Reducing the defining polynomial of a hyperelliptic curve

[sagetrac-florian]

A method which reduces the height of the polynomial defining a Hyperelliptic curve over the rationals

• Apply patch attachment: 12204_reduce_height.patch

Depends on #6341
Depends on #14755
Depends on #14756

Component: number theory

Keywords: hyperelliptic curves sd35 sd51

Work Issues: need to recheck once dependencies are finalised

Author: Florian Bouyer

Reviewer: Marco Streng

Issue created by migration from https://trac.sagemath.org/ticket/12204

[sagetrac-florian]

comment:1

Attachment: trac_12204_reduce_poly.patch.gz

[sagetrac-florian]

Author: Florian Bouyer

[sagetrac-florian]

Description changed:

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+++ 
@@ -1 +1,3 @@
 A method for hyperellipt curves over rational field which reduces the defining polynomial
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+* Apply patch [trac_12204_reduce_poly.patch](https://github.com/sagemath/sage-prod/files/10654372/trac_12204_reduce_poly.patch.gz)

[mstreng]

Reviewer: Marco Streng

[mstreng]

comment:4

1. The output of this new method is another curve over QQ, which is isomorphic over QQbar, but possibly not isomorphic over QQ. That is not clear from the documentation.
   2. Also, why is it called "reduce_poly" and not simply "reduce"?
   3. Related to 1. it would be great to also have a function that gives something isomorphic over QQ, and in that case also an isomorphism defined over QQ. This could be done with the same function if you make it (for example) "def reduce(self, rational=True, isomorphism=False)".

I'd say 1. is required for a positive review. 3 may be something for a later ticket if it is too much work.

[sagetrac-florian]

comment:5

Created ticket #12209 for number 3.

It is called reduce_poly as there is already a general scheme method called reduce which 

"Return the corresponding reduced algebraic space associated to this scheme."

[sagetrac-florian]

Attachment: trac_12204_modify_doc.patch.gz