In[]:=
LayeredGraphPlot[MultiwayOperatorSystem[{f[x_,y_]f[y,x]},{f[f[a,b],f[c,d]]},2,"EvolutionCausalGraph"]]
Out[]=
In[]:=
MultiwayOperatorSystem[{f[x_,y_]f[y,x]},{f[f[a,b],f[c,d]]},3,"StatesGraph"]
Out[]=
In[]:=
rules=#1/.{a.a_,b.b_,c.c_}#2/.{a.a,b.b,c.c}&@@@Join[#,Reverse/@#]&a.⊗b.b.⊗a.,a.⊕b.b.⊕a.,a.⊗b.⊕
b.
a.,a.⊕b.⊗
b.
a.,a.⊗b.⊕c.a.⊗b.⊕a.⊗c.,a.⊕b.⊗c.a.⊕b.⊗(a.⊕c.)
Out[]=
{a_⊗b_b⊗a,a_⊕b_b⊕a,a_⊗(b_⊕
b_
)a,a_⊕b_⊗
b_
a,a_⊗(b_⊕c_)a⊗b⊕a⊗c,a_⊕b_⊗c_(a⊕b)⊗(a⊕c),b_⊗a_a⊗b,b_⊕a_a⊕b,a_a⊗(b⊕
b
),a_a⊕b⊗
b
,a_⊗b_⊕a_⊗c_a⊗(b⊕c),(a_⊕b_)⊗(a_⊕c_)a⊕b⊗c}
¬
In[]:=
%277/.OverBarSquare
Out[]=
{a_⊗b_b⊗a,a_⊕b_b⊕a,a_⊗(b_⊕b_)a,a_⊕b_⊗b_a,a_⊗(b_⊕c_)a⊗b⊕a⊗c,a_⊕b_⊗c_(a⊕b)⊗(a⊕c),b_⊗a_a⊗b,b_⊕a_a⊕b,a_a⊗(b⊕b),a_a⊕b⊗b,a_⊗b_⊕a_⊗c_a⊗(b⊕c),(a_⊕b_)⊗(a_⊕c_)a⊕b⊗c}
In[]:=
MultiwayOperatorSystem[{a_⊗b_b⊗a,a_⊕b_b⊕a},{p⊗(q⊗r)},3,"StatesGraph"]
Out[]=
In[]:=
%281
Out[]=
{a_⊗b_b⊗a,a_⊕b_b⊕a,a_⊗(b_⊕b_)a,a_⊕b_⊗b_a,a_⊗(b_⊕c_)a⊗b⊕a⊗c,a_⊕b_⊗c_(a⊕b)⊗(a⊕c),b_⊗a_a⊗b,b_⊕a_a⊕b,a_a⊗(b⊕b),a_a⊕b⊗b,a_⊗b_⊕a_⊗c_a⊗(b⊕c),(a_⊕b_)⊗(a_⊕c_)a⊕b⊗c}
In[]:=
MultiwayOperatorSystem[{a_⊗b_b⊗a,a_⊕b_b⊕a,a_a⊗(b⊕g[b])},{p⊗(q⊗r)},3,"StatesGraph"]
Catenate
:The argument (List⊗(b⊕g[b]))[p⊗(q⊗r)] is not a valid Association or a list.
Catenate
:The argument Catenate[{{p ⊗ (r ⊗ q)}, {(q ⊗ r) ⊗ p}, (List ⊗ (b ⊕ g[b]))[p ⊗ (q ⊗ r)], {(CircleTimes ⊗ (b ⊕ g[b]))[p, q ⊗ r]}, {(p ⊗ (b ⊕ g[b])) ⊗ (q ⊗ r)}, {p ⊗ (CircleTimes ⊗ (b ⊕ g[b]))[q, r]}, {p ⊗ ((q ⊗ (b ⊕ g[b])) ⊗ r)}, {p ⊗ (q ⊗ (r ⊗ (b ⊕ g[b])))}, {p ⊗ ((q ⊗ r) ⊗ (b ⊕ g[b]))}, {(p ⊗ (q ⊗ r)) ⊗ (b ⊕ g[b])}}13] is not a valid Association or a list.
GatherBy
:List expected at position 1 in GatherBy[Catenate[{Catenate[296p ⊗ (q ⊗ r)]}],First].
Part
:Part specification First〚1,1〛 is longer than depth of object.
Sort
:Nonatomic expression expected at position 1 in Sort[First].
GatherBy
:List expected at position 1 in GatherBy[Catenate[296p ⊗ (q ⊗ r)]Catenate[Catenate[296p ⊗ (q ⊗ r)]],First〚1,1〛Sort[First]].
GatherBy
:List expected at position 1 in GatherBy[Catenate[296p ⊗ (q ⊗ r)]Catenate[Catenate[296p ⊗ (q ⊗ r)]],First〚1,1〛Sort[First]].
General
:Further output of GatherBy::list will be suppressed during this calculation.
