WOLFRAM NOTEBOOK

In[]:=
NestGraphTagged[n|->{2n,n+1},1,5,"StateLabeling"->True]
Out[]=
In[]:=
NestGraphTagged[n|->{2n,n+1},1,10]
Out[]=
In[]:=
Log[2.,500*^6]
Out[]=
28.8974
In[]:=
n|->1+
1
2
-
4
n,1+Conjugate
1
2
-
4
n
Out[]=
Functionn,1+
1
2
-
4
n,1+Conjugate
1
2
-
4
n
In[]:=
Fold[{n,i}|->1+{c,c}[[i]]n,{1,1,2,1,2,1}]
In[]:=
Fold[{n,i}|->1+{a+bI,a-bI}[[i]]n,{1,1,2,1,2,1}]//Expand
Out[]=
1+a+
2
a
+
3
a
+
4
a
+
5
a
+b+
2
a
b+
4
a
b+
2
b
+a
2
b
+2
2
a
2
b
+2
3
a
2
b
+
3
b
+2
2
a
3
b
+
4
b
+a
4
b
+
5
b
In[]:=
Fold[{n,i}|->1+{c,c}[[i]]n,{1,2,2,1,1,1}]
Out[]=
1+c(1+c(1+c(1+Conjugate[c](1+Conjugate[c]))))
In[]:=
Tuples[{1,2},3]
Out[]=
{{1,1,1},{1,1,2},{1,2,1},{1,2,2},{2,1,1},{2,1,2},{2,2,1},{2,2,2}}
In[]:=
Expand[Fold[{n,i}|->1+{a+bI,a-bI}[[i]]n,#]]&/@Tuples[{1,2},3]
Out[]=
{1+a+
2
a
+b+2ab-
2
b
,1+a+
2
a
-b+
2
b
,1+a+
2
a
+b+
2
b
,1+a+
2
a
-b-2ab-
2
b
,1+a+2
2
a
+b+4ab-2
2
b
,1+a+2
2
a
-b+2
2
b
,1+a+2
2
a
+b+2
2
b
,1+a+2
2
a
-b-4ab-2
2
b
}
In[]:=
Expand[Fold[{n,i}|->1+{a+bI,a-bI}[[i]]n,#]]&/@Tuples[{1,2},2]
Out[]=
{1+a+b,1+a-b,1+2a+2b,1+2a-2b}
In[]:=
DeleteCases[Flatten[Outer[Equal,%,%]],True]
Out[]=
{1+a+b1+a-b,1+a+b1+2a+2b,1+a+b1+2a-2b,1+a-b1+a+b,1+a-b1+2a+2b,1+a-b1+2a-2b,1+2a+2b1+a+b,1+2a+2b1+a-b,1+2a+2b1+2a-2b,1+2a-2b1+a+b,1+2a-2b1+a-b,1+2a-2b1+2a+2b}
SubtractSides
In[]:=
ComplexExpand[1+a+b1+a-b]
In[]:=
SubtractSides[1+a+b1+a-b]
Out[]=
2b0
In[]:=
Coefficient[1+a+Ib,I]
Coefficient
: is not a valid variable.
In[]:=
1+a+Ib/.I->i
Out[]=
1+a+bi
In[]:=
EquationsFromSequences[seqs_List]:=Module[{u=Expand[Fold[{n,i}|->1+{a+bI,a-bI}[[i]]n,1,#]]&/@seqs,eqns},eqns=Thread[#==0]&/@(ComplexExpand[ReIm[First[#]]]&/@Union[SubtractSides/@DeleteCases[Flatten[Outer[Equal,u,u]],True|False]])]
In[]:=
ExprsFromSequences[seqs_]:=Expand[Fold[{n,i}|->1+{a+bI,a-bI}[[i]]n,1,#]]&/@seqs
In[]:=
ExprsFromSequences[Tuples[{1,2},2]]
Out[]=
{1+a+
2
a
+b+2ab-
2
b
,1+a+
2
a
-b+
2
b
,1+a+
2
a
+b+
2
b
,1+a+
2
a
-b-2ab-
2
b
}
In[]:=
EquationsFromSequences[Tuples[{1,2},2]]
Out[]=
{{True,-2b0},{True,2b0},{True,-2b-4ab0},{True,2b+4ab0},{-2
