Dear support,

sage: M = matrix(RDF,[[1.,2.],[3.,4.]])
sage: M.LU()

([0.0 1.0]
[1.0 0.0],
 [           1.0            0.0]
[0.333333333333            1.0],
 [           3.0            4.0]
[           0.0 0.666666666667])
sage: N = matrix([[1.,2.],[3.,4.]]) # N.L[tab] does nothing
sage: O = matrix([[1,2],[3,4]]) # O.L[tab] only gives lattice stuff

Is there a mathematical reason LU decomposition isn't available for
these, or was it simply never implemented?  It seems it is only
available for
sage.matrix.matrix_real_double_dense.Matrix_real_double_dense, not for
sage.matrix.matrix_generic_dense.Matrix_generic_dense (floats, RR).

And would it be mathematically correct to place that code in place if
all entries could be RDFed, or not?  Any equivalent for symbolic
matrices (even if slow)?

(On a related note,

sage: O = matrix([[1,2],[3,4]])
sage: O.echelon_form()

[1 0]
[0 2]

so apparently we have yet to implement the (agreed on sage-devel?)
decision that echelon_form should be over the most sensible quotient
field...)

- kcrisman

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