-- -*- M2-comint -*- hash: 1609363193008906781

i1 : F1 = lieAlgebra({a,b,c},Weights => {{1,0},{2,1},{3,2}},
          Signs => {1,1,1},LastWeightHomological => true)

o1 = F1

o1 : LieAlgebra

i2 : D1=differentialLieAlgebra{0_F1,a a,a b}

o2 = D1

o2 : LieAlgebra

i3 : describe D1

o3 = generators => {a, b, c}
     Weights => {{1, 0}, {2, 1}, {3, 2}}
     Signs => {1, 1, 1}
     ideal => { - (a a a)}
     ambient => F1
     diff => {0, (a a), (a b)}
     Field => QQ
     computedDegree => 0


i4 : F2 = lieAlgebra({a,b,c2,c3,c4},Signs => {0,0,1,0,1},
          Weights => {{1,0},{1,0},{2,1},{3,2},{5,3}},
          LastWeightHomological => true)

o4 = F2

o4 : LieAlgebra

i5 : D2=differentialLieAlgebra{0_F2,0_F2,a b,a c2,a b c3}

o5 = D2

o5 : LieAlgebra

i6 : describe D2

o6 = generators => {a, b, c2, c3, c4}
     Weights => {{1, 0}, {1, 0}, {2, 1}, {3, 2}, {5, 3}}
     Signs => {0, 0, 1, 0, 1}
     ideal => { - (a b a), (a b a c2)}
     ambient => F2
     diff => {0, 0,  - (b a), (a c2), (a b c3)}
     Field => QQ
     computedDegree => 0


i7 : 
     d2 = differential D2

o7 = d2

o7 : LieDerivation

i8 : x = a c3 + b c3 + (1/2) c2 c2

o8 = (1/2)(c2 c2) + (a c3) + (b c3)

o8 : D2

i9 : d2 x

o9 = (a a c2) + (a b c2)

o9 : D2

i10 : F3 = lieAlgebra({a,b,c},Signs => 1,
             Weights => {{1,0},{1,0},{2,1}},
             LastWeightHomological => true)

o10 = F3

o10 : LieAlgebra

i11 : D3 = differentialLieAlgebra{0_F3,0_F3,a b}

o11 = D3

o11 : LieAlgebra

i12 : L3 = D3/{b c,c c}

o12 = L3

o12 : LieAlgebra

i13 : describe L3

o13 = generators => {a, b, c}
      Weights => {{1, 0}, {1, 0}, {2, 1}}
      Signs => {1, 1, 1}
      ideal => {(b c), (c c),  - (b b a), (b a c) + (a b c) - (c b a)}
      ambient => F3
      diff => {0, 0, (b a)}
      Field => QQ
      computedDegree => 0


i14 : use D3

i15 : L4 = D3/{a a,b b}

o15 = L4

o15 : LieAlgebra

i16 : H4 = lieHomology L4

o16 = H4

o16 : VectorSpace

i17 : B4 = boundaries L4

o17 = B4

o17 : LieSubAlgebra

i18 : C4 = cycles L4

o18 = C4

o18 : LieSubAlgebra

i19 : dims(5,H4)

o19 = | 2 0 0 0 0 |
      | 0 0 2 1 0 |
      | 0 0 0 0 0 |
      | 0 0 0 0 0 |
      | 0 0 0 0 0 |

               5       5
o19 : Matrix ZZ  <-- ZZ

i20 : basis(4,1,H4)

o20 = {(b a c)}

o20 : List

i21 : basis(4,1,B4)

o21 = {(a b c) + (b a c)}

o21 : List

i22 : basis(4,1,C4)

o22 = {(b a c), (a b c)}

o22 : List

i23 : (b a c) (b a c + (a b c))

o23 =  - (c b a b a c) + (a b c b a c) + (b a c b a c)

o23 : L4

i24 : member(oo,B4)

o24 = true

i25 : basis(3,1,H4)

o25 = {(b c), (a c)}

o25 : List

i26 : basis(3,1,B4)

o26 = {}

o26 : List

i27 : basis(5,1,B4)

o27 = {(b a b c), (a b a c)}

o27 : List

i28 : basis(5,1,L4)

o28 = {(a b a c), (b a b c)}

o28 : List

i29 : d4 = differential L4

o29 = d4

o29 : LieDerivation

i30 : b52 = basis(5,2,L4)

o30 = {(a c c), (b c c)}

o30 : List

i31 : d4\b52

o31 = { - 2 (a b a c),  - 2 (b a b c)}

o31 : List

i32 : basis(5,2,C4)

o32 = {}

o32 : List

i33 : 
      
