Hi,
Thanks. Since I want to do exterior algebra, I am using a null
metric.
Also, I am not in 3-dim and so I don't have a cross product.
Let's suppose we have the following code:
#######################
#!/bin/env python
from sympy.galgebra.GAsympy import *
set_main(sys.modules[__name__])
MV.setup('e0 e1 e2 e3', '0 0 0 0, 0 0 0 0, 0 0 0 0, 0 0 0 0')
a = e0*e1*e2*e3
######################
We know that in this case
a = e0^e1^e2^e3 and
*a = 1 (one)
but I don't know how to obtain this value (one) with sympy,
starting from 'a'. I suspect it should be trivial, but I
don't see how to do.
Luis
---------------------------
On Jan 18, 7:24 pm, Alan Bromborsky <[email protected]> wrote:
> luis wrote:
> > Hi,
>
> > Is there some way in 'galgebra.GAsympy'
> > to apply the Hodge-* operator?
>
> > Thanks,
>
> > Luis
>
> > PS. I am using MV.setup(basis,metric) with a null metric.
>
> Seehttp://en.wikipedia.org/wiki/Geometric_algebra. I think the Hodge
> dual of a vector, v, is just the geometrics product of the vector and
> the pseudoscalar I that is
>
> v* = v*I
>
> for 3-dimensions (signature(+++)) we have the relation that the cross
> product of two vectors a and b is
>
> a x b = -I a ^ b
>
> where I is the pseudo-scalar and ^ is the outer (exterior) product
>
> seehttp://wiki.sympy.org/wiki/Geometric_Algebra_Modulefor how to set
> up your metric.
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