Algebra of Lie symmetries of linear Heat equation .
 Kai - Seng Chou, Guan - Xin Li, Changzheng Qu . A note on optimal systems for the heat equation .
 Journal of Mathematical Analysis and Applicatons, 261, 741 - 751, 2001.

SetDirectory[NotebookDirectory[]];

<< "SymboLie.wl"

vars={x,t,u};gens={{0,1,0},{1,0,0},{x,2t,0},{0,0,u},{2 t,0,-x u},{4t x,4 t^2,-(x^2 +2 t) u}};pars={{},{}};

cs=StructureConstants[gens,vars];

ct=CommutatorTable[cs];ct//MatrixForm

FastRun=1;

Timing[alg1=SubAlgebra[cs,{{},{}},1];]

PrintOptimal[alg1]

PrintGraph[alg1,1]

Timing[alg2=SubAlgebra[cs,{{},{}},2];]

PrintOptimal[alg2]

PrintGraph[alg2,1]

Timing[alg3=SubAlgebra[cs,{{},{}},3];]

PrintOptimal[alg3]

PrintGraph[alg3,1]

Timing[alg4=SubAlgebra[cs,{{},{}},4];]

PrintOptimal[alg4]

PrintGraph[alg4,1]

Timing[alg5=SubAlgebra[cs,{{},{}},5];]

PrintOptimal[alg5]

PrintGraph[alg5,1]

alg={alg1,alg2,alg3,alg4,alg5}

SessionTime[]