[Axiom-mail] The Cayley-Hamilton theorem and finite fields - a small problem

[Alasdair McAndrew]

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