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← Revision 356 as of 20191203 21:20:51 ⇥
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* ([[http://trac.sagemath.org/ticket/28773#28773]]) new: Implementing is_chebyshev over finite fields * ([[http://trac.sagemath.org/ticket/28772#28772]]) positivereview: Kneading sequences for the doubling map  John Doyle * ([[http://trac.sagemath.org/ticket/28771#28771]]) new: Improve computation of canonical height for dynamical systems * ([[http://trac.sagemath.org/ticket/28753#28753]]) positivereview: Ramification Type for Rational Maps  Andrew O'Desky * ([[http://trac.sagemath.org/ticket/28316#28316]]) positivereiew: Making an is_dynamical_belyi_map() function  Bella Tobin, Jamie Juul * ([[http://trac.sagemath.org/ticket/28292#28292]]) positivereview: Implemented is_chebyshev and is_lattes for one dimensional projective dynamical systems  Trevor Hyde, Fiona Lu, Alex Shearer * ([[http://trac.sagemath.org/ticket/28263#28263]]) positivework: Degree for Affine Morphism or Affine Dynamical System  Anna Chlopecki, Juliano LevierGomes * ([[http://trac.sagemath.org/ticket/28173#28173]]) positivereview: Implemented Is_Newton for Dynamical Systems  Anna Chlopecki, Simon Xu, Juliano LevierGomes, Grayson Jorgenson * ([[http://trac.sagemath.org/ticket/28170#28170]]) positivework: enhance is_postcritically_finite, critical_point_portrait, and multiplier_spectra to work over number fields and finite fields  Heidi Benham, Julia Cai, Leopold Mayer * ([[http://trac.sagemath.org/ticket/28107#28107]]) needswork: allowing invariant_generators() to take arbitrary character  Brandon Gontmacher, Ben Hutz * ([[http://trac.sagemath.org/ticket/25745#25745]]) needswork: Periodic Proportion Homomorphism over Finite Fields  Rebecca Lauren Miller * ([[http://trac.sagemath.org/ticket/23806#23806]]) needsinfo: don't choose default affine patch on projective point init  Ben Hutz * ([[http://trac.sagemath.org/ticket/23047#23047]]) positivereview: Meta Ticket: Utilize coercion framework for scheme points and morphisms * ([[http://trac.sagemath.org/ticket/21129#21129]]) needsreview: implementation of ArakelovZhang pairing for rational maps  Paul Fili, Holly Krieger\ 
* ([[https://trac.sagemath.org/ticket/28773#28773]]) new: Implementing is_chebyshev over finite fields * ([[https://trac.sagemath.org/ticket/28772#28772]]) positivereview: Kneading sequences for the doubling map  John Doyle * ([[https://trac.sagemath.org/ticket/28771#28771]]) new: Improve computation of canonical height for dynamical systems * ([[https://trac.sagemath.org/ticket/28753#28753]]) positivereview: Ramification Type for Rational Maps  Andrew O'Desky * ([[https://trac.sagemath.org/ticket/28316#28316]]) positivereiew: Making an is_dynamical_belyi_map() function  Bella Tobin, Jamie Juul * ([[https://trac.sagemath.org/ticket/28292#28292]]) positivereview: Implemented is_chebyshev and is_lattes for one dimensional projective dynamical systems  Trevor Hyde, Fiona Lu, Alex Shearer * ([[https://trac.sagemath.org/ticket/28263#28263]]) positivework: Degree for Affine Morphism or Affine Dynamical System  Anna Chlopecki, Juliano LevierGomes * ([[https://trac.sagemath.org/ticket/28173#28173]]) positivereview: Implemented Is_Newton for Dynamical Systems  Anna Chlopecki, Simon Xu, Juliano LevierGomes, Grayson Jorgenson * ([[https://trac.sagemath.org/ticket/28170#28170]]) positivework: enhance is_postcritically_finite, critical_point_portrait, and multiplier_spectra to work over number fields and finite fields  Heidi Benham, Julia Cai, Leopold Mayer * ([[https://trac.sagemath.org/ticket/28107#28107]]) needswork: allowing invariant_generators() to take arbitrary character  Brandon Gontmacher, Ben Hutz * ([[https://trac.sagemath.org/ticket/25745#25745]]) needswork: Periodic Proportion Homomorphism over Finite Fields  Rebecca Lauren Miller * ([[https://trac.sagemath.org/ticket/23806#23806]]) needsinfo: don't choose default affine patch on projective point init  Ben Hutz * ([[https://trac.sagemath.org/ticket/23047#23047]]) positivereview: Meta Ticket: Utilize coercion framework for scheme points and morphisms * ([[https://trac.sagemath.org/ticket/21129#21129]]) needsreview: implementation of ArakelovZhang pairing for rational maps  Paul Fili, Holly Krieger\ 
