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GradedLieAlgebras :: random(ZZ,LieAlgebra)

random(ZZ,LieAlgebra) -- get a random element of a Lie algebra

Synopsis

Description

The optional inputs given above are not relevant for Lie algebras. Below is an example of a periodic Lie algebra (a periodization of $sl_3$) with five generators and seven random quadratic relations.

Synopsis

  • Usage:
    random(d,L)
  • Inputs:
  • Outputs:
    • an instance of the type LieElement, a random Lie element of degree $d$

Synopsis

  • Usage:
    random(m,L)
  • Inputs:
  • Outputs:
    • an instance of the type LieElement, a random Lie element of multi-degree $m$

Synopsis

  • Usage:
    random(m,n,L)
  • Inputs:
  • Outputs:
    • an instance of the type LieElement, a random Lie element of degree $m$ and homological degree $n$
i1 : L = lieAlgebra({a,b,c,d,e}, Field=>ZZ/7)

o1 = L

o1 : LieAlgebra
i2 : Q = L/apply(7,i->random(2,L))

o2 = Q

o2 : LieAlgebra
i3 : dims(1,8,Q)

o3 = {5, 3, 5, 3, 5, 3, 5, 3}

o3 : List
i4 : random({4,0},Q)

o4 = (-2)(d e e a) - (e e e a) + (-3)(e e e d)

o4 : Q