CharP.MNLASolve |
Syntax |
CharP.MNLASolve(F:LIST):LIST |
Description |
Example |
Use Z/(2)[x[1..4]]; F:=[ x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1, x[1]x[2] + x[1]x[3] + x[1]x[4] + x[3]x[4] + x[2] + x[3] + 1, x[1]x[2] + x[1]x[3] + x[2]x[3] + x[3]x[4] + x[1] + x[4] + 1, x[1]x[3] + x[2]x[3] + x[1]x[4] + x[2]x[4] + 1 ]; -- Then we compute the solution with CharP.MNLASolve(F); -- And we achieve the following information on the screen together with the solution at the end. ---------------------------------------- Finding Variable: x[4] The size of Matrix is: No. of Rows=4 No. of Columns=11 Appling Gaussian Elimination for finding Mutants... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Compeleted The size of Matrix is: No. of Rows=4 No. of Columns=11 Appling Gaussian Elimination for finding Mutants... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Compeleted The size of Matrix is: No. of Rows=11 No. of Columns=5 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The size of Matrix is: No. of Rows=11 No. of Columns=5 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The No. of Mutants found = 0 The size of Matrix is: No. of Rows=8 No. of Columns=11 Appling Gaussian Elimination for finding Mutants... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Compeleted The size of Matrix is: No. of Rows=11 No. of Columns=8 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0.015 ------------------------------- Gaussian Elimination Completed. The size of Matrix is: No. of Rows=11 No. of Columns=8 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The No. of Mutants found = 1 The size of Matrix is: No. of Rows=11 No. of Columns=11 Appling Gaussian Elimination for finding Mutants... -- CoCoAServer: computing Cpu Time = 0.016 ------------------------------- Gaussian Elimination Compeleted The size of Matrix is: No. of Rows=11 No. of Columns=10 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The size of Matrix is: No. of Rows=11 No. of Columns=10 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. x[4] = 1 Finding Variable: x[3] The size of Matrix is: No. of Rows=4 No. of Columns=7 Appling Gaussian Elimination for finding Mutants... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Compeleted The size of Matrix is: No. of Rows=4 No. of Columns=7 Appling Gaussian Elimination for finding Mutants... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Compeleted The size of Matrix is: No. of Rows=7 No. of Columns=5 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The size of Matrix is: No. of Rows=7 No. of Columns=5 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The No. of Mutants found = 0 The size of Matrix is: No. of Rows=7 No. of Columns=7 Appling Gaussian Elimination for finding Mutants... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Compeleted The size of Matrix is: No. of Rows=7 No. of Columns=7 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. x[3] = 0 Finding Variable: x[2] The size of Matrix is: No. of Rows=3 No. of Columns=4 Appling Gaussian Elimination for finding Mutants... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Compeleted The size of Matrix is: No. of Rows=3 No. of Columns=4 Appling Gaussian Elimination for finding Mutants... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Compeleted The size of Matrix is: No. of Rows=4 No. of Columns=4 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The size of Matrix is: No. of Rows=4 No. of Columns=4 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. x[2] = 1 [0, 1, 0, 1] |
Example |
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. ---------------------------------------- Finding Variable: x[4] The size of Matrix is: No. of Rows=4 No. of Columns=9 Appling Gaussian Elimination for finding Mutants... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Compeleted The size of Matrix is: No. of Rows=3 No. of Columns=9 Appling Gaussian Elimination for finding Mutants... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Compeleted The size of Matrix is: No. of Rows=9 No. of Columns=4 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The size of Matrix is: No. of Rows=9 No. of Columns=4 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The No. of Mutants found = 0 The size of Matrix is: No. of Rows=15 No. of Columns=14 Appling Gaussian Elimination for finding Mutants... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Compeleted The size of Matrix is: No. of Rows=14 No. of Columns=12 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The size of Matrix is: No. of Rows=14 No. of Columns=12 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The No. of Mutants found = 4 The size of Matrix is: No. of Rows=27 No. of Columns=14 Appling Gaussian Elimination for finding Mutants... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Compeleted The size of Matrix is: No. of Rows=14 No. of Columns=13 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The size of Matrix is: No. of Rows=14 No. of Columns=13 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The No. of Mutants found = 0 The size of Matrix is: No. of Rows=12 No. of Columns=14 Appling Gaussian Elimination for finding Mutants... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Compeleted The size of Matrix is: No. of Rows=14 No. of Columns=13 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0.016 ------------------------------- Gaussian Elimination Completed. The size of Matrix is: No. of Rows=14 No. of Columns=13 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The No. of Mutants found = 0 The size of Matrix is: No. of Rows=19 No. of Columns=15 Appling Gaussian Elimination for finding Mutants... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Compeleted The size of Matrix is: No. of Rows=15 No. of Columns=14 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The size of Matrix is: No. of Rows=15 No. of Columns=14 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The No. of Mutants found = 0 The size of Matrix is: No. of Rows=14 No. of Columns=15 Appling Gaussian Elimination for finding Mutants... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Compeleted The size of Matrix is: No. of Rows=15 No. of Columns=14 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- Gaussian Elimination Completed. The size of Matrix is: No. of Rows=15 No. of Columns=14 Appling Gaussian Elimination to check solution coordinate... -- CoCoAServer: computing Cpu Time = 0 ------------------------------- 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. |
See Also |