# NOT RUN {
A <- to.tensor(rnorm(120),c(a=2,b=2,c=5,d=3,e=2))
AAt <- A %e% mark(A,"'",c("a","b"))
AAt
power.tensor(AAt,c("a","b"),c("a'","b'"),-1)
inv.tensor(AAt,c("a","b"))
power.tensor(AAt,c("a","b"),c("a'","b'"),2)
mul.tensor(AAt,c("a","b"),AAt,c("a'","b'"))
power.tensor(power.tensor(AAt,c("a","b"),c("a'","b'"),1/pi),
c("a","b"),c("a'","b'"),pi)
AAt <- einstein.tensor(A , mark(A,"'",c("a","b")),by="e")
power.tensor(AAt,c("a","b"),c("a'","b'"),-1,by="e")
inv.tensor(AAt,c("a","b"),by="e")
power.tensor(AAt,c("a","b"),c("a'","b'"),2,by="e")
mul.tensor(AAt,c("a","b"),AAt,c("a'","b'"),by="e")
power.tensor(power.tensor(AAt,c("a","b"),c("a'","b'"),1/pi,by="e"),
c("a","b"),c("a'","b'"),pi,by="e")
# }
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