Hi,
I am fairly certain the following two things are bugs, but I want to
double-check that I'm not doing something stupid before submitting a ticket:
sage: R.<x,y> = QQ[]
sage: P1 = ProjectiveSpace(R)
sage: H = P1.Hom(P1)
sage: f = H([x-y, x*y])
sage: f
Scheme endomorphism of Projective Space of dimension 1 over Rational Field
Defn: Defined on coordinates by sending (x : y) to
(x - y : x*y)
This is nonsense: there is no morphism from P1 to P1 given by those
equations, since the two polynomials x-y and x*y are not homogeneous of
the same degree. I think Sage should throw a ValueError here.
The second example:
sage: R.<x,y> = QQ[]
sage: P1 = ProjectiveSpace(R)
sage: H = P1.Hom(P1)
sage: f = H([x^2, x*y])
sage: f
Scheme endomorphism of Projective Space of dimension 1 over Rational Field
Defn: Defined on coordinates by sending (x : y) to
(x^2 : x*y)
This is also bad: the two polynomials are now homogeneous of degree 2,
but they are not relatively prime (and so this is not a morphism from P1
to P1, but rather a rational map since it is not defined at (0 : y)). I
think Sage should also throw a ValueError here.
(Or maybe I'm doing things wrong, in which case I'd love to find out how
to make this work.)
Cheers,
Alex
--
Alexandru Ghitza
Lecturer, Pure Mathematics
Department of Mathematics and Statistics
The University of Melbourne
Parkville, VIC, 3010
Australia
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