Oddities modulo multivariate polynomials

[Jeroen Demeyer <jdemeyer@cage.ugent.be>]

Could anyone please explain what is happening here:

                  GP/PARI CALCULATOR Version 2.1.5 (released)
                i686 running linux (ix86 kernel) 32-bit version
                (readline v4.3 enabled, extended help available)

? Y                   /* Make sure Y is defined first */
%1 = Y
? (Y^2) % (X^3 - Y^2)
%2 = X^3
? (X^3) % (X^2 + 1)
%3 = -X
? ((Y^2) % (X^3 - Y^2)) % (X^2 + 1)
%4 = 0

How come the outputs of the two last statements are different?  Is this
a bug or am I doing something wrong?  Any help would be appreciated.

--
Finding a good signature is left as an exercise for the reader.