def intersect(self, other):
u = self % other
t = u.transposition().simplify()
a = []
isPivot = [False for i in range(t.m)]
for i in range(t.n):
for j in range(t.m):
if (t.e[i][j] != rational.number(0)):
if j < self.n:
a += [self.row(j)]
isPivot[j] = True
break
e = []
for i in range(self.n, t.m):
if isPivot[i] == False:
v = matrix(1, self.m,
[[rational.number(0) for x in range(self.m)]])
for j in range(len(a)):
v += a[j].multiply(t.e[j][i])
e += [copy.deepcopy(v.e[0])]
return matrix(len(e), self.m, e)
def value(x):
if (x.n != x.m):
raise Exception("Error: The matrix isn't a determinant.")
x = x.guass()
product = rational.number(1)
for i in range(x.n):
product *= x.e[i][i]
print product
def union(self, other):
u = self % other
t = u.transposition().simplify()
e = []
for i in range(t.n):
pivot = -1
for j in range(t.m):
if (t.e[i][j] != rational.number(0)):
pivot = j
break
if pivot >= 0:
e += [u.e[pivot]]
return matrix(len(e), self.m, e)
def simplify(self):
c = self.guass()
e = c.e
for i in range(c.n):
pivot = -1
for j in range(c.m):
if e[i][j] != rational.number(0):
pivot = j
break
for j in range(c.m)[::-1]:
e[i][j] /= e[i][pivot]
for j in range(i):
for k in range(pivot, c.m)[::-1]:
e[j][k] -= e[i][k] * e[j][pivot] / e[i][pivot]
return c
def __mul__(self, other):
if self.m != other.n:
raise Exception(
"Error: The first matrix's number of cloumns isn't equal to the second matrix's number of rows."
)
return False
e = []
for i in range(self.n):
row = []
for j in range(other.m):
count = rational.number(0)
for k in range(self.m):
count += self.e[i][k] * other.e[k][j]
row += [count]
e += [row]
return matrix(self.n, other.m, e)
def guass(self):
c = copy.deepcopy(self)
e = c.e
n = 0
for i in range(c.m):
pivot = -1
for j in range(n, c.n):
if (e[j][i] != rational.number(0)):
if (pivot == -1 or e[j][i] < e[pivot][i]):
pivot = j
if (pivot == -1):
continue
e[n], e[pivot] = e[pivot], e[n]
for j in range(n + 1, c.n):
for k in range(i, c.m)[::-1]:
e[j][k] -= e[j][i] / e[n][i] * e[n][k]
n += 1
c.n = n
return c
def identity(n):
e = [[rational.number(0) for i in range(n)] for j in range(n)]
for i in range(n):
e[i][i] = rational.number(1)
return matrix(n, n, e)
def solve(self):
t = self.guass()
if (t.n == t.m):
print "It seems that there is no solution to this equation."
return
sol = [0 for i in range(t.m - 1)]
isPivot = [False for i in range(t.m - 1)]
for x in range(t.n)[::-1]:
pivot = -1
for i in range(t.m - 1):
if t.e[x][i] != rational.number(0):
pivot = i
break
isPivot[pivot] = True
sol[pivot] = t.e[x][t.m - 1] / t.e[x][pivot]
for i in range(0, x):
t.e[i][t.m - 1] -= sol[pivot] * t.e[i][pivot]
for i in range(t.m - 1):
sol[i] = str(sol[i])
print str(sol).replace('\'', '')
print '+'
free = []
for i in range(t.m - 1):
if isPivot[i] == False:
free += [i]
freeCount = len(free)
k = [[rational.number(0) for i in range(t.m - 1)]
for i in range(t.m - 1)]
for x in range(t.n)[::-1]:
pivot = -1
for i in range(t.m - 1):
if (pivot == -1):
if t.e[x][i] != rational.number(0):
pivot = i
else:
if isPivot[i]:
for j in range(t.m - 1):
k[pivot][j] -= k[i][j] * t.e[x][i] / t.e[x][pivot]
else:
k[pivot][i] -= t.e[x][i] / t.e[x][pivot]
e = []
for x in range(freeCount):
vector = []
for i in range(t.m - 1):
if i == free[x]:
vector += ['1']
elif isPivot[i]:
vector += [str(k[i][free[x]])]
else:
vector += ['0']
print 'C' + str(x) + str(vector).replace('\'', '')
if x == freeCount - 1:
print 'C0...C' + str(x) + ' can be any integer.'
else:
print '+'
e += vector
return matrix(freeCount, t.m - 1, e)
def parseNumber(s):
if '/' in s:
ss = s.split('/')
return rational.number(int(ss[0]), int(ss[1]))
else:
return rational.number(int(s))