Version: 0.9
Date:    2002-11-07

This .zip file contains 13 very basic functions for symbolic manipulation of quaternions.
I hope to add a better version before the year ends.

All the following functions accept algebraic and symbolic arguments, for example,
you can define a quaternion as 7-g*i+(x^2-3)j+k.

Characters i, j and k are reserved because they represent the imaginary units of the
system.

+ cmx2cuat:
  Receives two arguments. The first one is a complex number and the second one, an
  imaginary vector written algebraically, and returns a quaternion with the same
  modulus and real part of the complex number in the direction of the vector.

  Example:  cmx2cuat(2+6ï,i+2j+k)

  Note: I use the "ï" to represent the imaginary unit symbol that TIs use, in contrast
        to the ordinary letter "i".

+ cuat2cmx:
  Receives a quaternion, and returns the complex mudulus of the cuaternion, as a
  complex number.

  Example:  cuat2cmx(3-4i+2j+8k)

+ cuat2vec:
  Converts a quaternion into a 4-vector.

  Example:  cuat2cmx(-3-4j+k)

+ qabs:
  Obtains the absolute value of a quaternion.

  Example:  qabs(-3-4j+k)

+ qexp:
  Calculates the function e^Q for a received cuaternion Q.

  Example:  qexp(3+j-k)

+ qimag:
  Obtains the imaginary part of a cuaterion, in its full 3D form.

  Example:  qexp(a+j*b-8k)

+ qimagm:
  Same than above, but the answer is the magnitude of the imaginary part.

+ qimagu:
  Returns an imaginary unit in the same direction that the imaginary part of the input
  quaternion.

+ qreal:
  Returns the real part of a quaternion.

+ qprod:
  Returns the full Grassman product of two received quaternions.

  Example:  qprod(i+j,3-j+k)

+ qinv:
  Returns Q^-1 for an input quaternion Q.

+ qrot:
  Returns the Rotational function of the first argument around the second.
  This function does not allow scalling.

  Note:  The function expects two receive two quaternions, where the second one has
         to be purely imaginary. If it's not the case, the real part will be made 0.

+ vec2cuat:
  Receives a 4D vector and returns the dot product with [1,i,j,k].


I'd really appreciate any comments or suggestions.

Ricardo A. Espinoza Reyes
ricardo_arturo@gmx.net