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Computational Number Theory is for explicit calculations or algorithms involving anything of interest to number theorists.
0
votes
Accepted
Computing the fixed field of an automorphism of a function field
Colin Weir, suggested the following algorithm to solve the problem in non-rational case, I thought for the sake of others who probably have the same question, I'll post it, here:
Suppose that $\sigma …
6
votes
2
answers
2k
views
Computing the fixed field of an automorphism of a function field
Let say we have a function field $k(x,y)$ defined by $f(x,y)$ over $k$, with $\sigma \in Aut(k(x,y)/k)$ and. Suppose, I'm not that out of luck, so that either of $\prod \sigma^i(x)$ or $\sum \sigma^i( …
1
vote
0
answers
204
views
Which rational subfields are corresponding to the two dimensional subspaces of holomorphic d...
I implemented the algorithm that Felipe Voloch's suggested in his reply to the question:
Subfields of a function field
the algorithm is here:
Subfields of a function field
I considered the functio …
1
vote
0
answers
107
views
Why do subspaces of the space of Global holomorphic differentials of a function field corres...
I'm asking this question as a follow up to the Felipe Voloch's answer to this question:
Subfields of a function field
which you can read it here:
Subfields of a function field
(I just didn't have …
0
votes
0
answers
263
views
Computing the function field of a curve given as a subvariety of the Jacobian of its cover o...
I read following paragraph from:
G. Tamme, Teilkörper höheren Geschlechts eines algebraischen Funktionenkörpers, Arch. Math. 23 (1972), 257--259
Here $C$ is a curve of genus $\ge 2$ and $J$ is the …
1
vote
0
answers
238
views
How to ask Magma to compute the induced morphisim on divisor group
Suppose Magma has computed homomorphism $h$ between function fields $F1 \to F2$. Then we have an induced homomorphism $h$ on the divisor group. Now my question is that if there's a better way to compu …
0
votes
1
answer
342
views
Necessary/Sufficient condition/Algorithm that tells me a function field is a kummer extension
I start my question with an example. Suppose $F/K$ be the function field generated by $x^n - yx^{n-1} - 1 = 0$. It is not a cyclic over K(y), but if I set $t = yx^{n-1}$ then we have $K(x,t) \subset K …
14
votes
2
answers
1k
views
Subfields of a function field
Is there an algorithm for generating (some or all) subfields of a certain genus of a given function field (even a random one,I mean for example generating a random elliptic subfield of a certain given …
4
votes
1
answer
411
views
Computing places over x in F/K(x)
Let $F$ be a function field of "transcendental degree one" over its full constant field $K$. Let $x \in F \backslash K$. We know the divisor of $(x) = (x) - (1/x)$ in $K(x)$. Could you please give me …