Hyperelliptic curves

Open discussion for MAGMA library (Matrix Algebra on GPU and Multicore Architectures)
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symbolic
Posts: 1
Joined: Sun Mar 01, 2015 9:49 pm

Hyperelliptic curves

Post by symbolic » Sun Mar 01, 2015 10:02 pm

Hi,
I'm new to MAGMA and I have an elementary question about finding hyerelliptic models of plane curves. I mimic the example (H117E15) in the manual
http://magma.maths.usyd.edu.au/magma/ha ... 1333#14548
and I tried

A<x,y>:=AffineSpace(Rationals(),2);
C:=Curve(A,[ y^2-(x^3+405)]);
D:=ProjectiveClosure(C);
boo,hy,mp := IsHyperelliptic(D);
boo;

and to my surprise, I got the answer "false" (for boo). The curve C of course is hyperelliptic; what syntax error did I made?

More generally, I have an affine plane curve F(x,y)=0. What is the MAGMA command for determining if this plane curve is hyperelliptic, and if so, produce a hyperelliptic model? I look throught the aforementioned section of the manual but I couldn't find the command for that; your help and assistance is most appreciative. THANKS!

(In case that matters: I am moving from maple to magma; the maple command I would have used is `Weierstrassform')

mgates3
Posts: 918
Joined: Fri Jan 06, 2012 2:13 pm

Re: Hyperelliptic curves

Post by mgates3 » Thu Mar 05, 2015 11:29 am

I think you're interested in the other MAGMA library.
http://magma.maths.usyd.edu.au/magma/

This forum is for the MAGMA library that does linear algebra on GPUs.
-mark

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