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The two trivial ternary codes below are obviously not permutably equivalent (they are monomially equivalent). But the method is_permutation_equivalent returns True (and only the permutation part of the monomial equivalence):

C1 = LinearCode(matrix(GF(3),[1,1]))
C2 = LinearCode(matrix(GF(3),[1,2]))
print( C1.is_permutation_equivalent(C2,algorithm='verbose') )

The same for larger codes (over GF(3), GF(4), ?). A temporary SageMathCell link: sagecell.sagemath.org/?q=zxvabh

The two trivial ternary codes below are obviously not permutably equivalent (they are monomially equivalent). But the method is_permutation_equivalent returns True (and only the permutation part of the monomial equivalence):

C1 = LinearCode(matrix(GF(3),[1,1]))
C2 = LinearCode(matrix(GF(3),[1,2]))
print( C1.is_permutation_equivalent(C2,algorithm='verbose') )

The same for larger codes (over GF(3), GF(4), ?). A temporary SageMathCell link: sagecell.sagemath.org/?q=zxvabh

The two trivial ternary codes below are obviously not permutably equivalent (they are monomially equivalent). But the method is_permutation_equivalent returns True (and only the permutation part of the monomial equivalence):

C1 = LinearCode(matrix(GF(3),[1,1]))
C2 = LinearCode(matrix(GF(3),[1,2]))
print( C1.is_permutation_equivalent(C2,algorithm='verbose') )

The same for larger codes (over GF(3), GF(4), ?). A temporary SageMathCell link: sagecell.sagemath.org/?q=zxvabh

The two trivial ternary codes below are obviously not permutably equivalent (they are monomially equivalent). But the method is_permutation_equivalent returns True (and only the permutation part of the monomial equivalence):

C1 = LinearCode(matrix(GF(3),[1,1]))
C2 = LinearCode(matrix(GF(3),[1,2]))
print( C1.is_permutation_equivalent(C2,algorithm='verbose') )

The same for larger codes (over GF(3), GF(4), ?). A temporary SageMathCell link: sagecell.sagemath.org/?q=zxvabhhttps://sagecell.sagemath.org/?q=zxvabh