Lill
Lill
Appendix C
Lill’s method
Lill’s method
Lill's polygonal (line) segment is a geometric representation of a polynomial p(x) in x with coefficients in a field of Reals
p(x)=++...+x+
a
n
n
x
a
n-1
n-1
x
a
1
a
0
In[]:=
Clear[CToRR];CToRR[z_]:={Re[z],Im[z]}
In[]:=
poly=x^3+2x^2-5x-6
Out[]=
-6-5x+2+
2
x
3
x
In[]:=
x^3+2x^2-5x-6//Factor
Out[]=
(-2+x)(1+x)(3+x)
In[]:=
coef=Reverse[CoefficientList[poly,x]]
Out[]=
{1,2,-5,-6}
In[]:=
Hold[Table[Sum[coef〚k〛*^(k-1),{k,1,j}],{j,1,4}]]//StandardForm
Out[]//StandardForm=
HoldTablecoefk,{j,1,4}
j
∑
k=1
k-1
In[]:=
cpnt=Prepend[Table[Sum[coef〚k〛*^(k-1),{k,1,j}],{j,1,4}],0]
Out[]=
{0,1,1+2,6+2,6+8}
In[]:=
g0=ListLinePlot[{{0,0},{1,0},{1,2},{6,2},{6,8}}{Style[0,Larger],Style[1,Larger],Style[2,Larger],Style[5,Larger],Style[6,Larger]},ImageSizeLarge,PlotStyleThickness[(*0.015*)0.007],AspectRatio1]
Out[]=
In[]:=
g1=ListLinePlot[{{0,0},{1,1},{0,2},{6,8}},AspectRatio1]
Out[]=
In[]:=
g2=ListLinePlot[{{0,0},{1,3},{3,2},{6,8}},AspectRatio1]
Out[]=
In[]:=
g3=ListLinePlot[{{0,0},{1,-2},{8,2},{6,8}},AspectRatio1]
Out[]=
In[]:=
gx1=ListLinePlot[{{1,-2},{1,8}},PlotStyleThick,AspectRatio1]
Out[]=
In[]:=
gx2=ListLinePlot[{{0,2},{8,2}},PlotStyleThick,AspectRatio1]
Out[]=