Re: [Maxima-discuss] sign error with determinant_by_lu

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

I can confirm that a self-compiled maxima 5.47.0 doesn't have this sign problem.
So for me this can be ignored.

Regards Andre

On 1/10/24 02:26, Richard Fateman wrote:
> I get 2 for determinant_by_lu in  Maxima 5.47.0 without loading anything.
>
>
> On Tue, Jan 9, 2024 at 5:10 PM andre maute via Maxima-discuss <
> max...@li...> wrote:
>
>> 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"
>>
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