-- -*- M2-comint -*- hash: 3324014145686074357

i1 : F = frac(ZZ/7[x])

o1 = F

o1 : FractionField

i2 : L = lieAlgebra({a_1,a_2,a_3},Field => F)/
          {3 a_1 a_2 a_3+(5*x) a_2 a_1 a_3,
           a_3 a_2 a_3 a_1}

o2 = L

o2 : LieAlgebra

i3 : L = lieAlgebra({a,b,c},Weights => {{1,-1},{1,4},{2,3}})

o3 = L

o3 : LieAlgebra

i4 : weight b

o4 = {1, 4, 0}

o4 : List

i5 : ex = a b+(1/3) c

o5 = (1/3)c - (b a)

o5 : L

i6 : weight ex

o6 = {2, 3, 0}

o6 : List

i7 : firstDegree ex

o7 = 2

i8 : L1 = lieAlgebra({a,b,c},Weights => {1,1,2})

o8 = L1

o8 : LieAlgebra

i9 : describe L1

o9 = generators => {a, b, c}
     Weights => {{1, 0}, {1, 0}, {2, 0}}
     Signs => {0, 0, 0}
     ideal => {}
     ambient => L1
     diff => {}
     Field => QQ
     computedDegree => 0


i10 : L = lieAlgebra({a,b,c},Weights => {{1,-1},{1,4},{2,3}},
            Signs=>{0,1,1})

o10 = L

o10 : LieAlgebra

i11 : ex = a b+(1/3) c

o11 = (1/3)c - (b a)

o11 : L

i12 : sign ex

o12 = 1

i13 : M = lieAlgebra{a,b,c}

o13 = M

o13 : LieAlgebra

i14 : L = M/{a b}

o14 = L

o14 : LieAlgebra

i15 : a c

o15 =  - (c a)

o15 : L

i16 : Q = L/{a c}

o16 = Q

o16 : LieAlgebra

i17 : ideal(Q)

o17 = { - (b a),  - (c a)}

o17 : List

i18 : oo_1

o18 =  - (c a)

o18 : M

i19 : ambient Q

o19 = M

o19 : LieAlgebra

i20 : F = lieAlgebra({a,b,c},Weights => {1,1,2},
            Signs=>{1,0,0})

o20 = F

o20 : LieAlgebra

i21 : L = F/{-c+a a,(a b) a}

o21 = L

o21 : LieAlgebra

i22 : dims(1,4,L)

o22 = {2, 2, 1, 2}

o22 : List

i23 : describe L

o23 = generators => {a, b, c}
      Weights => {{1, 0}, {1, 0}, {2, 0}}
      Signs => {1, 0, 0}
      ideal => { - c + (a a),  - (1/2)(b a a)}
      ambient => F
      diff => {}
      Field => QQ
      computedDegree => 4


i24 : M = minimalPresentation(4,L)

o24 = M

o24 : LieAlgebra

i25 : describe M

o25 = generators => {a, b}
      Weights => {{1, 0}, {1, 0}}
      Signs => {1, 0}
      ideal => {(b a a)}
      ambient => LieAlgebra{...10...}
      diff => {}
      Field => QQ
      computedDegree => 0


i26 : 
      L = lieAlgebra{a,b}/{a a a b,b b b a}

o26 = L

o26 : LieAlgebra

i27 : dims(1,4,L)

o27 = {2, 1, 2, 1}

o27 : List

i28 : peek L#cache

o28 = CacheTable{ambient => LieAlgebra{...10...}                                         }
                 basis => MutableHashTable{...15...}
                 degree => 4
                 degrees => MutableHashTable{...4...}
                 dim => MutableHashTable{...5...}
                 gb => MutableHashTable{...4...}
                 generators => {a, b}
                 lieRing => QQ[aR ..aR ]
                                 0    9
                 max => 5
                 mbRing => QQ[mb      , mb      , mb      , mb      , mb      , mb      ]
                                {1, 0}    {1, 1}    {2, 0}    {3, 0}    {3, 1}    {4, 0}
                 opL => MutableHashTable{}

i29 : L#cache.basis#4

o29 = {aR aR aR aR }
         0  3  4  7

o29 : List

i30 : basis(4,L)

o30 = {(b a b a)}

o30 : List

i31 : L#cache.gb#4

o31 = ideal (aR aR aR aR , aR aR aR aR  - aR aR aR aR , aR aR aR aR )
               0  3  5  7    0  3  5  6     0  3  4  7    0  3  4  6

o31 : Ideal of QQ[aR ..aR ]
                    0    9

i32 : a b b a

o32 = (b a b a)

o32 : L

i33 : dims(1,6,L)

o33 = {2, 1, 2, 1, 2, 1}

o33 : List

i34 : peek L#cache

o34 = CacheTable{ambient => LieAlgebra{...10...}                                                                       }
                 basis => MutableHashTable{...28...}
                 degree => 6
                 degrees => MutableHashTable{...6...}
                 dim => MutableHashTable{...7...}
                 gb => MutableHashTable{...6...}
                 generators => {a, b}
                 lieRing => QQ[aR ..aR  ]
                                 0    21
                 max => 11
                 mbRing => QQ[mb      , mb      , mb      , mb      , mb      , mb      , mb      , mb      , mb      ]
                                {1, 0}    {1, 1}    {2, 0}    {3, 0}    {3, 1}    {4, 0}    {5, 0}    {5, 1}    {6, 0}
                 opL => MutableHashTable{...10...}

i35 : L = lieAlgebra{a,b,c}

o35 = L

o35 : LieAlgebra

i36 : x = (a b c a) (b c)

o36 = (b c a c b a) - (b c b a c a) - (b c c a b a) - (c b a c b a) + (c b b a c a) + (c b c a b a)

o36 : L

i37 : Q = L#cache.mbRing

o37 = Q

o37 : PolynomialRing

i38 : numgens Q

o38 = 196

i39 : indexForm x

o39 = mb        - mb        - mb        + mb        + mb        - mb
        {6, 22}     {6, 24}     {6, 43}     {6, 45}     {6, 74}     {6, 76}

o39 : Q

i40 : standardForm(oo,L)

o40 = (b c a c b a) - (b c b a c a) - (b c c a b a) - (c b a c b a) + (c b b a c a) + (c b c a b a)

o40 : L

i41 : 
      
      
      
      
      
      