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* ([[http://trac.sagemath.org/ticket/28779#28779]]) closed sage9.0: Error in "primes_of_bad_reduction" for DynamicalSystem  Paul Fili * ([[http://trac.sagemath.org/ticket/25701#25701]]) closed sage9.0: Implement Sieve algorithm for product_projective space  Raghukul Raman * ([[http://trac.sagemath.org/ticket/23740#23740]]) closed sage9.0: Plotting Julia sets for general polynomials  Ben Barros * ([[http://trac.sagemath.org/ticket/23720#23720]]) closed sage9.0: Plotting Mandelbrot sets for general polynomials  Ben Barros, Colby Kelln * ([[http://trac.sagemath.org/ticket/28316#28316]]) closed sage9.0: Making an is_dynamical_belyi_map() function  Bianca Thompson, John Doyle, Adam Towsley * ([[http://trac.sagemath.org/ticket/28214#28214]]) closed sage9.0: Compute and display graph of nthpreimage tree  Brandon Gontmacher, Joey Lupo, Wayne Peng * ([[http://trac.sagemath.org/ticket/28213#28213]]) closed sage9.0: Renaming rational_preperiodic_points() to all_preperiodic_points()  Eric Zhu, Alex Galarraga, Bianca Thompson * ([[http://trac.sagemath.org/ticket/28212#28212]]) closed sage9.0: Optimizing all_periodic_points() for small periods  Eric Zhu, Alex Galarraga, Bianca Thompson * ([[http://trac.sagemath.org/ticket/23816#23816]]) closed sage9.0: left matrix action on scheme points  Ben Hutz * ([[http://trac.sagemath.org/ticket/23807#23807]]) closed sage8.9: fix issues with identical affine patches  Ben Hutz, Peter Bruin, Raghukul Raman * ([[http://trac.sagemath.org/ticket/28200#28200]]) closed sage8.9: reduce base field for scheme morphisms  Ben Hutz * ([[http://trac.sagemath.org/ticket/28174#28174]]) closed sage8.9: Fixed typo for dehomogenization of nonendomorphisms  Matt Torrence, Henry Talbott * ([[http://trac.sagemath.org/ticket/28169#28169]]) closed sage8.9: Option for adjugate in conjugation function with normalize_coordinates  Meghan Grip, Emily Rachfal, Talia Blum, John Doyle * ([[http://trac.sagemath.org/ticket/28161#28161]]) closed sage8.9: Make _number_field_from_algebraics() return a dynamical system  Jasmine Camero, Olivia Schwager * ([[http://trac.sagemath.org/ticket/28148#28148]]) closed sage8.9: sigma_invariants() bug over FunctionFields  Joey Lupo * ([[http://trac.sagemath.org/ticket/28109#28109]]) closed sage8.9: Renaming and improvement of periodic point methods  Erich Zhu, Alex Galarrage, Biance Thompson * ([[http://trac.sagemath.org/ticket/28071#28071]]) closed sage8.9: Enhance global_height functionality for other fields  Talia Blum, Trevor Hyde, Joey Lupo, Matt Torrence * ([[http://trac.sagemath.org/ticket/28070#28070]]) closed sage8.9: is_conjugate bug fix and enhancements  Colby Kelln, Leopold Mayer, Wayne Peng, Srinjoy Srimani, Ben Hutz * ([[http://trac.sagemath.org/ticket/28065#28065]]) closed sage8.9: Rational Preimages of Nonendomorphisms  Anna Chlopecki * ([[http://trac.sagemath.org/ticket/28032#28032]]) closed sage8.9: Automorphism group for some degree 1 maps  Shuofeng Xu, Max Weinreich, Brandon Gontmacher, Heidi Benham * ([[http://trac.sagemath.org/ticket/28028#28028]]) closed sage8.9: Enhance change_ring method on morphisms to use canonical embedding when possible, give clearer error in other cases  Henry Talbot * ([[http://trac.sagemath.org/ticket/28027#28027]]) closed sage8.9: Adding cyclegraph functionality to product projective dynamical systems  Alex Galarrage, Alex Shearer, Eric Zhu * ([[http://trac.sagemath.org/ticket/28026#28026]]) closed sage8.9: missing parameter in critical_point_portrait for dynamical systems  Brandon Gontmacher, Max Weinreich, Juliano Leveier * ([[http://trac.sagemath.org/ticket/28024#28024]]) closed sage8.9: Add FractionField support to specialization  Matt Torrence * ([[http://trac.sagemath.org/ticket/27995#27995]]) closed