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Question: Problem with certain series

Question:Problem with certain series

markweitzman 100 Maple
series eigenvalues numeric division-by-zero
February 17 2016
2

I am having difficulty helping someone series expand an eigenvector solution.  I can expand the eigenvalues easily but get a numeric exception divide by zero when I attempt to expand a component of an eigenvector.  Mathematica seems to have no problem solving this problem.  Any help would be appreciated.

 

 

 

 

 

> 

assume(varepsilon > 0)
> 

H := Matrix(3, 3, {(1, 1) = 0, (1, 2) = -epsilon, (1, 3) = epsilon, (2, 1) = -epsilon, (2, 2) = 2-2*epsilon, (2, 3) = 0, (3, 1) = epsilon, (3, 2) = 0, (3, 3) = 2+2*epsilon})

Matrix(%id = 18446744078100429630)

 (1)
> 

with(LinearAlgebra):
> 

evals, evecs := Eigenvectors(H):
> 

e1 := convert(simplify(series(evals[1], varepsilon = 0, 4)), polynom)

2+2*varepsilon+(1/2)*varepsilon^2-(7/16)*varepsilon^3

 (2)
> 

e2 := convert(simplify(series(evals[2], varepsilon = 0, 4)), polynom)

-varepsilon^2

 (3)
> 

e3 := convert(simplify(series(evals[3], varepsilon = 0, 4)), polynom)

2-2*varepsilon+(1/2)*varepsilon^2+(7/16)*varepsilon^3

 (4)
> 

simplify(series(evecs[1][1], epsilon = 0, 4))

Error, (in simplify/sqrt/local) numeric exception: division by zero

  
> 

``

 

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