Pensieve header: Testing notebook for Scatter and Glow in OneCo. Continues pensieve://2015-12/, continued pensieve://2016-02/.

In the U(T)U(H) conventions.

SetDirectory["C:\\drorbn\\AcademicPensieve\\2016-01"];
<< SnG.m

Bases

UUBasis[{1,2},{3,4},f]

Meta-associativity for tm

((# // tm[1,2,1] // tm[1,3,1]) == (# // tm[2,3,2] // tm[1,2,1]))& /@ UUBasis[{1,2,3,4},{5,6},f] // Union

Meta-associativity for hm

((# // hm[1,2,1] // hm[1,3,1]) == (# // hm[2,3,2] // hm[1,2,1]))& /@ UUBasis[{5,6},{1,2,3,4},f] // Union

Compatibility between tm and hts

(((# // tm[1,2,1] // hts[4,1]) == (# // hts[4,1] // hts[4,2] // tm[1,2,1]))& /@ UUBasis[{1,2,3},{4,5},f]) // Union

Compatibility between hm and hts

(((# // hm[1,2,1] // hts[1,4]) == (# // hts[2,4] // hts[1,4] // hm[1,2,1]))& /@ UUBasis[{4,5},{1,2,3},f]) // Union

Meta-associativity for dm

((# // dm[1,2,1] // dm[1,3,1]) == (# // dm[2,3,2] // dm[1,2,1]))& /@ UUBasis[4,f] // Union

Meta-Jacobi for tb

tbAS[u_,v_] := tb[0][u, v] + tb[0][v,u];
DeleteCases[
Flatten[Outer[
{##} -> tbAS[##]&,
UUBasis[{0,1},{1,2}, f], UUBasis[{0,2},{3,4},f]
]],
_ -> UU[0]
]

tbJacobi[u_,v_,w_] := tb[0][u, tb[0][v,w]] + tb[0][v, tb[0][w,u]] + tb[0][w, tb[0][u,v]];
DeleteCases[
Flatten[Outer[
{##} -> tbJacobi[##]&,
UUBasis[{0,1},{1,2}, f], UUBasis[{0,2},{3,4},g], UUBasis[{0,3},{5,6},h]
]],
_ -> UU[0]
]

Meta-Jacobi for hb

hbAS[u_,v_] := hb[0][u, v] + hb[0][v,u];
DeleteCases[
Flatten[Outer[
{##} -> hbAS[##]&,
UUBasis[{1,2},{0,1}, f], UUBasis[{3,4},{0,2},f]
]],
_ -> UU[0]
]

hbJacobi[u_,v_,w_] := hb[0][u, hb[0][v,w]] + hb[0][v, hb[0][w,u]] + hb[0][w, hb[0][u,v]];
DeleteCases[
Flatten[Outer[
{##} -> hbJacobi[##]&,
UUBasis[{1,2},{0,1}, f], UUBasis[{3,4},{0,2},g], UUBasis[{5,6},{0,3},h]
]],
_ -> UU[0]
]

ct (contract) poperties

Outer[
Equal[
ct[#1 // tm[1,2,1], #2],
ct[#1, #2] // tm[1,2,1]
]&,
UUBasis[{1,2,3},{0,1},f], UUBasis[{0,4},{2,3},g]
] //Flatten// Union

Outer[
{#1,#2} -> Equal[
ct[#1 // hm[1,2,1], #2],
ct[#1, #2] // hm[1,2,1]
]&,
UUBasis[{1,2},{0,1,2,3},f], UUBasis[{0,4},{4,5},g]
] //Flatten // DeleteCases[#, _->True]&

Outer[
{#1,#2} -> Equal[
ct[#1, #2 // hm[2,3,2]],
ct[#1, #2] // hm[2,3,2]
]&,
UUBasis[{1,2},{0,1},f], UUBasis[{0,3},{2,3,4},g]
] //Flatten // DeleteCases[#, _->True]&

Outer[
{#1,#2} -> Equal[
ct[#1, #2 // tm[3,4,3]],
ct[#1, #2] // tm[3,4,3]
]&,
UUBasis[{1,2},{0,1},f], UUBasis[{0,3,4,5},{2,3},g]
] //Flatten // DeleteCases[#, _->True]&