sage8.9: normal_form should Return the Embedding when working over a Finite Field  Meghan Grip, Julia Cai, Srinjoy Srimani, Grayson Jorgenson * ([[http://trac.sagemath.org/ticket/27994#27994]]) closed sage8.9: Name mismatch on affine space and projective space constructors  Matt Torrence, Olivia Schwager, Shuofeng Xu * ([[http://trac.sagemath.org/ticket/27992#27992]]) closed sage8.9: sanity check parameter added to prime_list in minimal_model  Talia Blum, Jasmine Camero, Joey Lupo * ([[http://trac.sagemath.org/ticket/27985#27985]]) closed sage8.9: Make dynatomic polynomial coerce base ring  Henry Talbot * ([[http://trac.sagemath.org/ticket/27984#27984]]) closed sage8.9: Coercion of inputs of orbit into projective space  Emily Rachfal * ([[http://trac.sagemath.org/ticket/27983#27983]]) closed sage8.9: Add monic=True option for chebyshev creator  Leo Mayer 
* ([[https://trac.sagemath.org/ticket/28779#28779]]) closed sage9.0: Error in "primes_of_bad_reduction" for DynamicalSystem  Paul Fili * ([[https://trac.sagemath.org/ticket/25701#25701]]) closed sage9.0: Implement Sieve algorithm for product_projective space  Raghukul Raman * ([[https://trac.sagemath.org/ticket/23740#23740]]) closed sage9.0: Plotting Julia sets for general polynomials  Ben Barros * ([[https://trac.sagemath.org/ticket/23720#23720]]) closed sage9.0: Plotting Mandelbrot sets for general polynomials  Ben Barros, Colby Kelln * ([[https://trac.sagemath.org/ticket/28316#28316]]) closed sage9.0: Making an is_dynamical_belyi_map() function  Bianca Thompson, John Doyle, Adam Towsley * ([[https://trac.sagemath.org/ticket/28214#28214]]) closed sage9.0: Compute and display graph of nthpreimage tree  Brandon Gontmacher, Joey Lupo, Wayne Peng * ([[https://trac.sagemath.org/ticket/28213#28213]]) closed sage9.0: Renaming rational_preperiodic_points() to all_preperiodic_points()  Eric Zhu, Alex Galarraga, Bianca Thompson * ([[https://trac.sagemath.org/ticket/28212#28212]]) closed sage9.0: Optimizing all_periodic_points() for small periods  Eric Zhu, Alex Galarraga, Bianca Thompson * ([[https://trac.sagemath.org/ticket/23816#23816]]) closed sage9.0: left matrix action on scheme points  Ben Hutz * ([[https://trac.sagemath.org/ticket/23807#23807]]) closed sage8.9: fix issues with identical affine patches  Ben Hutz, Peter Bruin, Raghukul Raman * ([[https://trac.sagemath.org/ticket/28200#28200]]) closed sage8.9: reduce base field for scheme morphisms  Ben Hutz * ([[https://trac.sagemath.org/ticket/28174#28174]]) closed sage8.9: Fixed typo for dehomogenization of nonendomorphisms  Matt Torrence, Henry Talbott * ([[https://trac.sagemath.org/ticket/28169#28169]]) closed sage8.9: Option for adjugate in conjugation function with normalize_coordinates  Meghan Grip, Emily Rachfal, Talia Blum, John Doyle * ([[https://trac.sagemath.org/ticket/28161#28161]]) closed sage8.9: Make _number_field_from_algebraics() return a dynamical system  Jasmine Camero, Olivia Schwager * ([[https://trac.sagemath.org/ticket/28148#28148]]) closed sage8.9: sigma_invariants() bug over FunctionFields  Joey Lupo * ([[https://trac.sagemath.org/ticket/28109#28109]]) closed sage8.9: Renaming and improvement of periodic point methods  Erich Zhu, Alex Galarrage, Biance Thompson * ([[https://trac.sagemath.org/ticket/28071#28071]]) closed sage8.9: Enhance global_height functionality for other fields  Talia Blum, Trevor Hyde, Joey Lupo, Matt Torrence * ([[https://trac.sagemath.org/ticket/28070#28070]]) closed sage8.9: is_conjugate bug fix and enhancements  Colby Kelln, Leopold Mayer, Wayne Peng, Srinjoy Srimani, Ben Hutz * ([[https://trac.sagemath.org/ticket/28065#28065]]) closed sage8.9: Rational Preimages of Nonendomorphisms  Anna Chlopecki * ([[https://trac.sagemath.org/ticket/28032#28032]]) closed sage8.9: Automorphism group for some degree 1 maps  Shuofeng Xu, Max Weinreich, Brandon Gontmacher, Heidi Benham * ([[https://trac.sagemath.org/ticket/28028#28028]]) closed sage8.9: Enhance change_ring method on morphisms to use canonical