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,
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b], [d, b], [e, b], [d, c], [e, c], [e, d]}}, {{0, -2, 0, -2, 3, -2, 0,
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-2, 2, 3}, {[b, a], [c, a], [d, a], [e, a], [c, b], [d, b], [e, b], [d,
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c], [e, c], [e, d]}}, {{-1, -1, 3, -1, 0, 2, -1, 1, 3, -1}, {[b, a], [c,
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a], [d, a], [e, a], [c, b], [d, b], [e, b], [d, c], [e, c], [e, d]}},
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{{1, -1, 2, -1, 0, 2, -1, 1, -2, -1}, {[b, a], [c, a], [d, a], [e, a],
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[c, b], [d, b], [e, b], [d, c], [e, c], [e, d]}}, {{3, -2, -1, 3, -2,
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-1, 1, 3, -3, 2}, {[b, a], [c, a], [d, a], [e, a], [c, b], [d, b], [e,
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b], [d, c], [e, c], [e, d]}}, {{-2, 0, -1, -3, 3, 3, 1, 0, 3, -1}, {[b,
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a], [c, a], [d, a], [e, a], [c, b], [d, b], [e, b], [d, c], [e, c], [e,
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d]}}, {{1, 1, 2, 2, 1, -1, -1, -1, -1, 2}, {[b, a], [c, a], [d, a], [e,
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a], [c, b], [d, b], [e, b], [d, c], [e, c], [e, d]}}}
o1 : List
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i2 : L = lieAlgebra({a,b,c,d,e}, rels, field=>ZZ/7)
o2 = L
o2 : LieAlgebra
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i3 : computeLie 8
o3 = {5, 3, 5, 3, 5, 3, 5, 3}
o3 : List
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i4 : randomLie({4,0})
o4 = {{-2, -1, -3}, {[d, e, e, a], [e, e, e, a], [e, e, e, d]}}
o4 : List
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