, . Mathematica , ( , ).
3.4.8.
.
.
L=CoefficientList[f[x],x];
n=Length[L]
L=Reverse[L];
n1=(n-1)/2;
A=Table[0,{n,1,2*n1}];
B=Table[0,{n,1,2*n1}];
Do[A[[n]]=L[[2*n-1]],{n,1,n1+1}]
Do[B[[n]]=L[[2*n]],{n,1,n1}]
H={{0},{0}};G=Table[0,{n,1,n1}];
<<LinearAlgebra`MatrixManipulation`
G[[1]]={B,A};
Do[G1=G[[1]];Do[G1=TakeColumns[AppendRows[H,G1],2*n1],
{m,1,k-1}];G[[k]]=G1,{k,2,n1}]
GG=G[[1]];
Do[GG=AppendColumns[GG,G[[k]]],{k,2,n1}]
T=Table[Det[SubMatrix[GG,{1,1},{m,m}]],{m,2*n1}];
R=T[[1]]>0;Do[R=R&&T[[n]]>0,{n,2,4}]
N[Reduce[R,a]]
a>1.98271
, .
3.4.9.
.
.
L=CoefficientList[f[x],x];
n=Length[L]
L=Reverse[L];
n1=(n-1)/2;
A=Table[0,{n,1,2*n1}];
B=Table[0,{n,1,2*n1}];
Do[A[[n]]=L[[2*n-1]],{n,1,n1+1}]
Do[B[[n]]=L[[2*n]],{n,1,n1}]
H={{0},{0}};G=Table[0,{n,1,n1}];
<<LinearAlgebra`MatrixManipulation`
G[[1]]={B,A};
Do[G1=G[[1]];Do[G1=TakeColumns[AppendRows[H,G1],2*n1],
{m,1,k-1}];G[[k]]=G1,{k,2,n1}]
GG=G[[1]];
Do[GG=AppendColumns[GG,G[[k]]],{k,2,n1}]
T=Table[Det[SubMatrix[GG,{1,1},{m,m}]],{m,2*n1}];
R=T[[1]]>0;Do[R=R&&T[[n]]>0,{n,2,4}]
<<Graphics`InequalityGraphics`
InequalityPlot[ R, {a, -8, 8}, {b, -8, 8} ]
. .
3.4.10.
.
L=CoefficientList[f[x],x];
n=Length[L]
L=Reverse[L];
n1=(n-1)/2;
A=Table[0,{n,1,2*n1}];
B=Table[0,{n,1,2*n1}];
Do[A[[n]]=L[[2*n-1]],{n,1,n1+1}]
Do[B[[n]]=L[[2*n]],{n,1,n1}]
H={{0},{0}};G=Table[0,{n,1,n1}];
<<LinearAlgebra`MatrixManipulation`
G[[1]]={B,A};
Do[G1=G[[1]];Do[G1=TakeColumns[AppendRows[H,G1],2*n1],
{m,1,k-1}];G[[k]]=G1,{k,2,n1}]
GG=G[[1]];
Do[GG=AppendColumns[GG,G[[k]]],{k,2,n1}]
T=Table[Det[SubMatrix[GG,{1,1},{m,m}]],{m,2*n1}];
R=T[[1]]>0;Do[R=R&&T[[n]]>0,{n,2,4}]
<<Graphics`InequalityGraphics`
InequalityPlot3D[ R, {a, -1, 1}, {b, -1, 1},
{c,-1,1}]
.
, . .
3.5.1.
. .
|
|
d[x_]=PolynomialGCD[g[x],f[x]]
R=Solve[d[x]0,x];
x=x/.R;
.
,
(5.4.1)
, .
(5.4.1)
(5.4.2)
, , .
Mathematica .
3.5.1.
.
Resultant[f[x],g[x],x]
, . , , ( .
, , , .
, , , , , .
3.5.2. ,
.
.
.
f1[x_]=D[f[x],x];
Resultant[f[x],f1[x],x]
3.5.3. ,
.
.
f1[x_]=D[f[x],x];
R=Resultant[f[x],f1[x],x];
Solve[R0,l]
.
7 - . , , , , , . , .
. . - P. . n , . , n .
, . .
, , , , .. (.. , , , ).
, , , . , , .
, . - , , .
|
|
, . ( ) , , . .
, .
(3.6.1)
.
3.6.1. .
.
T=Table[Coefficient[f[x],x,n-1],{n,1,5}]
T[[4]]
T[[5]]
- , ,
. (3.6.2)
: , . .
Mathematica .
3.6.2.
.
.
<<Algebra`SymmetricPolynomials`