embedding when possible, give clearer error in other cases  Henry Talbot * ([[https://trac.sagemath.org/ticket/28027#28027]]) closed sage8.9: Adding cyclegraph functionality to product projective dynamical systems  Alex Galarrage, Alex Shearer, Eric Zhu * ([[https://trac.sagemath.org/ticket/28026#28026]]) closed sage8.9: missing parameter in critical_point_portrait for dynamical systems  Brandon Gontmacher, Max Weinreich, Juliano Leveier * ([[https://trac.sagemath.org/ticket/28024#28024]]) closed sage8.9: Add FractionField support to specialization  Matt Torrence * ([[https://trac.sagemath.org/ticket/27995#27995]]) closed sage8.9: normal_form should Return the Embedding when working over a Finite Field  Meghan Grip, Julia Cai, Srinjoy Srimani, Grayson Jorgenson * ([[https://trac.sagemath.org/ticket/27994#27994]]) closed sage8.9: Name mismatch on affine space and projective space constructors  Matt Torrence, Olivia Schwager, Shuofeng Xu * ([[https://trac.sagemath.org/ticket/27992#27992]]) closed sage8.9: sanity check parameter added to prime_list in minimal_model  Talia Blum, Jasmine Camero, Joey Lupo * ([[https://trac.sagemath.org/ticket/27985#27985]]) closed sage8.9: Make dynatomic polynomial coerce base ring  Henry Talbot * ([[https://trac.sagemath.org/ticket/27984#27984]]) closed sage8.9: Coercion of inputs of orbit into projective space  Emily Rachfal * ([[https://trac.sagemath.org/ticket/27983#27983]]) closed sage8.9: Add monic=True option for chebyshev creator  Leo Mayer 
Arithmetic and Complex Dynamics
The goal of sagedynamics 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
Sage Days 104  Sage Days on Arithmetic Dynamics  November 17, 2019  November 20, 2019, Saint Louis University
Past News
[email protected]  REU Program on Computational Arithmetic Dynamics  June 10, 2019  August 2, 2019
NSF DMS1415294  Computational Tools for Dynamical Systems 9/2014  8/2017 (P.I.: Hutz)
[email protected]  Program on Computational Arithmetic Dynamics  July 25, 2016  July 29, 2016
Sage Days Held Sage Days 55 (November 710, 2013) at Florida Institute of Technology.
January 30, 2012  May 4, 2012 ICERM semester program on Complex and Arithmetic Dynamics
How to participate and contribute
sagedynamics: Google group
 anyone may subscribe by sending an email to: sagedynamics+subscribe at googlegroups dot com
Documentation and Tutorials
Quick reference card for dynamics available on the Sage Quickref page (https://wiki.sagemath.org/quickref/)
sagecombinat 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
(#28773) new: Implementing is_chebyshev over finite fields
(#28772) positivereview: Kneading sequences for the doubling map  John Doyle
(#28771) new: Improve computation of canonical height for dynamical systems
(#28753) positivereview: Ramification Type for Rational Maps  Andrew O'Desky
(#28316) positivereiew: Making an is_dynamical_belyi_map() function  Bella Tobin, Jamie Juul
(#28292) positivereview: Implemented is_chebyshev and is_lattes for one dimensional projective dynamical systems  Trevor Hyde, Fiona Lu, Alex Shearer
(#28263) positivework: Degree for Affine Morphism or Affine Dynamical System  Anna Chlopecki, Juliano LevierGomes
(#28173) positivereview: Implemented Is_Newton for Dynamical Systems  Anna Chlopecki, Simon Xu, Juliano LevierGomes, Grayson Jorgenson
(#28170) positivework: enhance is_postcritically_finite, critical_point_portrait, and multiplier_spectra to work over number fields and finite fields  Heidi Benham, Julia Cai, Leopold Mayer
(#28107) needswork: allowing invariant_generators() to take arbitrary character  Brandon Gontmacher, Ben Hutz
(#25745) needswork: Periodic Proportion Homomorphism over Finite Fields  Rebecca Lauren Miller
(#23806) needsinfo: don't choose default affine patch on projective point init  Ben Hutz
(#23047) positivereview: Meta Ticket: Utilize coercion framework for scheme points and morphisms
(#21129) needsreview: implementation of ArakelovZhang pairing for rational maps  Paul Fili, Holly Krieger\
Wishlist
 PLEASE ADD MORE...
