Random free objects

Creates a vector of random free objects. Intended as a quick “get you going” example of free group objects

Usage

rfree(n = 7, size = 4, number = size, powers = seq(from = -size, to = size))
rfreee(n = 30, size = 8, number = size, powers = seq(from = -size, to = size))
rfreeee(n = 40, size = 25, number = size, powers = seq(from = -size, to = size))

Arguments

n: Length of random vector to generate
size: Maximum length of each element
number: How many distinct letters to sample from
powers: Powers in resulting polynomial. An integer n is interpreted (via sample()) as seq_len(n)

Details

The auxiliary arguments specify the general complexity of the returned object with small meaning simpler.

Functions rfreee() and rfreeee() give, by default, successively more complicated expressions.

Author

Robin K. S. Hankin

Examples


rfree()
#> [1] c^3.d^-3.c^3.d^4  a^-4.d^2          a^-1.b^2.c^2.b^-4 b^2.d^-1         
#> [5] c^-2.a^-3.b^2     d.c^2.d^2         a^2.b^-4.d.a^-1  

abelianize(rfree())
#> [1] b^3.c^2.d^-2 d^4          a^-1.b^-1    a^-1.b^2.c^8 b^-1.c^4    
#> [6] b^3.c^2      a.d^7       

rfree(10,2)
#>  [1] a       b^-1    a^-2    a^2.b   a^2.b^2 a^3     b.a     b^-3    b      
#> [10] a      
rfree(10,30,26)
#>  [1] k^-22.g^-4.z^-4.e^-14.p^-12.g^-9.k^-5.e^-1.o^-30.d^10.p^-17.t^15.b^3.g^-12.t^-7.d^30.o^-19.m^-27.h^7.e^16.l^18.y^-19.m^-14.n^19.z^-6.k^-22.p^-12.o^-26.p^30.b^29
#>  [2] z^8.y^-5.p^25.c^-12.p^-20.n.p.u^-15.p^3.e^27.z^-14.b^30.p^-24.t^-21.k^15.n^-14.b^29.u^-13.t^23.l^-21.s^-12.h^-26.a^6.j^8.c^28.y^44                              
#>  [3] b^-3.j^-26.r^-13.k^9.a^-8.p^-23.y^-1.s^13.n^26.g^7.e^-28.b^19.e^25.b^13.j^8.e^-24.d^-26.t^-25.x^-14.u^28.n^-4.e^-27.q^-28.j^-30.u^-2.o^-7.d^-17.w^-24           
#>  [4] u^25.p^-25.s^7.h^-26.u^13.t^14.a^-5.s^19.v^-6.y^20.o^8.b^11.v^21.e.j^-13.z^-17.n.w^-17.o^-27.l^4.f^-4.o^17.q^21.f^13.m^13.d^-13.k^-24.e^-27                     
#>  [5] w^-17.u^-26.w^-28.y^-16.a^12.o^21.z^21.r.z^-14.f^26.r^29.n^-11.a^3.x^-21.e^-4.g^20.c^2.t^-23.c^-20.k^25.a^12.o^5.z^27.a^14.j^13.i^-14.c^-3.q^-6                 
#>  [6] i^-23.c^-26.w^-30.r^12.v^11.f^-1.b^-8.t^-13.z^-2.t^22.o^17.a^-27.h^11.q^28.a^-7.y^28.x^-3.t^5.r^-5.c^-5.u^-15.m^-3.o^-18.v^6.j^-28.t^29.z^-2.v^-9.t^12          
#>  [7] a^14.c^-7.j^-4.k^9.t^11.i^-12.t^13.i^5.z^20.i^14.w^4.t^5.z^-30.i^-12.q^-19.s^-3.e^-3.m^-18.e^13.k^10.o^-20.s^-1.i^16.f^17.c^7.l^25.v^-20                        
#>  [8] j^-10.s^-5.w^2.t^4.x^2.g^24.h^-6.r^7.v^-21.c^2.v^-8.p^-3.u^-21.a^-3.u^-23.w^-15.h^-3.d^12.w^18.a^-14.l^-1.k.t^6.n^-7.d^16.u^-8.e^-2.d^2.v^6                     
#>  [9] a^25.h^18.u^13.q^-16.i^-28.w^10.s^8.c^20.l^5.u^-19.p^-24.b^-1.l^-4.j^-19.n^23.u^-10.x^29.l^10.p^3.c^14.g^9.r^28.s^-6.j^-26.m^-3.u^11.p^-17.s^-22                
#> [10] c^-1.q^-9.y^5.f^-24.n^6.e^14.a^5.x^-17.p^-6.y^23.r^28.u^-8.c^15.v^21.g^-20.q^3.p^18.u^24.c^15.b^-24.t^25.u^-11.j^3.z^-12.c^24.a^-7.d^-18.u^-23.n^11             

rfree(powers=5)
#> [1] c^5.b^4.a^2.d^3 d^3.c^5.d^2.c^5 a.d^2.c^5.d^2   a^2.c^5.b^5    
#> [5] c^2.b^2.c^2     b^2.a^2.b^3.d^4 a^4.d^8        
rfree(powers=5:6)
#> [1] b^5.c^6.d^6.a^6 a^6.c^11.b^6    b^6.a^5.c^5.d^6 d^6.c^6.d^11   
#> [5] d^5.a^5.b^5.d^5 c^6.d^6.a^5.d^6 d^5.b^6.c^6.d^5

rfree(20,2)^alpha(26)
#>  [1] z^-1.b^-2.a.z    z^-1.b^-2.a^2.z  z^-1.a.b^-2.z    z^-1.b.a^-2.z   
#>  [5] 0                z^-1.a^-1.z      z^-1.b^-2.a^-1.z z^-1.a^-2.b^-1.z
#>  [9] z^-1.b^2.z       z^-1.a^3.z       z^-1.b^-1.a^2.z  z^-1.b.z        
#> [13] z^-1.b^-3.z      z^-1.a^2.b^2.z   z^-1.b^-2.a^-2.z z^-1.b^-3.z     
#> [17] z^-1.b.a^-2.z    z^-1.b^4.z       z^-1.a^4.z       z^-1.a^2.z

Usage

Arguments

Details

Author

See also

Examples