How to do symbolic computation with quaternions
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.