# minimalPresentation(ZZ,LieAlgebra) -- compute a minimal presentation

## Description

The optional input given above is not relevant for Lie algebras. A minimal set of generators and relations for the Lie algebra $L$ (without differential) is given. In general the presentation applies to $H_0(L)$. The example $L$ below is the Lie algebra of strictly upper triangular $4\times 4$-matrices given by its multiplication table on the natural basis.

 i1 : L=lieAlgebra({e12,e23,e34,e13,e24,e14},Weights=>{1,1,1,2,2,3})/ {e12 e34,e12 e13,e12 e14, e23 e13,e23 e24,e23 e14, e34 e24,e34 e14,e13 e24, e13 e14,e24 e14, e12 e23 - e13, e12 e24 - e14, e13 e34 - e14, e23 e34 - e24} o1 = L o1 : LieAlgebra i2 : M=minimalPresentation(3,L) o2 = M o2 : LieAlgebra i3 : describe M o3 = generators => {e12, e23, e34} Weights => {{1, 0}, {1, 0}, {1, 0}} Signs => {0, 0, 0} ideal => {(e34 e12), (e34 e34 e23), (e23 e34 e23), (e23 e23 e12), (e12 e23 e12)} ambient => LieAlgebra{...10...} diff => {} Field => QQ computedDegree => 0 i4 : dims(1,4,M) o4 = {3, 2, 1, 0} o4 : List