Converting a rotation matrix to a quaternion

I found a very good link about quaternions in Mathematica , but I don't know how to create a quaternion from a rotation matrix. Can anyone help me, please?

Update

I need this:

A rotation may be converted back to a quaternion through the use of the following algorithm. The process is performed in the following stages, which are as follows:

Calculate the trace of the matrix T from the equation:

  T = 4 - 4x^2  - 4y^2  - 4z^2
    = 4( 1 - x^2  - y^2  - z^2 )
    = mat[0] + mat[5] + mat[10] + 1

If the trace of the matrix is greater than zero, then perform an "instant" calculation.

  S = 0.5 / sqrt(T)
  W = 0.25 / S
  X = ( mat[9] - mat[6] ) * S
  Y = ( mat[2] - mat[8] ) * S
  Z = ( mat[4] - mat[1] ) * S

If the trace of the matrix is less than or equal to zero then identify which major diagonal element has the greatest value.

Depending on this value, calculate the following:

Column 0:

    S  = sqrt( 1.0 + mr[0] - mr[5] - mr[10] ) * 2;
    Qx = 0.5 / S;
    Qy = (mr[1] + mr[4] ) / S;
    Qz = (mr[2] + mr[8] ) / S;
    Qw = (mr[6] + mr[9] ) / S;

Column 1:

    S  = sqrt( 1.0 + mr[5] - mr[0] - mr[10] ) * 2;
    Qx = (mr[1] + mr[4] ) / S;
    Qy = 0.5 / S;
    Qz = (mr[6] + mr[9] ) / S;
    Qw = (mr[2] + mr[8] ) / S;

Column 2:

    S  = sqrt( 1.0 + mr[10] - mr[0] - mr[5] ) * 2;

    Qx = (mr[2] + mr[8] ) / S;
    Qy = (mr[6] + mr[9] ) / S;
    Qz = 0.5 / S;
    Qw = (mr[1] + mr[4] ) / S;

The quaternion is then defined as:

   Q = | Qx Qy Qz Qw |