Matrix of operations after gaussian elimination

[Juan Grados]

I need the Matrix of operations after gaussian elimination in sage. How Can I get that?

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MSc. Juan del Carmen Grados Vásquez
Laboratório Nacional de Computação Científica 
Tel: +55 21 97633 3228

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http://juaninf.blogspot.com
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[Kwankyu]

Is this what you want?

sage: m = matrix(2,[1,2,3,4])
sage: H,U = m.echelon_form(transformation=True)
sage: H
[1 0]
[0 2]
sage: U
[-2 1]
[ 3 -1]
sage: U * m == H
True

[Juan Grados]

Thank by I get

ValueError: too many values to unpack

I think because my matrix has entries in GF(2).

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[Simon King]

Hi Juan,

On 2017-06-10, Juan Grados <jua...@gmail.com> wrote:
> Thank by I get
>
> ValueError: too many values to unpack
>
> I think because my matrix has entries in GF(2).

You are right. According to the documentation:
* "transformation" -- boolean. Whether to also return the
transformation matrix. Some matrix backends do not provide this
information, in which case this option is ignored.

So, unfortunately, it doesn't give the desired transformation
matrix.

Depending on your application, it could be that LU decomposition
does what you need.

Best regards,
Simon

[Juan Grados]

I need an implementaton to perfom a Gaussian elimination on a matrix with entries in GF(2). This implementation should return a transformation matrix and the result of the gassual elimination.

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[Juan Grados]

More specifically, I need transform a partity check matrix into a systematic form, but I need the transform matrix

[Johan S. H. Rosenkilde]

Hi Juan

You can just compute it from the result:

sage: H = random_matrix(GF(2), 15, 20)
sage: S = H.echelon_form(transformation=True)
sage: full_rank_submatrix = H.matrix_from_columns(S.pivots())
sage: U = full_rank_submatrix.inverse()
sage: U*H == S
True

Note: this only works if m has full row rank (which it should have if
your input is a parity check matrix). Otherwise, one has to do slightly
more work.

Best,
Johan

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>>
>>
>>
>> --
>> ---------------------------------------------------------------------
>> MSc. Juan del Carmen Grados Vásquez
>> Laboratório Nacional de Computação Científica

>> Tel: +55 21 97633 3228 <(21)%2097633-3228>