Hi all,

Having trouble with the matrix multiplication which I first explained 
in 
https://ask.sagemath.org/question/64194/determinants-over-cyclotomic-fields-are-broken/
If I define two matrices (L and U) over CyclotomicField and then multiply 
then like L*U and via the definition then the results are sometimes 
different. An example is:

K.<z> = CyclotomicField(16)
OK = K.ring_of_integers()
L = [[-575*z^7 - 439*z^6 - 237*z^5 + 237*z^3 + 439*z^2 + 575*z + 623, 0],
[0,     -114*z^7 - 88*z^6 - 48*z^5 + 48*z^3 + 88*z^2 + 114*z + 123]]
U = [[-1926*z^7 - 1474*z^6 - 798*z^5 + 798*z^3 + 1474*z^2 + 1926*z + 2085, 
0],
[0,   -1014*z^7 - 777*z^6 - 421*z^5 + 421*z^3 + 777*z^2 + 1014*z + 1097]]
L, U = matrix(K,L), matrix(K,U)
LU = matrix( [ [L[i].inner_product(U.transpose()[j]) for j in range(2)] for 
i in range(2)] )
assert LU == L*U

Where the last assertion must clearly sucseed but it doesn't.

Note: if I define L, U = matrix(K,L), matrix(K,U) then the matrices are no 
longer Matrix_cyclo_dense but Matrix_generic_dense and the last assertion 
sucseeds!

Checked that one on Ubuntu 22.04.01 and MacOS on sage 9.4, 9.5 and 9.6. Is 
this the known issue? Am doing it wrong?

Kind regards,
Alexander

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