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GradedLieAlgebras :: randomLie

randomLie -- gives a random element of a lie algebra

Synopsis

Description

Below is an example of a periodic Lie algebra (a periodization of sl3) with random quadratic relations.

i1 : rels=apply(7,i->randomLie(2,{a,b,c,d,e}, field => ZZ/7))

o1 = {{{3, 0, 1, 3, 0, 2, 3, -3, 3, 3}, {[b, a], [c, a], [d, a], [e, a], [c,
     ------------------------------------------------------------------------
     b], [d, b], [e, b], [d, c], [e, c], [e, d]}}, {{0, -2, 0, -2, 3, -2, 0,
     ------------------------------------------------------------------------
     -2, 2, 3}, {[b, a], [c, a], [d, a], [e, a], [c, b], [d, b], [e, b], [d,
     ------------------------------------------------------------------------
     c], [e, c], [e, d]}}, {{-1, -1, 3, -1, 0, 2, -1, 1, 3, -1}, {[b, a], [c,
     ------------------------------------------------------------------------
     a], [d, a], [e, a], [c, b], [d, b], [e, b], [d, c], [e, c], [e, d]}},
     ------------------------------------------------------------------------
     {{1, -1, 2, -1, 0, 2, -1, 1, -2, -1}, {[b, a], [c, a], [d, a], [e, a],
     ------------------------------------------------------------------------
     [c, b], [d, b], [e, b], [d, c], [e, c], [e, d]}}, {{3, -2, -1, 3, -2,
     ------------------------------------------------------------------------
     -1, 1, 3, -3, 2}, {[b, a], [c, a], [d, a], [e, a], [c, b], [d, b], [e,
     ------------------------------------------------------------------------
     b], [d, c], [e, c], [e, d]}}, {{-2, 0, -1, -3, 3, 3, 1, 0, 3, -1}, {[b,
     ------------------------------------------------------------------------
     a], [c, a], [d, a], [e, a], [c, b], [d, b], [e, b], [d, c], [e, c], [e,
     ------------------------------------------------------------------------
     d]}}, {{1, 1, 2, 2, 1, -1, -1, -1, -1, 2}, {[b, a], [c, a], [d, a], [e,
     ------------------------------------------------------------------------
     a], [c, b], [d, b], [e, b], [d, c], [e, c], [e, d]}}}

o1 : List
i2 : L = lieAlgebra({a,b,c,d,e}, rels, field=>ZZ/7)

o2 = L

o2 : LieAlgebra
i3 : computeLie 8

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

o3 : List
i4 : randomLie({4,0})

o4 = {{-2, -1, -3}, {[d, e, e, a], [e, e, e, a], [e, e, e, d]}}

o4 : List

Ways to use randomLie :