RECIP -- REpository of Complex multIPlication sage code.
This started out as code meant for computing with Shimura's RECIProcity law,
but grew into a collection of much of the Sage code written by me for my
research.
When using this package in a publication, it is highly likely that it is
approprate to cite certain publications. Please CITE the relevant JOURNAL publications,
as well as giving the URL of this repository.
Here is a list of functionalities of this repository, together with the
publications that should be cited when you use them, and the name of the file
that has examples.
-
Igusa class polynomials (proven correct)
See both "Igusa class polynomials (not proven correct)" and
"Denominators of Igusa class polynomials" below.
- Non-maximal orders of CM-fields and their polarized ideal classes and Igusa
class polynomials.
cite [BissonStreng] (code is written for, part of, and based on, this publication)
see orders.sage for examples
- (n,n)-isogenies between polarized ideal classes
cite [BLS]
see bls.sage for examples
- Computations related to Shimura's reciprocity law
cite [Streng12] (code is written for, part of, and based on, this publication)
see article.sage for examples
- Igusa class polynomials (not proven correct)
cite [Streng14], [vWamelen], [Weng] (code is based on these publications)
- Denominators of Igusa class polynomials
cite [BouyerStreng] (code is written for, and hence part of, this publication)
and depending on how the code is used, and on the kind of quartic CM-field
also cite one or more of:
[BouyerStreng], [GL], [LV], [Yang] (large parts of the code are based on these)
see denominators.sage for examples
Here is a list of Sage programs written by my students and me that is not part
of this repository.
-
Height reduction of binary forms and hyperelliptic curves.
(with Florian Bouyer)
https://bitbucket.org/mstreng/reduce
cite [BouyerS] (code is written for, part of, and based on, this publication)
- Solving conics and Mestre's algorithm
(with Florian Bouyer)
now part of the standard Sage functionality
- Hilbert modular polynomials
(by Chloe Martindale)
contact her if you are interested
- The CM class number one problem for genus 2 and 3
(by Pınar Kılıçer)
contact her if you are interested
To use the latest version of this package directly from the web, start Sage
and type::
sage: load("https://bitbucket.org/mstreng/recip/raw/master/recip_online.sage")
To use this package offline, download it first and extract it to some
directory, say "somewhere_on_my_drive/recip", then start Sage and type::
sage: load_attach_path("somewhere_on_my_drive/recip")
sage: load("recip.sage")
To view the code, see::
https://bitbucket.org/mstreng/recip
References:
For [BissonStreng], [BouyerStreng], [BLS (Bröker-Lauter-Streng)], [Streng12 (An explicit version of Shimura's reciprocity law for Siegel
modular functions)], [Streng14 (Computing Igusa Class Polynomials)],
see
Publications.
-
[GL] - Genus 2 curves with complex multiplication -- Eyal Goren and
Kristin Lauter
-
[LV] - An arithmetic intersection formula for denominators of Igusa class
polynomials -- Kristin Lauter and Bianca Viray
arXiv:1210.7841v1
-
[Yang] - Arithmetic interseciton on a Hilbert modular surface and the
Faltings height -- Tonghai Yang
http://www.math.wisc.edu/~thyang/general4L.pdf
More:
(Very) old versions of recip:
- version 0.2.1, 26 August 2013, tested with Sage 5.12.beta1
- version 0.2, 17 August 2013, tested with Sage 5.11
- version 0.1.3, 21 November 2012
- version 0.1.2, 7th August 2012
- version 0.1, 17th July 2012