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| Deletions are marked like this. | Additions are marked like this. |
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| * MacCaulay Resultant ([[http://trac.sagemath.org/ticket/15382|#15382]]) - Soli Vishkautsan, Hao Chen | * --([[http://trac.sagemath.org/ticket/15382|#15382]])-- neeeds_work: MacCaulay Resultant - Soli Vishkautsan, Hao Chen |
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| * Krumm-Doyle Small Points Algorithm - needs review [[http://trac.sagemath.org/ticket/15389|#15389]] - David Krumm, John Doyle | * --([[http://trac.sagemath.org/ticket/15389|#15389]])-- needs-review: Krumm-Doyle Small Points Algorithm - David Krumm, John Doyle |
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| * Bruin-Molnar Algorithm into a patch [[http://trac.sagemath.org/ticket/15392|#15392]] (needs review) - Brian Stout, Ben Hutz | * --([[http://trac.sagemath.org/ticket/15392|#15392]])-- needs-review: Bruin-Molnar Algorithm for minimal models - Brian Stout, Ben Hutz |
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| & [[http://trac.sagemath.org/ticket/15376|#15376]], positively reviewed ) and canonical heights for points in number fields - Paul Fili | * --([[http://trac.sagemath.org/ticket/15376|#15376]])-- positively reviewed: canonical heights for points with integer fix - Paul Fili |
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| * FMV Algorithm into a patch ([[http://trac.sagemath.org/ticket/15393|#15393]]) - Bianca Thompson, Ben Hutz, Joao Faria | * --([[http://trac.sagemath.org/ticket/15393|#15393]])-- in-progress: FMV Algorithm for automorphism groups - Bianca Thompson, Ben Hutz, Joao Faria |
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| * Review [[http://trac.sagemath.org/ticket/14219|#14219]] (positively reviewed)- Adam Towsley, Vincent Delecroix, Ben Hutz | * --([[http://trac.sagemath.org/ticket/14219|#14219]])-- positive-review:- Adam Towsley, Vincent Delecroix, Ben Hutz |
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| * Lattes map from an Elliptic Curve ([[http://trac.sagemath.org/ticket/15394|#15394]])- Patrick Ingram | * --([[http://trac.sagemath.org/ticket/15394|#15394]])-- Lattes map from an Elliptic Curve - Patrick Ingram |
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| * Composition of Morphisms ([[http://trac.sagemath.org/ticket/15378|#15378]]) - Vincent Delecroix, Donald Richardson, Soli Vishkautsan | * --([[http://trac.sagemath.org/ticket/15378|#15378]])-- Composition of Morphisms - Vincent Delecroix, Donald Richardson, Soli Vishkautsan |
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| * Implement .an_element() for ProjectiveSpace (it currently makes the TestSuite fai): [[trac.sagemath.org/ticket/15396 | Ticket #15396]] (needs review) - Ben Hutz * [[http://trac.sagemath.org/sage_trac/ticket/14219 | Trac #14219 - Needs-Review]]: QQ-rational preperiodic algorithms |
* --([[http://trac.sagemath.org/ticket/15396|#15396]])-- needs-review: Implement .an_element() for ProjectiveSpace - Ben Hutz |
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| * --([[http://trac.sagemath.org/sage_trac/ticket/13130 |Trac #13130]])-- closed sage-5.8.beta3: Basic architecture changes : support for projective spaces over rings - Ben Hutz | * --([[http://trac.sagemath.org/ticket/13130|#13130]])-- closed sage-5.8.beta3: Basic architecture changes : support for projective spaces over rings - Ben Hutz |
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| * --([[http://trac.sagemath.org/sage_trac/ticket/14217 | Trac #14217]])-- closed sage-5.10.beta3: Basic iteration functionality for projective and affine spaces - new directory structure in schemes - Ben Hutz | * --([[http://trac.sagemath.org/ticket/14217|#14217]])-- closed sage-5.10.beta3: Basic iteration functionality for projective and affine spaces - new directory structure in schemes - Ben Hutz |
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| * --([[http://trac.sagemath.org/sage_trac/ticket/14218 | Trac #14218]])-- closed sage-5.13.beta2: Height and canonical heights for points and morphisms - Ben Hutz | * --([[http://trac.sagemath.org/ticket/14218|#14218]])-- closed sage-5.13.beta2: Height and canonical heights for points and morphisms - Ben Hutz |
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| * Chebyshev creator (if it doesn't already exist) |
Arithmetic and Complex Dynamics
The goal of sage-dynamics is to improve the open source mathematical software Sage for computer exploration in dynamical systems and foster code sharing between researchers in this area. This portion focuses on the Arithmetic (Number Theoretic) and Complex aspects of dynamical systems.
