rform.RdRandom \(k\)-form objects and \(k\)-tensors, intended as quick “get you going” examples
rform(terms=9,k=3,n=7,coeffs,ensure=TRUE)
rtensor(terms=9,k=3,n=7,coeffs)Number of distinct terms
A \(k\)-form maps \(V^k\) to \(\mathbb{R}\), where \(V=\mathbb{R}^n\)
The coefficients of the form; if missing use
seq_len(terms)
Boolean with default TRUE meaning to ensure that
the dovs() of the returned value is in fact equal to
n. If FALSE, sometimes the dovs() is strictly
less than n because of random sampling
Random \(k\)-form objects and \(k\)-tensors, of moderate complexity.
Note that argument terms is an upper bound, as the index matrix
might contain repeats which are combined.
All functions documented here return an object of class kform or
ktensor.
(a <- rform())
#> An alternating linear map from V^3 to R with V=R^7:
#> val
#> 1 4 7 = 6
#> 3 5 6 = -8
#> 2 6 7 = 3
#> 2 3 5 = 2
#> 2 3 7 = -2
#> 1 3 4 = 4
(b <- rform())
#> An alternating linear map from V^3 to R with V=R^7:
#> val
#> 4 5 7 = 9
#> 1 2 6 = -6
#> 1 3 6 = 4
#> 1 5 7 = 5
#> 1 6 7 = 4
#> 2 4 6 = 7
a ^ b
#> An alternating linear map from V^6 to R with V=R^7:
#> val
#> 1 2 3 5 6 7 = -8
a
#> An alternating linear map from V^3 to R with V=R^7:
#> val
#> 1 4 7 = 6
#> 3 5 6 = -8
#> 2 6 7 = 3
#> 2 3 5 = 2
#> 2 3 7 = -2
#> 1 3 4 = 4
a ^ dx
#> An alternating linear map from V^4 to R with V=R^7:
#> val
#> 1 2 3 5 = -2
#> 1 2 3 7 = 2
#> 1 2 6 7 = -3
#> 1 3 5 6 = 8
a ^ dx ^ dy
#> An alternating linear map from V^5 to R with V=R^6:
#> val
#> 1 2 3 5 6 = -8
(x <- rtensor())
#> A linear map from V^3 to R with V=R^7:
#> val
#> 1 4 7 = 8
#> 5 2 2 = 15
#> 5 1 5 = 5
#> 7 3 7 = 4
#> 3 1 7 = 2
#> 3 2 7 = 7
#> 5 1 4 = 3
#> 7 2 5 = 1
x %X% x
#> A linear map from V^6 to R with V=R^7:
#> val
#> 7 2 5 7 2 5 = 1
#> 3 2 7 7 2 5 = 7
#> 3 1 7 7 3 7 = 8
#> 5 1 5 7 3 7 = 20
#> 7 2 5 3 1 7 = 2
#> 5 2 2 7 3 7 = 60
#> 3 1 7 5 1 4 = 6
#> 7 2 5 5 1 5 = 5
#> 5 2 2 5 1 5 = 75
#> 5 2 2 3 2 7 = 105
#> 7 3 7 7 3 7 = 16
#> 5 2 2 5 2 2 = 225
#> 3 2 7 5 1 4 = 21
#> 5 2 2 1 4 7 = 120
#> 1 4 7 5 2 2 = 120
#> 5 1 4 7 2 5 = 3
#> 1 4 7 5 1 5 = 40
#> 3 1 7 7 2 5 = 2
#> 7 2 5 5 2 2 = 15
#> 5 1 5 1 4 7 = 40
#> 5 1 5 5 1 5 = 25
#> 7 2 5 1 4 7 = 8
#> 5 1 4 7 3 7 = 12
#> 3 1 7 1 4 7 = 16
#> 5 1 4 5 1 5 = 15
#> 3 2 7 5 1 5 = 35
#> 3 2 7 3 1 7 = 14
#> 5 1 5 5 2 2 = 75
#> 3 2 7 7 3 7 = 28
#> 5 1 4 5 2 2 = 45
#> 3 2 7 5 2 2 = 105
#> 5 1 5 3 2 7 = 35
#> 3 1 7 5 1 5 = 10
#> 7 3 7 5 2 2 = 60
#> 3 2 7 3 2 7 = 49
#> 3 1 7 5 2 2 = 30
#> 5 2 2 3 1 7 = 30
#> 5 1 5 3 1 7 = 10
#> 7 3 7 3 1 7 = 8
#> 7 3 7 3 2 7 = 28
#> 3 2 7 1 4 7 = 56
#> 5 1 5 5 1 4 = 15
#> 3 1 7 3 1 7 = 4
#> 5 1 4 3 1 7 = 6
#> 1 4 7 3 2 7 = 56
#> 3 1 7 3 2 7 = 14
#> 1 4 7 7 3 7 = 32
#> 7 2 5 7 3 7 = 4
#> 5 1 4 3 2 7 = 21
#> 7 3 7 1 4 7 = 32
#> 5 1 4 1 4 7 = 24
#> 1 4 7 3 1 7 = 16
#> 7 2 5 3 2 7 = 7
#> 1 4 7 5 1 4 = 24
#> 7 3 7 7 2 5 = 4
#> 5 2 2 5 1 4 = 45
#> 7 3 7 5 1 4 = 12
#> 5 1 4 5 1 4 = 9
#> 7 2 5 5 1 4 = 3
#> 1 4 7 7 2 5 = 8
#> 7 3 7 5 1 5 = 20
#> 5 2 2 7 2 5 = 15
#> 1 4 7 1 4 7 = 64
#> 5 1 5 7 2 5 = 5