Names attributes of free group elements
donames.RdGet and set names of free group elements and arithmetic operations
Details
Function donames() is a low-level helper function that ensures
that the result of arithmetic operations such as + and ^
have the correct names attributes. The behaviour is inherited from
that of base::`+`.
Examples
x <- rfree(9,4)
x
#> [1] a^-1.b^4 c^-4 b^4.c^4.b^4 a^3.b^-3.a^-1.b
#> [5] c^4.b^-2 b.a^-1.d^2 d^2.c^3 c^-3.d^2.a^-4
#> [9] b^2.c^-5.d^-1
names(x) <- letters[1:9]
x
#> a b c d e
#> a^-1.b^4 c^-4 b^4.c^4.b^4 a^3.b^-3.a^-1.b c^4.b^-2
#> f g h i
#> b.a^-1.d^2 d^2.c^3 c^-3.d^2.a^-4 b^2.c^-5.d^-1
z <- as.free('z')
x + x
#> a b
#> a^-1.b^4.a^-1.b^4 c^-8
#> c d
#> b^4.c^4.b^8.c^4.b^4 a^3.b^-3.a^-1.b.a^3.b^-3.a^-1.b
#> e f
#> c^4.b^-2.c^4.b^-2 b.a^-1.d^2.b.a^-1.d^2
#> g h
#> d^2.c^3.d^2.c^3 c^-3.d^2.a^-4.c^-3.d^2.a^-4
#> i
#> b^2.c^-5.d^-1.b^2.c^-5.d^-1
x^z
#> a b c
#> z^-1.a^-1.b^4.z z^-1.c^-4.z z^-1.b^4.c^4.b^4.z
#> d e f
#> z^-1.a^3.b^-3.a^-1.b.z z^-1.c^4.b^-2.z z^-1.b.a^-1.d^2.z
#> g h i
#> z^-1.d^2.c^3.z z^-1.c^-3.d^2.a^-4.z z^-1.b^2.c^-5.d^-1.z
z^x
#> a b
#> b^-4.a.z.a^-1.b^4 c^4.z.c^-4
#> c d
#> b^-4.c^-4.b^-4.z.b^4.c^4.b^4 b^-1.a.b^3.a^-3.z.a^3.b^-3.a^-1.b
#> e f
#> b^2.c^-4.z.c^4.b^-2 d^-2.a.b^-1.z.b.a^-1.d^2
#> g h
#> c^-3.d^-2.z.d^2.c^3 a^4.d^-2.c^3.z.c^-3.d^2.a^-4
#> i
#> d.c^5.b^-2.z.b^2.c^-5.d^-1
n <- 1:9
names(n) <- LETTERS[1:9]
x*n
#> a
#> a^-1.b^4
#> b
#> c^-8
#> c
#> b^4.c^4.b^8.c^4.b^8.c^4.b^4
#> d
#> a^3.b^-3.a^-1.b.a^3.b^-3.a^-1.b.a^3.b^-3.a^-1.b.a^3.b^-3.a^-1.b
#> e
#> c^4.b^-2.c^4.b^-2.c^4.b^-2.c^4.b^-2.c^4.b^-2
#> f
#> b.a^-1.d^2.b.a^-1.d^2.b.a^-1.d^2.b.a^-1.d^2.b.a^-1.d^2.b.a^-1.d^2
#> g
#> d^2.c^3.d^2.c^3.d^2.c^3.d^2.c^3.d^2.c^3.d^2.c^3.d^2.c^3
#> h
#> c^-3.d^2.a^-4.c^-3.d^2.a^-4.c^-3.d^2.a^-4.c^-3.d^2.a^-4.c^-3.d^2.a^-4.c^-3.d^2.a^-4.c^-3.d^2.a^-4.c^-3.d^2.a^-4
#> i
#> b^2.c^-5.d^-1.b^2.c^-5.d^-1.b^2.c^-5.d^-1.b^2.c^-5.d^-1.b^2.c^-5.d^-1.b^2.c^-5.d^-1.b^2.c^-5.d^-1.b^2.c^-5.d^-1.b^2.c^-5.d^-1
n*x # note different names
#> a
#> a^-1.b^4
#> b
#> c^-8
#> c
#> b^4.c^4.b^8.c^4.b^8.c^4.b^4
#> d
#> a^3.b^-3.a^-1.b.a^3.b^-3.a^-1.b.a^3.b^-3.a^-1.b.a^3.b^-3.a^-1.b
#> e
#> c^4.b^-2.c^4.b^-2.c^4.b^-2.c^4.b^-2.c^4.b^-2
#> f
#> b.a^-1.d^2.b.a^-1.d^2.b.a^-1.d^2.b.a^-1.d^2.b.a^-1.d^2.b.a^-1.d^2
#> g
#> d^2.c^3.d^2.c^3.d^2.c^3.d^2.c^3.d^2.c^3.d^2.c^3.d^2.c^3
#> h
#> c^-3.d^2.a^-4.c^-3.d^2.a^-4.c^-3.d^2.a^-4.c^-3.d^2.a^-4.c^-3.d^2.a^-4.c^-3.d^2.a^-4.c^-3.d^2.a^-4.c^-3.d^2.a^-4
#> i
#> b^2.c^-5.d^-1.b^2.c^-5.d^-1.b^2.c^-5.d^-1.b^2.c^-5.d^-1.b^2.c^-5.d^-1.b^2.c^-5.d^-1.b^2.c^-5.d^-1.b^2.c^-5.d^-1.b^2.c^-5.d^-1