Pensieve header: Testing the FreeLie package.

SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\WKO4"];
<< FreeLie.m
$SeriesShowDegree=4

{α=RandomLieSeries[{1,2}], β=RandomLieSeries[{1,2}]}

EulerE[α]

BCH[LW@x,LW@y]

α // (Subscript[CC, 1])[β]

α // (Subscript[RC, 1])[β]

(α // (Subscript[RC, 1])[β])[3]

Do[Echo@Timing[k->Length[AllLyndonWords[k,{x,y,z}]]], {k,15}]

Log[3,956576]//N

Timing[Length[alw=AllLyndonWords[13,{x,y}]]]

Timing[ι /@ alw;]

ι[alw[[1]]]

div[x,alw[[1]]]

div[y,alw[[1]]]

Timing[div[x,#]& /@ alw;]

A=LS[{x,y}, As]; dxA=div[x,A]

dxA[3]

Do[Print[Timing[dxA[d];d]], {d,13}]

Do[Print[Timing[A[d];d]], {d,13}]

Do[Print[Timing[div[x,A[d]];d]], {d,13}]

Do[Print[Timing[div[x,List@@(A[d])];d]], {d,13}]

div[x,List@@(A[4])]

Do[Print[Timing[Total[div[x,List@@(A[d])]]//Expand;d]], {d,13}]

Table[(Total[div[x,List@@(A[d])]]//Expand) == div[x,A[d]], {d,13}] // Timing