v cykle
AA=[]
for j in range(len(A)):
    AA.append(vymen_PS(A,PS,j))
    
#print(AA)    
#print(AA[0])
#print(AA[1])
#print(AA[2])

print("x=",det(AA[0])/det(A))
print("y=",det(AA[1])/det(A))
print("z=",det(AA[2])/det(A))

#alebo v cykle po uprave - s printom - aj viac neznámych ako 3
A=[[10,2,-1,-2],[5,1,-2,-3],[4,-2,5,-2],[1,1,1,1]]
PS=[11,1,15,20]

AA=[]
for j in range(len(A)):
    AA.append(vymen_PS(A,PS,j))
    print("x{}=".format(j+1),det(AA[j])/det(A))


"""
#dokaz pre pouzitie copy
import copy
A=[[1,2],[3,4],[5,6]]
print("A1",A)
B=A
C=copy.deepcopy(A)
B[0][1]=22
C[1][1]=222
print("A2",A)
print("B",B)
print("C",C)
"""