[Maxima-discuss] sign error with determinant_by_lu

[andre m. <and...@gm...>]

Hi list,

this one from Michel Talon's post on the bird algorithm caught my attention.
So I did some quick tests, mostly for checking that invert_by_lu, which I use a lot, is not affected.

See the output below, my file is attached.
One can see the matrices from the P.L.U decomposition don't have issues.
But determinant_by_lu for the permutation matrix looks to be broken.

Is this a known defect/bug?

Regards Andre

--------------------------
Maxima 5.45.1 https://maxima.sourceforge.io
using Lisp SBCL 2.0.1-8.fc36
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) batch("detbylu.mac")

read and interpret /home/user/detbylu.mac
(%i2) display2d:false
(%o2) false
(%i3) A:matrix([1,0,-1,-1],[-1,0,1,-1],[0,0,-1,1],[1,-1,0,1])
(%o3) matrix([1,0,-1,-1],[-1,0,1,-1],[0,0,-1,1],[1,-1,0,1])
(%i4) determinant(A)
(%o4) 2
(%i5) determinant_by_lu(A)
(%o5) -2
(%i6) Ainv:invert_by_lu(A)
(%o6) matrix([0,-1,-1,0],[-1/2,-3/2,-1,-1],[-1/2,-1/2,-1,0],[-1/2,-1/2,0,0])
(%i7) Ainv . A
(%o7) matrix([1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1])
(%i8) determinant(Ainv)
(%o8) 1/2
(%i9) determinant_by_lu(Ainv)
(%o9) -1/2
(%i10) [P,L,U]:get_lu_factors(lu_factor(A))
(%o10) [matrix([1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]),matrix([1,0,0,0],[1,1,0,0],[0,0,1,0],[-1,0,0,1]),matrix([1,0,-1,-1],[0,-1,1,2],[0,0,-1,1],[0,0,0,-2])]
(%i11) M:P . L . U-A
(%o11) matrix([0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0])
(%i12) P
(%o12) matrix([1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0])
(%i13) determinant(P)
(%o13) -1
(%i14) determinant_by_lu(P)
(%o14) 1
(%i15) L
(%o15) matrix([1,0,0,0],[1,1,0,0],[0,0,1,0],[-1,0,0,1])
(%i16) determinant(L)
(%o16) 1
(%i17) determinant_by_lu(L)
(%o17) 1
(%i18) U
(%o18) matrix([1,0,-1,-1],[0,-1,1,2],[0,0,-1,1],[0,0,0,-2])
(%i19) determinant(U)
(%o19) -2
(%i20) determinant_by_lu(U)
(%o20) -2
(%i21) B:matrix([1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0])
(%o21) matrix([1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0])
(%i22) determinant(B)
(%o22) -1
(%i23) determinant_by_lu(B)
(%o23) 1
(%o24) "/home/user/detbylu.mac"
-------------------------------