2
b
0,-2ab0},{-2
2
b
0,-2b-2ab0},{-2
2
b
0,2ab0},{-2
2
b
0,2b+2ab0},{2
2
b
0,-2ab0},{2
2
b
0,-2b-2ab0},{2
2
b
0,2ab0},{2
2
b
0,2b+2ab0}}
In[]:=
Solve[#,{a,b},Reals]&/@%
Solve
:Equations may not give solutions for all "solve" variables.
Solve
:Equations may not give solutions for all "solve" variables.
Solve
:Equations may not give solutions for all "solve" variables.
General
:Further output of Solve::svars will be suppressed during this calculation.
Out[]=
{{b0}},{{b0}},a
-
1
2
if b>0||b<0
,{b0},a
-
1
2
if b>0||b<0
,{b0},{{b0}},{{b0}},{{b0}},{{b0}},{{b0}},{{b0}},{{b0}},{{b0}}
In[]:=
EquationsFromSequences[Tuples[{1,2},3]]
Out[]=
In[]:=
Solve[#,{a,b},Reals]&/@%
Solve
:Equations may not give solutions for all "solve" variables.
Solve
:Equations may not give solutions for all "solve" variables.
Solve
:Equations may not give solutions for all "solve" variables.
General
:Further output of Solve::svars will be suppressed during this calculation.
Out[]=
{{b0}},{{b0}},{{b0}},{{b0}},{{b0}},{{b0}},{{b0}},{{b0}},{{b0}},{{b0}},{{b0}},{{b0}},a-
1
2
,b
0 if a>-
1
2
||a<-
1
2
,{{b0}},a-
1
2
,b
0 if a>-
1
2
||a<-
1
2
,{{b0}},{{b0}},{{b0}},a-
1
2
,b
0 if a>-
1
2
||a<-
1
2
,{{b0}},a-
1
2
,b
0 if a>-
1
2
||a<-
1
2
,{{b0}},{{b0}},{{b0}},b
0 if a∈
,b
-
1-
2
a
if -1<a<1
,b
1-
2
a
if -1<a<1
,{{b0}},{b0},b-
1+2a+3
2
a
,b
1+2a+3
2
a
,{{b0}},{{b0}},{{b0}},{{b0}},{{b0}},{{b0}},b
0 if a>-
1
2
||a<-
1
2
,a-
1
2
,b0,a-
1
2
,b-
3
2
,a-
1
2
,b
3
2
,{{b0}},{{b0}},b
0 if a>-
1
2
||a<-
1
2
,a-
1
2
,b0,a-
1
2
,b-
3
2
,a-
1
2
,b
3
2
,{{b0}},b
0 if a∈
,b
-
1-
2
a
if -1<a<1
,b
1-
2
a
if -1<a<1
,{{b0}},{{b0}},{b0},b-
1+2a+3
2
a
,b
1+2a+3
2
a
,{{b0}},{{b0}},{{b0}},{{b0}},{{b0}},{{b0}},b
0 if a>-
1
2
||a<-
1
2
,a-
1
2
,b0,a-
1
2
,b-
3
2
,a-
1
2
,b
3
2
,{{b0}},{{b0}},b
0 if a>-
1
2
||a<-
1
2
,a-
1
2
,b0,a-
1
2
,b-
3
2
,a-
1
2
,b
3
2
In[]:=
a+bI/.a-
1
2
,b
3
2
Out[]=
-
1
2
+
3
2
I.e. not of bounded size... (unlike the other cases...)

Multiple Word Lengths Together

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