GaussJordan

    static void gaussJordan(BigRational[][] matrix) {
        final int rows = matrix.length, cols = matrix[0].length;
        int row = 0, col = 0, i, j;
        BigRational[] swapBuffer;
        BigRational multKoef;
        while (row < rows && col < cols) {
            i = row; //pos of non-null row
            while (i < rows && matrix[i][col].equals(BigRational.ZERO)) {
                i++;
            }
            if (i == rows) {
                //no pivots at all
                col++;
                continue;
            }
            if (i != row) {
                //need to swap
                swapBuffer = matrix[i];
                matrix[i] = matrix[row];
                matrix[row] = swapBuffer;
            }

            //set pivot to 1
            multKoef = matrix[row][col].reciprocal();
            matrix[row][col] = BigRational.ONE;
            for (j = col + 1; j < cols; j++) {
                matrix[row][j] = matrix[row][j].times(multKoef);
            }

            //set 0 over and under pivot
            for (i = 0; i < rows; i++) {
                if (i == row) {
                    continue;
                }
                if (matrix[i][col].equals(BigRational.ZERO)) {
                    continue;
                }
                multKoef = matrix[i][col].negate();
                matrix[i][col] = BigRational.ZERO;
                for (j = col + 1; j < cols; j++) {
                    matrix[i][j] = matrix[i][j].plus(matrix[row][j].times(multKoef));
                }
            }

            //now move to next pivot
            col++;
            row++;
        }
    }