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I have an equation of the form $AXB = V$, that I am trying to solve using Sage. All matrixes are in $GF(2)$, $A$ and $X$ are of size 32x32, and $B$ and $V$ column vectors of size 32.

My unknown matrix $X$ consists in zeros, except on the diagonal where I'd like to have 32 unknowns (representing each bit of a unknown 32-bits integer). I first tried to declare an array of variables like this:

vars_list = list(var("x_%d" % i) for i in range(32)) which throws me a "TypeError: x_0 is not a variable of Univariate Polynomial Ring in X over Finite Field of size 2 (using GF2X)". Looking at Sage documentation, I didn't find a way to declare them in $GF(2)$.

Using this link, I tried to declare my variables like this: x_1 = SR(GF(2)(1)) * var("x1") which gave me this time a "TypeError: positive characteristic not allowed in symbolic computations".

How should I setup $X$ so I can solve my equation?

Indeed, it wasn't very complex... Thank you for your help.

Thank you for the answer and the reference, I'll be sure to check it. A last question if I may: your answer worked fine,

Declare diagonal matrix with unknown variables in GF(2). I have an equation of the form $AXB = V$, that I am trying to s

Declare diagonal matrix with unknown variables in GF(2). I have an equation of the form $AXY = V$, that I am trying to s

Perfect, thank you very much for all your help!

Perfect, thank you very much for your help!

I guess it is invertible, yes. It is the Q one at the very end of the page 18 here : https://keccak.team/files/Keccak-re

I guess it is invertible, yes. It is the Q one at the very end of the page 18 here : https://keccak.team/files/Keccak-re

It gives me a TypeError : self must be an integral domain. Update : I also tried the inverse_of_unit() builtin of a poly

It gives me a TypeError : self must be an integral domain. Update : I also tried the inverse_of_unit() builtin of a poly

It gives me a TypeError : self must be an integral domain.

Thank you, it worked fine. Another question: how could I create a polynomial of the same nature, power -1 ? It tells me

Thank you, it worked fine. Another question: how could I create a polynomial of the same nature, power -1 ? It tells me

Creating a multivariate polynomial with ideal Hello, new user of sage here. I have a computation not too difficult too m