相关疑难解决方法(0)

我想测试特定类型的随机矩阵在有限域上是否可逆,特别是F_2.我可以使用以下简单代码测试矩阵在实数上是否可逆.

import random
from scipy.linalg import toeplitz
import numpy as np
n=10
column = [random.choice([0,1]) for x in xrange(n)]
row = [column[0]]+[random.choice([0,1]) for x in xrange(n-1)]
matrix = toeplitz(column, row)
if (np.linalg.matrix_rank(matrix) < n):
    print "Not invertible!"

有没有办法实现同样的事情,但超过F_2？

我想在galois字段(GF4)上使用numpy数组.所以,我将GF4类设置为数组元素.它适用于数组+整数计算,但它不适用于数组+数组计算.

import numpy

class GF4(object):
    """class for galois field"""
    def __init__(self, number):
        self.number = number
        self.__addL__ = ((0,1,2,3),(1,0,3,2),(2,3,0,1),(3,2,1,0))
        self.__mulL__ = ((0,0,0,0),(0,1,2,3),(0,2,3,1),(0,3,1,2))
    def __add__(self, x):
        return self.__addL__[self.number][x]
    def __mul__(self, x):
        return self.__mulL__[self.number][x]
    def __sub__(self, x):
        return self.__addL__[self.number][x]
    def __div__(self, x):
        return self.__mulL__[self.number][x]
    def __repr__(self):
        return str(self.number)

a = numpy.array([GF4(numpy.random.randint(4)) for i in range(18)]).reshape(3,6)
b = numpy.array([GF4(numpy.random.randint(4)) for i in range(18)]).reshape(3,6)

""""
In [261]: a
Out[261]: 
array([[1, 1, 2, 0, 2, 1],
       [0, 3, 1, 0, 3, 1],
       [1, 2, 0, 3, …