David Ponce wrote:

gap> R := PolynomialRing(Rationals,["x"]);
PolynomialRing(..., [ x ])
gap>
gap> f:=x^2+1;                            
1+x^2
gap> f in R;
false

return "true"? Am I using the "in" command wrong?

Where did you define the *variable* x? Your first line assigns a
*name* x to Indeterminate(Rationals,1). (If the above is your entire
GAP run. Otherwise it assigns the name "x" to
Indeterminate(Rationals, whichever number), see below.) The line
"f:=x^2+1;" should have produced an error, unless your excerpt is part
of a bigger GAP run, where x was assigned before.

Also, with `PolynomialRing', you have to be very careful with repeated
calls. See the GAP run below:

gap> R := PolynomialRing(Rationals,["x"]); 
PolynomialRing(..., [ x ])
gap> f:=x^2+1;
Variable: 'x' must have a value

gap> var:=Indeterminate(Rationals,1);
x
gap> f:=var^2+1;
1+x^2
gap> f in R;
true
gap> R := PolynomialRing(Rationals,["x"]); 
PolynomialRing(..., [ x ])
gap> f in R;
false
gap> var:=Indeterminate(Rationals,2);     
x
gap> f:=var^2+1;                          
1+x^2
gap> f in R;
true
gap> 

Sincerely,

Luc Teirlinck.

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