wedge.RdWedge products of \(k\)-forms
wedge2(K1,K2)
wedge(x, ...)Wedge product of \(k\)-forms.
The functions documented here return an object of class
kform.
In general use, use wedge() or ^ or %^%, as
documented under Ops. Function wedge() uses low-level
helper function wedge2(), which takes only two arguments.
A short vignette is provided with the package: type
vignette("wedge") at the commandline.
k1 <- as.kform(cbind(1:5,2:6),1:5)
k2 <- as.kform(cbind(5:7,6:8,7:9),1:3)
k3 <- kform_general(1:6,2)
a1 <- wedge2(k1,wedge2(k2,k3))
a2 <- wedge2(wedge2(k1,k2),k3)
is.zero(a1-a2) # NB terms of a1, a2 in a different order!
#> [1] TRUE
# This is why wedge(k1,k2,k3) is well-defined. Can also use ^:
k1 ^ k2 ^ k3
#> An alternating linear map from V^7 to R with V=R^9:
#> val
#> 2 3 4 5 7 8 9 = 27
#> 1 2 3 5 6 7 8 = 6
#> 1 2 5 6 7 8 9 = 18
#> 1 3 4 5 6 7 8 = 14
#> 1 2 4 6 7 8 9 = 3
#> 2 3 5 6 7 8 9 = 21
#> 1 3 4 5 7 8 9 = 21
#> 2 3 4 6 7 8 9 = 15
#> 2 4 5 6 7 8 9 = 27
#> 1 2 3 5 7 8 9 = 9
#> 1 2 3 4 5 6 7 = 6
#> 1 2 4 5 6 7 8 = 10
#> 3 4 5 6 7 8 9 = 36
#> 1 4 5 6 7 8 9 = 27
#> 1 2 4 5 7 8 9 = 15
#> 1 2 3 4 6 7 8 = 12
#> 2 3 4 5 6 7 8 = 18
#> 1 2 3 6 7 8 9 = 9
#> 1 2 3 4 7 8 9 = 18
#> 1 3 5 6 7 8 9 = 15
#> 1 3 4 6 7 8 9 = 9