Wishlist
Area
Description
Difficulty
Priority
Polynomials
specific functionality for regular polynomial endomorphisms of P^N
Attracting Cycles
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
NonIntegral Domains
Make projective space work over nonintegral domains. One method would be to make a valid point on which is valid for modulo all maximal ideals
Documentation
Write Tutorials
Complex Dynamics
Implement Thurston's algorithm. More precisely, develop an efficient method to determine if there is a Thurston obstruction. (Epstein, ICERM)
Dynamical Zeta Functions
Compute the dynamical zeta function
Miscellaneous
Implement a function which takes as input to rational functions f(x) and g(x), and determines whether or not f^n=g^m for some integers n,m \geq 1. (Zieve, ICERM)
fix inheritance structure in generic/morphism/py. see tracc 14711
implement more general schemes  charts, morphisms
color code cyclegraph. mark critical points for pcf potrait. perhaps color code points in intermediate fields for finite fields
Postcritically finite morphisms
given a number field enumerate pcf maps over that field
given a graph, find a pcf map with that graph (approximate with spider algorithm or exact?)
given a family, which members are pcf
Berkovich P1
Complete
#28779 closed sage9.0: Error in "primes_of_bad_reduction" for DynamicalSystem  Paul Fili
#25701 closed sage9.0: Implement Sieve algorithm for product_projective space  Raghukul Raman
#23740 closed sage9.0: Plotting Julia sets for general polynomials  Ben Barros
#23720 closed sage9.0: Plotting Mandelbrot sets for general polynomials  Ben Barros, Colby Kelln
#28316 closed sage9.0: Making an is_dynamical_belyi_map() function  Bianca Thompson, John Doyle, Adam Towsley
#28214 closed sage9.0: Compute and display graph of nthpreimage tree  Brandon Gontmacher, Joey Lupo, Wayne Peng
#28213 closed sage9.0: Renaming rational_preperiodic_points() to all_preperiodic_points()  Eric Zhu, Alex Galarraga, Bianca Thompson
#28212 closed sage9.0: Optimizing all_periodic_points() for small periods  Eric Zhu, Alex Galarraga, Bianca Thompson
#23816 closed sage9.0: left matrix action on scheme points  Ben Hutz
#23807 closed sage8.9: fix issues with identical affine patches  Ben Hutz, Peter Bruin, Raghukul Raman
#28200 closed sage8.9: reduce base field for scheme morphisms  Ben Hutz
#28174 closed sage8.9: Fixed typo for dehomogenization of nonendomorphisms  Matt Torrence, Henry Talbott
#28169 closed sage8.9: Option for adjugate in conjugation function with normalize_coordinates  Meghan Grip, Emily Rachfal, Talia Blum, John Doyle
#28161 closed sage8.9: Make _number_field_from_algebraics() return a dynamical system  Jasmine Camero, Olivia Schwager
#28148 closed sage8.9: sigma_invariants() bug over FunctionFields  Joey Lupo
#28109 closed sage8.9: Renaming and improvement of periodic point methods  Erich Zhu, Alex Galarrage, Biance Thompson
#28071 closed sage8.9: Enhance global_height functionality for other fields  Talia Blum, Trevor Hyde, Joey Lupo, Matt Torrence
#28070 closed sage8.9: is_conjugate bug fix and enhancements  Colby Kelln, Leopold Mayer, Wayne Peng, Srinjoy Srimani, Ben Hutz
#28065 closed sage8.9: Rational Preimages of Nonendomorphisms  Anna Chlopecki
#28032 closed sage8.9: Automorphism group for some degree 1 maps  Shuofeng Xu, Max Weinreich, Brandon Gontmacher, Heidi Benham
#28028 closed sage8.9: Enhance change_ring method on morphisms to use canonical embedding when possible, give clearer error in other cases  Henry Talbot
#28027 closed sage8.9: Adding cyclegraph functionality to product projective dynamical systems  Alex Galarrage, Alex Shearer, Eric Zhu
#28026 closed sage8.9: missing parameter in critical_point_portrait for dynamical systems  Brandon Gontmacher, Max Weinreich, Juliano Leveier
#28024 closed sage8.9: Add FractionField support to specialization  Matt Torrence
#27995 closed sage8.9: normal_form should Return the Embedding when working over a Finite Field  Meghan Grip, Julia Cai, Srinjoy Srimani, Grayson Jorgenson
#27994 closed sage8.9: Name mismatch on affine space and projective space constructors  Matt Torrence, Olivia Schwager, Shuofeng Xu
#27992 closed sage8.9: sanity check parameter added to prime_list in minimal_model  Talia Blum, Jasmine Camero, Joey Lupo
