[GiNaC-list] Matching both variances of varidx

[Matthew Lim]

Hi,

I wanted to implement a rule to replace the product of two epsilon 
tensors with the determinant of a matrix of metric tensors. I found that 
simplify_indexed works fine but only if at least one of the indices is 
summed over - calling it on an expression like

lorentz_eps(mu,nu,rho,sigma)*lorentz_eps(alpha,beta,gamma,delta)

results in no simplification.

Implementing this would be no problem if it weren't for the fact that 
the expression I want to make the replacement in has many instances of 
lorentz_eps called with different combinations of co- and contra-variant 
indices - it seems when I call subs, I need to specify the variance of 
the wildcard in order to make the match so that, for example,

ex test = lorentz_eps(mu.toggle_variance(),nu,rho,sigma)

test.subs(lorentz_eps(varidx(wildcard(1),4),varidx(wildcard(2),4),varidx(wildcard(3),4),varidx(wildcard(4),4))== 
#expression#)

does not result in any substitution being made.

I am not so keen on implementing separate substitutions for all the 
different combinatoric possibilities of index variances - is there 
perhaps a simpler way?

Thanks for your help,

Matthew