Sqrt of a matrix over Fp

[Habeeb Syed]

Hi,

I need to compute square roots of matrices defined over finite fields.

It seems sage has no such function. I am getting this error.

AttributeError: 'sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_float' object has no attribute 'sqrt'

Any help on this will be very useful to me.

Regards,

HS

[William Stein]

Hi,

You will probably have to implement a function to find a sqrt (if it exists) in terms of other higher level primitives.   

See https://en.wikipedia.org/wiki/Square_root_of_a_matrix and https://chat.openai.com/share/114817d2-908a-4776-b14a-5bc6e04b226b

William

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[Habeeb Syed]

Thanks for the reply Stein. It was very helpful.

To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CACLE5GApSjYYKq4GScRuqX6TfNNn8rOfut8SPeC-gzUjyVrtPg%40mail.gmail.com.

[cyrille....@univ-orleans.fr]

Hello (I do not know which is your given name),

I think what you are searching is called Cholesky factorization. It is implemented in SageMath

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De: "Habeeb Syed" <habeebb...@gmail.com>
À: "sage-support" <sage-s...@googlegroups.com>
Envoyé: Vendredi 9 Juin 2023 04:43:46
Objet: Re: [sage-support] Sqrt of a matrix over Fp

To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CAL0kVBJG5HCKMVH-coDhY5z2wFj5J7J4P3CbxBvRXM2SRqOBmw%40mail.gmail.com.

[Dima Pasechnik]

On Fri, Jun 9, 2023 at 8:33 AM cyrille....@univ-orleans.fr
<cyrille....@univ-orleans.fr> wrote:
>
> Hello (I do not know which is your given name),
>
> I think what you are searching is called Cholesky factorization. It is implemented in SageMath

this is not for finite fields, though.
Cholesky only make sense for ordered fields.

> To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/1456572348.177053719.1686296004210.JavaMail.zimbra%40univ-orleans.fr.