Re: The Cayley-Hamilton theorem and finite fields - a small problem

>
> What's going on, and why?
>

Don't know! I suspect that the interpreter is constructing some coercion that 
is doomed to failure. You can do the problem if you are more careful with 
your types

)cl c
D:=FFP(PF 2,x^4+x+1)
M:=matrix([[random()$D for i in 1..4] for j in 1..4])
p:=characteristicPolynomial(M,y)
SM:=SquareMatrix(4,D)
sp:=map(z+->(squareMatrix$SM)diagonalMatrix([z,z,z,z]),p)
sm:=squareMatrix(M)$SM
eval(sp,y=sm)
)cl c
D:=INT
M:=matrix([[random()$D for i in 1..4] for j in 1..4])
p:=characteristicPolynomial(M,y)
SM:=SquareMatrix(4,D)
sp:=map(z+->(squareMatrix$SM)diagonalMatrix([z,z,z,z]),p)
sm:=squareMatrix(M)$SM
eval(sp,y=sm)
)cl c
D:=PF 7
M:=matrix([[random()$D for i in 1..4] for j in 1..4])
p:=characteristicPolynomial(M,y)
SM:=SquareMatrix(4,D)
sp:=map(z+->(squareMatrix$SM)diagonalMatrix([z,z,z,z]),p)
sm:=squareMatrix(M)$SM
eval(sp,y=sm)
)cl c
D:=FF(2,4)
M:=matrix([[random()$D for i in 1..4] for j in 1..4])
p:=characteristicPolynomial(M,y)
SM:=SquareMatrix(4,D)
sp:=map(z+->(squareMatrix$SM)diagonalMatrix([z,z,z,z]),p)
sm:=squareMatrix(M)$SM
eval(sp,y=sm)

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