# Help regarding symbolic linear equation solve over GF(2).

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### Subrata Nandi

Nov 2, 2019, 5:33:37 AM11/2/19
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I need to solve a symbolic linear equation : x*A=b , where x is a 500 dimension unknown variable, A is a matrix of size 500 x 500 of symbolic variables over finite field, b is vector of length 500 like (0,......,1). I have defined the Boolean polynomial ring over finite field of 500 variables. I used solve_right() function in this case. It is taking infinite amount of time to solve the equation. Please help me to solve this problem. Thanks in advance.

### David Joyner

Nov 2, 2019, 5:37:25 AM11/2/19
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On Sat, Nov 2, 2019 at 5:33 AM Subrata Nandi <subrat...@iitg.ernet.in> wrote:
I need to solve a symbolic linear equation : x*A=b , where x is a 500 dimension unknown variable, A is a matrix of size 500 x 500 of symbolic variables over finite field, b is vector of length 500 like (0,......,1). I have defined the Boolean polynomial ring over

What do you mean that A has symbolic entries?
Is each entry a polynomial in one variable? Two variables? 500^2 variables? Is it sparse?

finite field of 500 variables. I used solve_right() function in this case. It is taking infinite amount of time to solve the equation. Please help me to solve this problem. Thanks in advance.

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### Subrata Nandi

Nov 2, 2019, 9:56:02 AM11/2/19
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Each entry of the A matrix is either boolean function of 256 variables or element in GF(2).

### David Joyner

Nov 2, 2019, 2:13:48 PM11/2/19
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On Sat, Nov 2, 2019 at 9:56 AM Subrata Nandi <subrat...@iitg.ernet.in> wrote:
Each entry of the A matrix is either boolean function of 256 variables or element in GF(2).

To start, I would try to find the inverse with a much smaller example
(small number of variables, small dimensions) using gauss elimination.

On Saturday, November 2, 2019 at 3:03:37 PM UTC+5:30, Subrata Nandi wrote:
I need to solve a symbolic linear equation : x*A=b , where x is a 500 dimension unknown variable, A is a matrix of size 500 x 500 of symbolic variables over finite field, b is vector of length 500 like (0,......,1). I have defined the Boolean polynomial ring over finite field of 500 variables. I used solve_right() function in this case. It is taking infinite amount of time to solve the equation. Please help me to solve this problem. Thanks in advance.

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### Subrata Nandi

Nov 2, 2019, 2:17:53 PM11/2/19
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I have tried for small matrix. It worked. But not getting for dimension 256.

On Saturday, November 2, 2019 at 11:43:48 PM UTC+5:30, David Joyner wrote:
On Sat, Nov 2, 2019 at 9:56 AM Subrata Nandi <subrat...@iitg.ernet.in> wrote:
Each entry of the A matrix is either boolean function of 256 variables or element in GF(2).

To start, I would try to find the inverse with a much smaller example
(small number of variables, small dimensions) using gauss elimination.

On Saturday, November 2, 2019 at 3:03:37 PM UTC+5:30, Subrata Nandi wrote:
I need to solve a symbolic linear equation : x*A=b , where x is a 500 dimension unknown variable, A is a matrix of size 500 x 500 of symbolic variables over finite field, b is vector of length 500 like (0,......,1). I have defined the Boolean polynomial ring over finite field of 500 variables. I used solve_right() function in this case. It is taking infinite amount of time to solve the equation. Please help me to solve this problem. Thanks in advance.

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