Hullo all,
Can someone explain the following behavior to me? I would like to to create
an extension of the field of rational functions in one variable 'y' over
the finite field of three elements by adjoining a root of unity 'Y' and an
element of Carlitz torsion 'X'.
I run the following commands:
sage: A.y = GF(3)[]; A
sage: w = polygen(A)
sage: K = Frac(A);K
sage: A1.X = K.extension(w^8 + (y^3 + y + 2)*w^2 + (y^2 + 2*y + 2)); A1
sage: B1.Y = A1.extension(w^2+2*w+2); B1
Note that 'w^2+2*w+2' is irreducible over GF(3), and 'w^8 + (y^3 + y +
2)*w^2 + (y^2 + 2*y + 2)' is irreducible over 'A'. All fields are generated
successfully. Trying to multiply 'X' and 'Y' or even 'y' and 'Y' then
yields a NotImplementedError. This seems crazy to me, since by the output
for 'B1', it knows it is an extension of 'A1', but it gets crazier.
If instead I restart my worksheet and run:
sage: A.y = GF(3)[]; A
sage: w = polygen(A)
sage: K = Frac(A);K
sage: A1.X = K.extension(w^9 + (y^3 + y + 2)*w^3 + (y^2 + 2*y + 2)*w); A1
sage: B1.Y = A1.extension(w^2+2*w+2); B1
where I have multiplied through by 'w' in the modulus of 'A1', the
extensions are generated correctly, and one may do arithmetic in all
variables 'X', 'Y', and 'y'.
I already have a workaround, but this behavior seems like a bug. So I
thought I would ask. What's going on here?
All the best, Rudy
--
You received this message because you are subscribed to the Google Groups
sage-support group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-support+unsubscr...@googlegroups.com.
To post to this group, send email to sage-support@googlegroups.com.
Visit this group at http://groups.google.com/group/sage-support.
For more options, visit https://groups.google.com/d/optout.