matrix.py

from functools import reduce
import twobytwo
def dot(a,b):
	return sum([x*y for x,y in zip(a,b)])

def addPart(array):
    return [sum([array[k][i] for k in range(len(array))]) for i in range(len(array[0]))]

class Matrix:
	def __init__(self, rows):
		self.row = rows
	def __repr__(self):
		return '\n'.join([str(i) for i in self.row])
	def __round__(self,n = 0):
		return Matrix([[round(self.row[r][column],n) for column in range(len(self.row[0]))] for r in range(len(self.row))])
	def __abs__(self):
		if len(self.row) > 2:
			a = 0
			for replace, place in enumerate(self.row[0]):
				sec = Matrix([[i for n,i in enumerate(self.row[j]) if (n != replace)] for j in range(1, len(self.row))])
				a += (-1)**replace * place * abs(sec)
			return a
		elif len(self.row) == 2:
			return (self.row[0][0] * self.row[1][1]) - (self.row[0][1] * self.row[1][0])
		else:
			return self.row[0][0]
	def __mul__(self, other):
		if type(other) == Matrix:
			return Matrix([[round(dot(i, [other.row[k][j] for k in range(len(other.row))]),4) for j in range(len(other.row[0]))] for i in self.row])
		return Matrix.scalar(self, other)
	def __add__ (self, other):
		return Matrix([[self.row[k][i] + other.row[k][i] for i in range(len(self.row[0]))] for k in range(len(self.row))])
	def __neg__(self):
		return Matrix([[-1 * i for i in j] for j in self.row])
	def __sub__(self,other):
		return Matrix([self + -other])
	def __truediv__(self, other):
		return Matrix(self * ~other)
	def transpose(self):
		return Matrix([[self.row[k][i] for k in range(len(self.row[0]))] for i in range(len(self.row))])
	def scalar(self, number):
		return Matrix([[round(number * i,4) for i in j] for j in self.row])
	def __pow__(self, power):
		g = [self for i in range(power)]
		return reduce(lambda x,y: x * y, g)
	def __invert__(self):
		try:
			determinant = abs(self)
		except:
			return self #Returns, if invertible
		news = Matrix.transpose(self)
		news = [[(-1) ** (column + row) * abs(Matrix([[news.row[k][i] for i in range(len(self.row[0])) if i != column] for k in range(len(self.row)) if k != row])) for column in range(len(self.row[0]))] for row in range(len(self.row))]
		return Matrix.scalar( Matrix(news),1/determinant)
	def ref(self): #row-eschilon form
		if len(self.row) == 2:
			return Matrix(twobytwo.func(self.row))
		else:
			array = twobytwo.toPos(self.row, 0)
			Barray = Matrix.ref(Matrix([i[1:] for i in array[1:]]))
			array = [array[0]]  + [[0] + Barray[i] for i in range(len(Barray.row))] #For n x m array, it solves the bottom right (n-1) x (m-1)
			for i in range(1,len(array)): #Can't do it inline
				array[0] = addPart([array[0], twobytwo.multList(-array[0][i],array[i])]) #Solves for one, but it still won't be simplified
			array[0] = twobytwo.multList(1/array[0][0], array[0]) #simplify
		return Matrix(array)
	def solve(self):
		a = Matrix.ref(self)
		b = '(' + ','.join([str(i[-1]) for i in a.row]) + ")"
		return b
	def __getitem__(self, item):
		return self.row[item]
                
mat = Matrix([[1,2,0,0],[0,1,9,0],[8,0,1,0],[4,3,5,1]])

a = Matrix([[1,2],[3,4]])
b = Matrix([[4,3],[2,1]])
g = [a-b,~a * abs(a), a ** 15, a * b, b * a, (b * a)[0], a / b]

x = Matrix([[1,3,7],[2,4,10]])
print(x.solve())
print()
print('\n\n'.join([str(i) for i in g]))