# Revision history [back]

even a bug for diagonal matrices..

sage: K.<z> = CyclotomicField(16)
sage: 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]
sage: 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]
sage: det(L*U)==det(L)*det(U)
False


even a bug for diagonal matrices..

sage: K.<z> = CyclotomicField(16)
sage: 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]
sage: 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]
sage: det(L*U)==det(L)*det(U)
False


where the product LU is not diagonal !?