X=T.Y
Expand[X.A.X]
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A
H=Eigenvectors[A]
{{-1,-1,1,1},{1,1,1,1},{1,-1,-1,1},{-1,1,-1,1}}
Do[H[[i]]=H[[i]]/Norm[H[[i]]],{i,1,4}];
,
T=Transpose[H];
X=H.Y
g=Expand[X.A.X]
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Eigenvalues[A]
{-5,5,-3,3}
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f[11]
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Expand[f[x]*g[x],Modulus2]
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f[x_]=
g[x_]=
q[x_]=PolynomialQuotient[f[x],g[x],x]
r[x_]=PolynomialRemainder[f[x],g[x],x]
2.1.
.
r[x_]=PolynomialRemainder[f[x],g[x],x]
-5+25 x
q[x_]=PolynomialQuotient[f[x],g[x],x]
2.2. 3.
.
r[x_]=PolynomialMod[
PolynomialRemainder[f[x],g[x],x],Modulus3]
x
q[x_]=PolynomialMod[
PolynomialQuotient[f[x],g[x],x],Modulus3]
Expand[g[x]*q[x]+r[x],Modulus3]