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[Axiom-mail] The Cayley-Hamilton theorem and finite fields - a small pro
From
:
Alasdair McAndrew
Subject
:
[Axiom-mail] The Cayley-Hamilton theorem and finite fields - a small problem
Date
:
Sun, 15 Jul 2007 23:30:31 +1000
Hi Axiom wizards,
I was experimenting with the Cayley-Hamilton theorem:
M:=matrix([[random(20) for i in 1..4] for j in 1..4])
p:=characteristicPolynomial(M,y)
eval(p,y=M
)
and we get a matrix of zeros, as we should. It also works if we take elements from a finite field:
M:=matrix([[random()$PF 7 for i in 1..4] for j in 1..4])
or
M:=matrix([[random()$FF(2,4) for i in 1..4] for j in 1..4])
But it
doesn't
work for a finite field with a defining polynomial:
M:=matrix([[random()$FFP(PF 2,x^4+x+1) for i in 1..4] for j in 1..4])
The next two commands produce:
>> Error detected within library code:
coerce: element doesn't belong to smaller field
What's going on, and why?
Thanks,
Alasdair
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Themos Tsikas
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2007/07/16
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