#27985 closed sage8.9: Make dynatomic polynomial coerce base ring  Henry Talbot
#27984 closed sage8.9: Coercion of inputs of orbit into projective space  Emily Rachfal
#27983 closed sage8.9: Add monic=True option for chebyshev creator  Leo Mayer
#27982 closed sage8.9: Make Lattes map for projective space coerce base ring  Ben Hutz
#25243 closed sage8.9: is postcritically finite failure for extensions  Ben Hutz
#25239 closed sage8.9: QQbar points of subschemes not valid  Ben Hutz
#25237 closed sage8.9: normlize_coordinates for projective morphism not fully normalized  Ben Hutz
#23813 closed sage8.9: matrix action on scheme morphism polynomials  Adam Towsley
#27900 closed sage8.8: removed deprecated dynamics code from schemes  Ben Hutz
#25952 closed sage8.4: smallest coefficient model for binary forms and dynamical systems  Ben Hutz
#25839 closed sage8.4: Raise Error if Univariate PR used to construct ProjectiveSpace  Joseph Lupo
#25795 closed sage8.4: minor optimization in comparison between morphisms  Raghukul Raman
#25939 closed sage8.4: error in Well's algorithm for canonical height  Ben Hutz
#25897 closed sage8.4: incorrect Comparison of embedding index in projective_embedding  Raghukul Raman
#25878 closed sage8.4: implement Height function for product morphism  Raghukul Raman
#25821 closed sage8.4: implement height functions for product points  Raghukul Raman
#25792 closed sage8.4: add dehomogenize function for product projective point  Raghukul Raman
#25781 closed sage8.4: add Comparison operator for morphism between product  Raghukul Raman
#25697 closed sage8.4: Implement enumeration over QQ for product projective schemes  Raghukul Raman
#25523 closed sage8.4: Raise Exception if DynamicalSystem initialized with coeffs not in given domain  Joseph Lupo
#25446 closed sage8.4: compute all orbits of minimal models of dynamical systems  Ben Hutz
#25241 closed sage8.4: fix issue with change_ring for polynomials with Maps  Ben Hutz
#25780 closed sage8.3: Normalize bound checking in points function  Raghukul Raman
#25592 closed sage8.3: enum_affine_rational_field function is missing points  Raghukul Raman
#25564 closed sage8.3: implement hash for affine_point  Raghukul Raman
#25529 closed sage8.3: Implement Sieving to replace search enumeration  Raghukul Raman
#25513 closed sage8.3: Scheme endomorphism as_dynamical_system() check if already DynamicalSystem  Joseph Lupo
#25242 closed sage8.3: is_polynomial fails when multiple roots  Ben Hutz
#25240 closed sage8.3: Chebyshev and Lattes maps should be created as dynamical systems  Ben Hutz
#23627 closed sage8.3: Update points() in projective_homset.py and affine_homset.py to work over CC and CDF  Ben Hutz, Rebecca Lauren Miller
#25242 closed sage8.3: is_polynomial fails when multiple roots  Ben Hutz
#25240 closed sage8.3: Chebyshev and Lattes maps should be created as dynamical systems  Ben Hutz
#24994 closed sage8.3: convert mandelbrot/julia interact to jupyter notebook  Frédéric Chapoton, Jeroen Demeyer
#22771 closed sage8.3: Numerical Precision for Heights in Number Fields  TJ, Raghukul Raman
#23814 closed sage8.1: fix is_preperiodic domain check  Paul Fili
#23811 closed sage8.1: fix bug is specialization  Paul Fili
#23810 closed sage8.1: fix typo is critical point portrait  Ben Hutz
#23805 closed sage8.1: implement coercion for scheme points  Ben Hutz
#23571 closed sage8.1: Implement Veronese Embedding  Grayson Jorgenson
#23434 closed sage8.1: move subscheme code  Ben Hutz
#23808 closed sage8.1: save embedding in _numberfield_from_algebraics  Paul Fili
#23809 closed sage8.1: fix normalization in canonical height  Paul Fili
#23497 closed sage8.1: relocate dynamics code  Ben Hutz, Xander Faber
#8423 closed sage8.1: Julia sets  Ben Barros
#23425 closed sage 8.1: Plotting external rays of mandelbrot set  Ben Barros
#23457 closed sage 8.1: allow infinity to initialize projective point  Ben Hutz
#23334 closed sage 8.1: Implement Well's canonical height algorithm  Lauren Miller
#23333 closed sage 8.1: Improve sigma invariant  Ben Hutz
#23257 closed sage 8.1: Plotting the Mandelbrot set in Sage  Ben Barros
#23086 closed sage 8.0: Cyclegraph for projective morphisms  Ben Barros
#22556 closed sage 8.0: implement periodic points for rational maps on projective space  Ben Hutz
