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How to do symbolic computation with quaternions

asked 2013-01-21 20:37:05 -0500

Gilles Falquet gravatar image

I need to do symbolic computations with quaternions. Ideally I'd like to enter something like

Q.<i,j,k> = QuaternionAlgebra(QQ,-1,-1)
a=var('a')
b=var('b')
c=var('c')
q = a*i+b*j+c*k

But it doesn't work : TypeError: unsupported operand parent(s) for '*': 'Symbolic Ring' and 'Quaternion Algebra (-1, -1) with base ring Rational Field'

Looks like SAGE doesn't know how to multiply a variable and a quaternion. Or should I specify the types of the variables ? How ?

Thanks for your help.

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answered 2013-01-22 07:00:21 -0500

benjaminfjones gravatar image

You should define Q as a QuaternionAlgebra over the symbolic ring SR instead of over the rationals:

sage: Q.<i,j,k> = QuaternionAlgebra(SR, -1, -1)
sage: q = a*i + b*j + c*k
sage: q
a*i + b*j + c*k
sage: q^2
-a^2 - b^2 - c^2
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answered 2015-07-30 20:24:24 -0500

uutzinger gravatar image

updated 2015-07-30 20:24:53 -0500

N.<c,d,a1,a2,a3,a4,b1,b2,b3,b4,s> = QQ[]
H.<i,j,k> = QuaternionAlgebra(c,d)
a = a1 + a2 * i + a3 * j + a4 * k
b = b1 + b2 * i + b3 * j + b4 * k
a+b
a*b

From http://www.wstein.org/edu/2010/414/pr...

Seems to give better results

Now I just need to figure out how to define vector and rotate it with quaternion.

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Asked: 2013-01-21 20:37:05 -0500

Seen: 898 times

Last updated: Jul 30 '15