News
Past News
Sage Days Currently holding Sage Days 55 (November 7-10, 2013) at Florida Institute of Technology.
January 30, 2012 - May 4, 2012 ICERM semeser program on Complex and Arithmetic Dynamics
How to participate and contribute
sage-dynamics: Google group
- anyone may subscribe by sending an e-mail to: sage-dynamics+subscribe at googlegroups dot com
Documentation and Tutorials
sage-combinat has many excellent tutorials combinat docs
Road Map
The arithmetic and complex dynamics functionality in Sage is currently in its infancy. A significant amount of functionality was developped at the ICERM semester in Spring 2012 and now we have started the process of moving this into Sage through a series of patches (trac tickets). Most of that functionality is current in experimental for that been greatly expanded upon at Sage Days 55. Much remains to be done. Below you will find a road map of what has been implemented, what is in the process of being implemented, and ideas for future functionality.
In Progress
#15382 neeeds_work: MacCaulay Resultant - Soli Vishkautsan, Hao Chen
#15389 needs-review: Krumm-Doyle Small Points Algorithm - David Krumm, John Doyle
#15392 needs-review: Bruin-Molnar Algorithm for minimal models - Brian Stout, Ben Hutz
#15376 positively reviewed: canonical heights for points with integer fix - Paul Fili
#15393 in-progress: FMV Algorithm for automorphism groups - Bianca Thompson, Ben Hutz, Joao Faria
#14219 positive-review:- Adam Towsley, Vincent Delecroix, Ben Hutz
Eigenvalues (see #14990 and #15390) for an implementation of the algebraic closure of finite field) - Vincent Delecroix , Ben Hutz
PostCriticallyFiniteMorphisms - Holly Krieger, Adam Towsley, Vincent Delecroix, Ben Hutz, Patrick Ingram
#15394 Lattes map from an Elliptic Curve - Patrick Ingram
#15378 Composition of Morphisms - Vincent Delecroix, Donald Richardson, Soli Vishkautsan
Enabled canonical height for maps of \PP^N over number fields. Here is an early draft worksheet: sws, for N>1 it requires the macaulay_resultant patch from above. - Adam Towsley, Paul Fili
#15396 needs-review: Implement .an_element() for ProjectiveSpace - Ben Hutz
Complete
#13130 closed sage-5.8.beta3: Basic architecture changes : support for projective spaces over rings - Ben Hutz
#14217 closed sage-5.10.beta3: Basic iteration functionality for projective and affine spaces - new directory structure in schemes - Ben Hutz
#14218 closed sage-5.13.beta2: Height and canonical heights for points and morphisms - Ben Hutz
#15377 closed sage-5.13.beta3: improve documentation of normalize_coordinates - Ben Hutz
#15373 closed sage-5.13.beta3: Global height for integer fix - Paul Fili
Wishlist
Check if for a given algebraic parameter c the map z -> z^2 + c is hyperbolic... and more generally for rational maps of P1 determine the existence (and list) of attracting cycles
- is_conjugate() for morphisms and iterator over morphisms of fixed degree up to conjugacy (medium)
- cyclegraph() and orbit_structure() to work with Zmod and other finite spaces not just finite fields (medium)
- primes_of_bad_reduction() and is_morphism() made to work for endomorphisms of subschemes (easy)
- products of projective space (Ben Hutz)
- dynamics on Wehler K3 surfaces (Joao de Faria)
error_bound computation for canonical height in dimension > 1
- update affine space to include the appropriate functionality from projective space
- enumeration of points of small height over number fields for affine and projective spaces
- fix all the white space issues in the projective and affine folders (easy)
- specific functionality for regular polynomial endomorphisms of P^N (Patrick might start implementing this someday)
- Chebyshev creator (if it doesn't already exist)
- Ponies (Patrick)
- PLEASE ADD MORE...