Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options not deleted user 6776

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 …
Syed's user avatar
  • 601
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( …
Syed's user avatar
  • 601
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 …
Syed's user avatar
  • 601
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 …
Syed's user avatar
  • 601
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 …
Syed's user avatar
  • 601
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 …
Syed's user avatar
  • 601
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 …
Syed's user avatar
  • 601
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 …
Syed's user avatar
  • 601
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 …
Syed's user avatar
  • 601