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import numpy as np
d = {'a': 0, 'b': 1, 'c': 2, 'd': 3}
d1 = 'abcd'
n = len(d)
cayley = [
list("abab"),
list("abab"),
list("abcd"),
list("abcd"),
]
for i in range(n):
for j in range(n):
elem = cayley[i][j]
cayley[i][j] = d[elem]
cayley = np.array(cayley, dtype=int)
for i in range(n):
for j in range(n):
for k in range(n):
p = cayley[j, i]
q = cayley[i, k]
pk = cayley[p, k]
jq = cayley[j, q]
print("\\begin{align*}")
print(f" \\text{{Рассмотрим }} &i = {i}, \\, j = {j} \\\\")
print(f" &k = {k} \\\\")
print(f" &m_{{ji}} = {d1[p]}, m_{{ik}} = {d1[q]} \\\\")
print(f" &(\\text{{Индекс }} m_{{ji}}) = p = {p}, \\, (\\text{{индекс }} m_{{ik}}) = q = {q} \\\\")
print(f" &m_{{pk}} = {d1[pk]}, \\, m_{{jq}} = {d1[jq]} \\\\")
if pk != jq:
raise ValueError("что-то пошло не так...")
print(f" &\\text{{Можно заметить, что }} m_{{pk}} = m_{{jq}}")
print("\\end{align*}")
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