Part
:Part specification First〚1,1〛 is longer than depth of object.
Sort
:Nonatomic expression expected at position 1 in Sort[First].
Part
:Part specification First〚1,1〛 is longer than depth of object.
General
:Further output of Part::partd will be suppressed during this calculation.
Sort
:Nonatomic expression expected at position 1 in Sort[First].
General
:Further output of Sort::normal will be suppressed during this calculation.
Catenate
:The argument GatherBy[Catenate[296p ⊗ (q ⊗ r)]Catenate[Catenate[296p ⊗ (q ⊗ r)]],First〚1,1〛Sort[First]] is not a valid Association or a list.
General
:Further output of Catenate::invrp will be suppressed during this calculation.
Out[]=
SimpleGraphGraphCatenate[Catenate[GatherBy[(getOperatorStateEvolutionFunction[getOperatorStateEvolutionFunction[Catenate[{{p ⊗ (r ⊗ q)}, {(q ⊗ r) ⊗ p}, (List ⊗ (b ⊕ g[b]))[p ⊗ (q ⊗ r)], {(CircleTimes ⊗ (b ⊕ g[b]))[p, q ⊗ r]}, {(p ⊗ (b ⊕ g[b])) ⊗ (q ⊗ r)}, {p ⊗ (CircleTimes ⊗ (b ⊕ g[b]))[q, r]}, {p ⊗ ((q ⊗ (b ⊕ g[b])) ⊗ r)}, {p ⊗ (q ⊗ (r ⊗ (b ⊕ g[b])))}, {p ⊗ ((q ⊗ r) ⊗ (b ⊕ g[b]))}, {(p ⊗ (q ⊗ r)) ⊗ (b ⊕ g[b])}}p ⊗ (q ⊗ r)]Catenate[{{p ⊗ (r ⊗ q)}, {(q ⊗ r) ⊗ p}, (List ⊗ (b ⊕ g[b]))[p ⊗ (q ⊗ r)], {(CircleTimes ⊗ (b ⊕ g[b]))[p, q ⊗ r]}, {(p ⊗ (b ⊕ g[b])) ⊗ (q ⊗ r)}, {p ⊗ (CircleTimes ⊗ (b ⊕ g[b]))[q, r]}, {p ⊗ ((q ⊗ (b ⊕ g[b])) ⊗ r)}, {p ⊗ (q ⊗ (r ⊗ (b ⊕ g[b])))}, {p ⊗ ((q ⊗ r) ⊗ (b ⊕ g[b]))}, {(p ⊗ (q ⊗ r)) ⊗ (b ⊕ g[b])}}p ⊗ (q ⊗ r)],{a_⊗b_b⊗a,a_⊕b_b⊕a,a_a⊗(b⊕g[b])}Catenate[{{p ⊗ (r ⊗ q)}, {(q ⊗ r) ⊗ p}, (List ⊗ (b ⊕ g[b]))[p ⊗ (q ⊗ r)], {(CircleTimes ⊗ (b ⊕ g[b]))[p, q ⊗ r]}, {(p ⊗ (b ⊕ g[b])) ⊗ (q ⊗ r)}, {p ⊗ (CircleTimes ⊗ (b ⊕ g[b]))[q, r]}, {p ⊗ ((q ⊗ (b ⊕ g[b])) ⊗ r)}, {p ⊗ (q ⊗ (r ⊗ (b ⊕ g[b])))}, {p ⊗ ((q ⊗ r) ⊗ (b ⊕ g[b]))}, {(p ⊗ (q ⊗ r)) ⊗ (b ⊕ g[b])}}p ⊗ (q ⊗ r)]]getOperatorStateEvolutionFunction[Catenate[{{p ⊗ (r ⊗ q)}, {(q ⊗ r) ⊗ p}, (List ⊗ (b ⊕ g[b]))[p ⊗ (q ⊗ r)], {(CircleTimes ⊗ (b ⊕ g[b]))[p, q ⊗ r]}, {(p ⊗ (b ⊕ g[b])) ⊗ (q ⊗ r)}, {p ⊗ (CircleTimes ⊗ (b ⊕ g[b]))[q, r]}, {p ⊗ ((q ⊗ (b ⊕ g[b])) ⊗ r)}, {p ⊗ (q ⊗ (r ⊗ (b ⊕ g[b])))}, {p ⊗ ((q ⊗ r) ⊗ (b ⊕ g[b]))}, {(p ⊗ (q ⊗ r)) ⊗ (b ⊕ g[b])}}p ⊗ (q ⊗ r)]Catenate[{{p ⊗ (r ⊗ q)}, {(q ⊗ r) ⊗ p}, (List ⊗ (b ⊕ g[b]))[p ⊗ (q ⊗ r)], {(CircleTimes ⊗ (b ⊕ g[b]))[p, q ⊗ r]}, {(p ⊗ (b ⊕ g[b])) ⊗ (q ⊗ r)}, {p ⊗ (CircleTimes ⊗ (b ⊕ g[b]))[q, r]}, {p ⊗ ((q ⊗ (b ⊕ g[b])) ⊗ r)}, {p ⊗ (q ⊗ (r ⊗ (b ⊕ g[b])))}, {p ⊗ ((q ⊗ r) ⊗ (b ⊕ g[b]))}, {(p ⊗ (q ⊗ r)) ⊗ (b ⊕ g[b])}}p ⊗ (q ⊗ r)],{a_⊗b_b⊗a,a_⊕b_b⊕a,a_a⊗(b⊕g[b])}Catenate[{{p ⊗ (r ⊗ q)}, {(q ⊗ r) ⊗ p}, (List ⊗ (b ⊕ g[b]))[p ⊗ (q ⊗ r)], {(CircleTimes ⊗ (b ⊕ g[b]))[p, q ⊗ r]}, {(p ⊗ (b ⊕ g[b])) ⊗ (q ⊗ r)}, {p ⊗ (CircleTimes ⊗ (b ⊕ g[b]))[q, r]}, {p ⊗ ((q ⊗ (b ⊕ g[b])) ⊗ r)}, {p ⊗ (q ⊗ (r ⊗ (b ⊕ g[b])))}, {p ⊗ ((q ⊗ r) ⊗ (b ⊕ g[b]))}, {(p ⊗ (q ⊗ r)) ⊗ (b ⊕ g[b])}}p ⊗ (q ⊗ r)]],{a_⊗b_b⊗a,a_⊕b_b⊕a,a_a⊗(b⊕g[b])}getOperatorStateEvolutionFunction[Catenate[{{p ⊗ (r ⊗ q)}, {(q ⊗ r) ⊗ p}, (List ⊗ (b ⊕ g[b]))[p ⊗ (q ⊗ r)], {(CircleTimes ⊗ (b ⊕ g[b]))[p, q ⊗ r]}, {(p ⊗ (b ⊕ g[b])) ⊗ (q ⊗ r)}, {p ⊗ (CircleTimes ⊗ (b ⊕ g[b]))[q, r]}, {p ⊗ ((q ⊗ (b ⊕ g[b])) ⊗ r)}, {p ⊗ (q ⊗ (r ⊗ (b ⊕ g[b])))}, {p ⊗ ((q ⊗ r) ⊗ (b ⊕ g[b]))}, {(p ⊗ (q ⊗ r)) ⊗ (b ⊕ g[b])}}p ⊗ (q ⊗ r)]Catenate[{{p ⊗ (r ⊗ q)}, {(q ⊗ r) ⊗ p}, (List ⊗ (b ⊕ g[b]))[p ⊗ (q ⊗ r)], {(CircleTimes ⊗ (b ⊕ g[b]))[p, q ⊗ r]}, {(p ⊗ (b ⊕ g[b])) ⊗ (q ⊗ r)}, {p ⊗ (CircleTimes ⊗ (b ⊕ g[b]))[q, r]}, {p ⊗ ((q ⊗ (b ⊕ g[b])) ⊗ r)}, {p ⊗ (q ⊗ (r ⊗ (b ⊕ g[b])))}, {p ⊗ ((q ⊗ r) ⊗ (b ⊕ g[b]))}, {(p ⊗ (q ⊗ r)) ⊗ (b ⊕ g[b])}}p ⊗ (q ⊗ r)],{a_⊗b_b⊗a,a_⊕b_b⊕a,a_a⊗(b⊕g[b])}Catenate[{{p ⊗ (r ⊗ q)}, {(q ⊗ r) ⊗ p}, (List ⊗ (b ⊕ g[b]))[p ⊗ (q ⊗ r)], {(CircleTimes ⊗ (b ⊕ g[b]))[p, q ⊗ r]}, {(p ⊗ (b ⊕ g[b])) ⊗ (q ⊗ r)}, {p ⊗ (CircleTimes ⊗ (b ⊕ g[b]))[q, r]}, {p ⊗ ((q ⊗ (b ⊕ g[b])) ⊗ r)}, {p ⊗ (q ⊗ (r ⊗ (b ⊕ g[b])))}, {p ⊗ ((q ⊗ r) ⊗ (b ⊕ g[b]))}, {(p ⊗ (q ⊗ r)) ⊗ (b ⊕ g[b])}}p ⊗ (q ⊗ r)]]]Catenate[getOperatorStateEvolutionFunction[First〚1,1〛First〚1,1〛,{a_⊗b_b⊗a,a_⊕b_b⊕a,a_a⊗(b⊕g[b])}First〚1,1〛]]){p ⊗ (q ⊗ r){}},(First〚1,1〛Sort[First]){p ⊗ (q ⊗ r){}}]]],VertexShapeFunctionText
stripMetadata[#2]
,#1,{0,0}&,EdgeStyleDirective
,Dashing[None],AbsoluteThickness[1],PerformanceGoalQuality,VertexWeightNone,{}