Python class for quaternions

Broom Bridge plaque

Last August in Dublin (at DCU) I presented a tutorial about Python in Scientific Computing.

While there I thought it was appropriate to give a native example (in Rome be Roman) and so I choose the Quaternions. This is a good excuse as any other to present the multiple features of python for science. :-)

The picture above is carved in the Broom Bridge, over the Royal Canal, and where supposedly Hamilton had the inspiration to come with such beasts :-) .

I had described before (in Portuguese) my hazard quest to find the place. An yearly event, at 16th of October, gets people together to visit the place and probably for a couple of drinks. :-)

While preparing the course I searched for python implementations of the quaternions and I have only found code related with graphics transforms (where the quaternions can be useful).

In the same spirit of Free/Open Source Software, to scratch a itch, I make available my implementation of a python class that implements the quaternions and that deals transparently with the complex numbers.

The code can be found at my homepage. Here it is a sample:

a = Quaternion(1, -2)
b = Quaternion(1, 2, -3, 4)
c = 1 - 2j
print "a =", a
print "b =", b
print "c =", c
print a + b
print a - c
print a*b
print a*c
print 2*a
print b*b.conjugate()
print abs(b)**2

And the resulting output:

a = +1-2*i+0*j+0*k
b = +1+2*i-3*j+4*k
c = (1-2j)

I hope this helps others who have the same problem I had. :-)