Algorithms and Implementations
- If you would like to port some of this code to another Computer Algeba System, I would be happy to assist any way I can.
- E-mail me if you find broken links, or for related work, potential improvements, test files, etc.
- Old version of this page.
Algorithms with former students:
Algorithms for polynomials and number fields:
Algorithms for Algebraic Curves In Maple:
Other algorithms for Algebraic Curves:
Algorithms for Differential Equations In Maple:
Other algorithms for Differential Equations:
Algorithms for Difference Equations:
- Note: The algorithms listed below with Imamoglu, Kunwar, Yuan, and Debeerst,
have now been combined into a single package that will be part of Maple 2021.
- Jonas Szutkoski (PhD 2017). Implementations
for computing subfields, and computing rational function decomposition
(now part of Magma).
- Erdal Imamoglu (PhD 2017). Implementation for finding hypergeometric
solutions of second order linear differential equations, in
- Wen Xu (PhD 2017). Implementation: two solvers and tools for A-hypergeometric functions.
- Vijay Kunwar (PhD 2014). Implementations for
2F1 type solutions for deg(pullback) <= 3, and for equations with
at most 5 true singularities, see FiveSing database.
- Tingting Fang (PhD 2012) (ISSAC'2011,
Find 2-descent for a differential equation, e-mail for implementation.
- Quan Yuan (PhD 2012) and Ruben Debeerst (a former visiting undergraduate student).
Implementation for computing Airy/Bessel/Kummer/Whittaker type solutions.
- Vivek Pal (at the time an undergraduate at FSU).
Implementation for Isomorphisms of Algebraic Number Fields.
- Yongjae Cha (PhD 2010).
closed form solutions of Linear Difference Equations. (2012): implementation
of algorithm Hom
- Giles Levy (PhD 2009). Implementation
to find relations to OEIS sequences, and
fastest algorithm for Liouvillian Solutions (for 2nd order Difference Equations).
- Andy Novocin (PhD 2008). Analyzed the complexity of factoring in Q[x]
which led to faster lattice reduction.