.


:




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, .




, . 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]Š0,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[RŠ0,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`





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