Difference between revisions of "ApCoCoA-1:LinBox.Solve"

Solve

solve linear equation system

Syntax

```LinBox.Solve(M:MAT, B:MAT):MAT
LinBox.Solve(M:MAT, B:MAT, METHOD:STRING):MAT
```

Description

Let M and B be matrices defined over the ring of integers, a finite field or the field of rationals. This function tries to solve the linear equation system M*X = B by using the ApCoCoAServer supported by the LinBox library. If your base ring is the ring of integers or a finite field, you can pass Wiedemann as METHOD to let the ApCoCoAServer compute the solution by using the LinBox Wiedemann implementation. If you pass BlasElim instead in this case, the solution will be computed by using the LinBox BLAS elimination implementation. If you omit the parameter METHOD, Wiedemann will be used as default value where applicable. Please note that the parameter METHOD will be ignored if your base ring is the field of rationals, i.e. in this case it is always the LinBox rational solver implementation that will be used for computing a solution.

The return value will be a solution vector of the linear equation system or an empty matrix if no solution has been found.

Example

```Use Z/(19)[x];
M := BringIn(Mat([[1,3,4], [0,2,1]]));
B := BringIn(Mat([[1], [2]]));
LinBox.Solve(M, B);
-------------------------------
Mat([
[-2 % 19],
[1 % 19],
[0 % 19]
])
-------------------------------

Use Q[x];
M := Mat([ [1,3,4], [0,2,1], [1,3,4] ]);
B := Mat([ [1], [2], [0] ]);
LinBox.Solve(M, B);
-------------------------------
Mat([
[ ]
])
-------------------------------
```