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.MXLSolve(F);
-- And we achieve the following information on the screen.
----------------------------------------
The size of Matrix is:
No. of Rows=4
No. of Columns=9
Appling Gaussian Elimination...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
The size of Matrix is:
No. of Rows=3
No. of Columns=9
Appling Gaussian Elimination...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
The variables found till now, if any are:
[x[1], x[2], x[3], x[4]]
The No. of Mutants found = 0
The size of Matrix is:
No. of Rows=14
No. of Columns=14
Appling Gaussian Elimination...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
The variables found till now, if any are:
[x[1], x[2], x[3], x[4]]
The No. of Mutants found = 4
The size of Matrix is:
No. of Rows=27
No. of Columns=14
Appling Gaussian Elimination...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
The variables found till now, if any are:
[x[1], x[2], x[3], x[4]]
The No. of Mutants found = 0
The size of Matrix is:
No. of Rows=12
No. of Columns=14
Appling Gaussian Elimination...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
The variables found till now, if any are:
[x[1], x[2], x[3], x[4]]
The No. of Mutants found = 0
The size of Matrix is:
No. of Rows=19
No. of Columns=15
Appling Gaussian Elimination...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
The variables found till now, if any are:
[x[1], x[2], x[3], x[4]]
The No. of Mutants found = 0
The size of Matrix is:
No. of Rows=14
No. of Columns=15
Appling Gaussian Elimination...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
The variables found till now, if any are:
[x[1], x[2], x[3], x[4]]
Please Check the uniqueness of solution.
The Given system of polynomials does not
seem to have a unique solution.
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