- You are free to use this code any way you want.
- If you would like to port 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.
- 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.
- 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, thesis, slides). 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). Implementation for 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.
- Fastest algorithm to factor in Q[x] is in Maple, Magma, NTL, FLINT, PARI/GP, and Sage and on French wikipedia.
- Bivariate polynomial factorization, in Magma and in Singular.
- Modular GCD (implementated in Maple and Magma by Michael Monagan, cited in Microsoft patent).
- Gradual sub-lattice reduction (with Andy Novocin)
- Isomorphisms between number fields (with Vivek Pal)
- Subfields and decomposing rational functions (with Jonas Szutkoski)
- Puiseux Expansion and Integral Basis, paper and implementation (1994).
- Parametrization of Rational Algebraic Curves, papers and implementations (1994,1997).
- Weierstrass Normal Form for elliptic (1995) and hyper-elliptic (1999) curves, papers and implementations.
- Overview of algcurves in 1996 (try plot_knot!).
- Joint with Bernard Deconinck: Riemann Matrices (2001) and Riemann Theta Functions (2004).
- FindDessins, Maple 2019 help page, source code, is an algorithm used to classify Belyi maps for the FiveSing database (2016).
- Algorithms (2013) such as ComputeBelyi for the Heun database with R. Vidunas.
- Integral basis in Characteristic p (with Mike Stillman) (nearly complete implementation available by e-mail)
- Finding a point on a conic over a rational function field (2006). Similar topic: ConicIsomorphism.
- