zero.RdCorrect idiom for generating zero k-tensors and k-forms
zeroform(n)
zerotensor(n)
is.zero(x)
is.empty(x)Idiom such as as.ktensor(rep(1,5),0) and
as.kform(rep(1,5),0) and indeed as.kform(1:5,0) will
return the zero tensor or k-form (in earlier versions of the
package, these were held to be incorrect as the arity of the tensor
was lost).
A 0-form is not the same thing as a zero tensor. A
0-form maps V0 to the reals; a scalar. A zero
tensor maps Vk to zero. Some discussion is given at
scalar.Rd.
Returns an object of class kform or ktensor.
zerotensor(5)
#> The zero linear map from V^5 to R with V=R^n:
#> empty sparse array with 5 columns
zeroform(3)
#> The zero alternating linear map from V^3 to R with V=R^n:
#> empty sparse array with 3 columns
x <- rform(k=3)
x*0 == zeroform(3) # should be true
#> [1] TRUE
x == x + zeroform(3) # should be true
#> [1] TRUE
y <- rtensor(k=3)
y*0 == zerotensor(3) # should be true
#> [1] TRUE
y == y+zerotensor(3) # should be true
#> [1] TRUE
## Following idiom is plausible but fails because as.ktensor(coeffs=0)
## and as.kform(coeffs=0) do not retain arity:
## as.ktensor(1+diag(5)) + as.ktensor(rep(1,5),0) # fails
## as.kform(matrix(1:6,2,3)) + as.kform(1:3,0) # also fails