(A1) Implement function constructing a rotation matrix from a unit quaternion.
(A2) Implement function constructing a unit quaternion from a rotation matrix.
(A3) Implement function returning a rational point on the circle, which is close to a given point with angle th.
(A4) Implement function returning a rational approximation to a given motion matrix E = <R|t>.
(A5) Solve the four given mechanisms.
(A6) Check that rational approximation of \lambda^2 & \mu^2=1.
(A7) Check that input MhV is not an exact rotation.
(A8) Check that MhR, which is a rational approximation to MhV, is an exact rotation.
(A9) Evaluate the Frobenius norm of the difference of the original pose MhV and the approximated pose MhR.
(A10)
Formulate the algebraic equations of the 6R Inverse Kinematics.
(A11) Solve the 6R IK by a general Groebner basis construction.
(A12) Check that the the equations have no solution for input the transformation MhV.
(A13) Extract solutions from the eigenvectors of the
multiplication matrix for a random linear polynomial.
(A14) Normalize eigenvectors to get their first coordinate equal to 1.
(A15) Select and show the real solutions for sines and cosines and their difference from the ground truth.
(A16) Recover the remaining sines and cosines if necessary.
(A17) Recover joint angles from their sines and cosines.