Use Z/(2)[x[1..4]];
F:=[
x[2]x[3] + x[1]x[4] + x[2]x[4] + x[3]x[4] + x[1] + x[2] + x[3] + x[4],
x[2]x[3] + x[2]x[4] + x[3]x[4] + x[2] + x[3] + x[4],
x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[2],
x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[2]
];
-- Solution is not unique i.e. [0, 1, 1, 1], [0, 0, 0, 0], and [1, 1, 1, 1] are solutions
-- Then we compute the solution with
CharP.MNLASolve(F);
-- And we achieve the following information on the screen.
----------------------------------------
The size of Matrix is:
No. of Rows=4
No. of Columns=9
Applying Gaussian Elimination finding Muatants...
Gaussian Elimination Compeleted
Finding Variable: x[4]
The size of Matrix is:
No. of Rows=9
No. of Columns=4
Applying Gaussian Elimination to check solution coordinate...
Gaussian Elimination Completed.
The size of Matrix is:
No. of Rows=9
No. of Columns=4
Applying Gaussian Elimination to check solution coordinate...
Gaussian Elimination Completed.
The size of Matrix is:
No. of Rows=3
No. of Columns=9
Applying Gaussian Elimination finding Muatants...
Gaussian Elimination Compeleted
The No. of Mutants found = 0
The size of Matrix is:
No. of Rows=14
No. of Columns=16
Applying Gaussian Elimination to check solution coordinate...
Gaussian Elimination Completed.
The size of Matrix is:
No. of Rows=14
No. of Columns=16
Applying Gaussian Elimination to check solution coordinate...
Gaussian Elimination Completed.
The size of Matrix is:
No. of Rows=15
No. of Columns=14
Applying Gaussian Elimination finding Muatants...
Gaussian Elimination Compeleted
The No. of Mutants found = 4
The size of Matrix is:
No. of Rows=14
No. of Columns=28
Applying Gaussian Elimination to check solution coordinate...
Gaussian Elimination Completed.
The size of Matrix is:
No. of Rows=14
No. of Columns=28
Applying Gaussian Elimination to check solution coordinate...
Gaussian Elimination Completed.
The size of Matrix is:
No. of Rows=27
No. of Columns=14
Applying Gaussian Elimination finding Muatants...
Gaussian Elimination Compeleted
The No. of Mutants found = 0
The size of Matrix is:
No. of Rows=14
No. of Columns=13
Applying Gaussian Elimination to check solution coordinate...
Gaussian Elimination Completed.
The size of Matrix is:
No. of Rows=14
No. of Columns=13
Applying Gaussian Elimination to check solution coordinate...
Gaussian Elimination Completed.
The size of Matrix is:
No. of Rows=12
No. of Columns=14
Applying Gaussian Elimination finding Muatants...
Gaussian Elimination Compeleted
The No. of Mutants found = 0
The size of Matrix is:
No. of Rows=15
No. of Columns=20
Applying Gaussian Elimination to check solution coordinate...
Gaussian Elimination Completed.
The size of Matrix is:
No. of Rows=15
No. of Columns=20
Applying Gaussian Elimination to check solution coordinate...
Gaussian Elimination Completed.
x[4] = NA
Please Check the uniqueness of solution.
The Given system of polynomials does not
seem to have a unique solution or it has
no solution over the finite field F2.
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