Dear GAP forum:

I'm curious about the following output:

gap> R:=PolynomialRing(GF(7),["x"]);
<algebra-with-one over GF(7), with 1 generators>
gap> p:=UnivariatePolynomial(GF(7),[1,2,3,4],1);
1+2*x+3*x^2+4*x^3
gap> Derivative(p);
0*x^-1+2+6*x+12*x^2
gap> p in R;
false
gap> q:=UnivariatePolynomial(GF(7),[Z(7),2*Z(7),3*Z(7),4*Z(7)],1);
Z(7)-x+Z(7)^2*x^2+Z(7)^5*x^3
gap> q in R;                                                      
true
gap> Derivative(q);
-Z(7)^0+Z(7)^4*x+x^2

(a) Why doesn't the definition of p automatically coerce the
coefficients 1,2,3,4 into the field GF(F)? Isn't this what the
documentation suggests? From the documentation, it seems to me that p
should be
equal to q.

(b) Why does the derivative of p contain 0*x^-1, but the
derivative of q doesn't?

- David

--
Prof David Joyner, Mathematics Department
U. S. Naval Academy, Annapolis, MD 21402
phone: (410) 293-6738

Miles-Receive-Header: reply