#21118 closed sage 8.0: list of degrees of iterates of function  Joseph Silverman, Ben Hutz
#22743 closed sage 8.0: little clean up of Wehler K3  Frederic Chapoton
#22580 closed sage 8.0: Normalize nth iterate in projective morphism  Rebecca Lauren Miller
#22268 closed sage 7.6: copy for scheme morphisms points not deep enough  Ben Hutz
#22265 closed sage 7.6: fix dynatomic polynomial  Rebecca Lauren Miller
#22293 closed sage 7.6: products and powers of schemes and subschemes  Ben Hutz
#22269 closed sage 7.6: Segre embedding for multiple component products  Ben Hutz
#21117 closed sage 7.6: specialization for subschemes and scheme_morphisms  Ben Hutz
#21248 closed sage 7.5: implementation of Reduced Binary Form by Stoll and Cremona Rebecca Lauren Miller
#21285 closed sage 7.4: error in change_ring for affine morphisms  Ben Hutz
#21100 closed  duplicate/won't fix: division error in normalize_coordinates  Ben Hutz
#21113 closed sage 7.4: unflattening morphism error  Ben Hutz
#21112 closed sage 7.4: wrong base ring in sigma invariants  Ben Hutz
#21108 closed sage 7.4: use flattening in quo_rem  Vincent Delacroix
#21106 closed sage 7.4: class for flattening morphism  Vincent Delecroix, Ben Hutz
#21104 closed sage 7.4: indeterminancy locus  Michelle Manes
#21099 closed sage 7.4: critical subscheme / critical points for a map on projective space  Michelle Manes
#21097 closed sage 7.4: incorrect parent in dynatomic_polynomial  Michelle Manes
#20227 closed sage 7.4: Chow form for projective subschemes  Ben Hutz
#15378 closed sage 7.4: Composition of Morphisms  Vincent Delecroix, Ben Hutz
#21091 closed sage 7.3: is_polynomial bug fix  Ben Hutz
#20820 closed sage 7.3: Conjugating sets of Rational Functions  Rebecca Lauren Miller
#20780 closed sage 7.3: add level parameter to rational_preimages  Ben Hutz
#20650 closed sage 7.3: Added is_polynomial and make_look_poly to projective morphism  Rebecca Lauren Miller, Ben Hutz
#19635 closed sage 7.3: Enumeration functionality for products of projective spaces over fields and finite fields  Grayson Jorgenson
#20079 closed sage 7.3: Chebyshev Polynomials  Joe Eisner, Ben Hutz
#20451 closed sage 7.2: canonical height error  Ben Hutz
#20262 closed sage 7.2: Add point transformation matrix for projective space  Rebecca Lauren Miller
#20168 closed sage 7.2: small improvements to projective morphism  Ben Hutz
#20059 closed sage 7.1: minimal periodic points code improvement  Ben Hutz
#20067 closed sage 7.1: Change ring to QQbar fails for subschemes  Ben Hutz
#20018 closed sage 7.1: init for endomorphism of projective subschemes fails  Ben Hutz
#19979 closed sage 7.1: Fix coding style and documentation in projective products  Rebecca Lauren Miller
#19889 closed sage 7.1: Fix coding style and documentation style in affine schemes  Rebecca Lauren Miller
#19991 closed sage 7.1: improve dimension function for subschemes of projective products  Ben Hutz
#19891 closed sage 7.1: Fix coding style and documentation in Projective schemes  Ben Hutz
#19551 closed sage 7.0: Basic failures in projective product morphisms  Ben Hutz
#19552 closed sage 7.0: images and preimages of projective subschemes  Ben Hutz
#19557 closed sage 6.10: Basic iteration functionality for products of projective spaces  Grayson Jorgenson
#19512 closed sage 6.10: is_morphism for maps of products of projective spaces  Grayson Jorgenson
#18443 closed sage 6.8: Multiplier spectra for projective morphisms  Grayson Jorgenson
#18374 closed sage 6.8: Inconsistency in dimension of total ideals.  Miguel Marco
#18281 closed sage 6.8: implement critical point functionality including is_pcf for projective morphisms  Ben Hutz
#17282 closed sage 6.8: Implementing Wehler K3 Surfaces  Joao Faria
#18409 closed sage 6.8: Dynatomic polynomial bug for fractional coefficients  Ben Hutz
#18399 closed sage 6.8: projective automorphism group fails for homogenized maps  Ben Hutz
#18279 closed sage 6.7: implement rational preperiodic points for polynomials over number fields  Ben Hutz
#18008 closed sage 6.7: Periodic points for projective/affine morphism  Grayson Jorgenson
#17855 closed sage 6.7: create is_preperiodic function for points of projective space  Ben Hutz
#17907 closed sage 6.6: Random failure in enum_projective_number_field  Ben Hutz
#17729 closed sage 6.6: Implement Weil restriction for affine schemes/points/morphisms  Ben Hutz
#17762 closed sage 6.6: Connected component for a rational preperiodic point  Grayson Jorgenson
#17323 closed sage 6.6: Implement "primes_of_bad_reduction" to work over Number Fields  Joao Faria
#17386 closed sage 6.6: Enumerate points of bounded height in projective/affine space over number fields  Grayson Jorgenson
#17326 closed sage 6.6: Implementing subschemes functionality for projective "is_morphism"  Joao Faria
#17067 closed sage 6.5: Enabled canonical height for maps of \PP^N over number fields  Ben Hutz, Paul Fili
#15393 closed sage 6.5: FMV Algorithm for automorphism groups  Bianca Thompson, Ben Hutz, Joao Faria
#17082 closed sage 6.5: Height Difference Bounds over number fields  Joao Faria
#17427 closed sage 6.5: x==y while hash(x)!=hash(y) with SchemeMorphism_point_projective_field  Ben Hutz
#17535 closed sage 6.5: Homogenize fails for affine space over function fields  Ben Hutz
#17433 closed sage 6.5: projective point equality fails for quoteint base rings  Ben Hutz
#17441 closed sage 6.5: Change ring fails for SchemeMorphism_polynomial defined with fraction field elements  Grayson Jorgenson
#17325 closed sage 6.5: clear denominators for projective points does not always work  Joao Faria
#17450 closed sage 6.5: Fix category for quotients of polynomial rings  Travis Scrimshaw
#17429 closed sage 6.5: projective point equality returns false positive for ComplexIntervalField  Ben Hutz
#17324 closed sage 6.5: implement eq and ne for affine morphisms  Ben Hutz
#15448 closed sage 6.5: cartesian products of projective space  Ben Hutz
#16986 closed sage 6.5: Rational Preimages and All Rational Preimages over number fields  Joao Faria
#17118 closed sage 6.4: Added multiplier computation to affine morphism  Grayson Jorgenson
#17001 closed sage 6.4: Functionality for fast evaluation of affine morphisms  Grayson Jorgeson
#16961 closed sage 6.4: Fix Dynatomic Polynomials to work over the Complex Numbers  Joao de Faria
#16960 closed sage 6.4: Orbit Structure for Affine Morphisms  Grayson Jorgenson
#16838 closed sage 6.4: make affine and projective dehomogenize and homogenize work together  Ben Hutz
#16833 closed sage 6.4: Use Macaulay resultant to compute resultant of projective morphisms  Joao de Faria
#16834 closed sage 6.4: Change ring fails for affine morphisms  Grayson Jorgenson
#16832 closed sage 6.4: Can't Coerce projective point to subscheme point  Peter Bruin
#15394 closed sage 6.4: Lattes map from an Elliptic Curve  Patrick Ingram, Ben Hutz
#15389 closed sage.6.3: KrummDoyle Small Points Algorithm  David Krumm, John Doyle
#15382 closed sage.6.3: MacCaulay Resultant  Soli Vishkautsan, Hao Chen
#15782 closed sage.6.3: Increase Performance of Multiplier in Projective Morphism  Dillon Rose and Ben Hutz
#15781 closed sage.6.3: Increase Performance of possible_periods in Projective Morphism  Dillon Rose and Ben Hutz
#15780 closed sage.6.3: Increase Performance in Projective Morphism  Dillon Rose
#16168 closed sage.6.3: use p_iter_fork in projective_morphism  Dillon Rose
#16051 closed sage.6.3: fast_callable can return ipow with exponents in the base ring  Ben Hutz
#15920 closed sage.6.2: Parallelize Possible Periods functions for Projective Morphisms  Dillon Rose
#15815 closed sage.6.2: rational preimages for projective morphisms returns incorrect points  Ben Hutz
#15490 closed sage.6.2: documentation fix for projective dynatomic polynomials  Weixin Wu
#15396 closed sage.6.1: Implement .an_element() for ProjectiveSpace  Ben Hutz
#15392 closed sage.5.13.rc0: BruinMolnar Algorithm for minimal models  Brian Stout, Ben Hutz
#15376 closed sage5.13.beta4: canonical heights for points with integer fix  Paul Fili
#14219 closed sage5.13.beta4: Rational preperiodic points  Ben Hutz
#15373 closed sage5.13.beta3: Global height for integer fix  Paul Fili
#15377 closed sage5.13.beta3: improve documentation of normalize_coordinates  Ben Hutz
#14218 closed sage5.13.beta2: Height and canonical heights for points and morphisms  Ben Hutz
#14217 closed sage5.10.beta3: Basic iteration functionality for projective and affine spaces  new directory structure in schemes  Ben Hutz
#13130 closed sage5.8.beta3: Basic architecture changes : support for projective spaces over rings  Ben Hutz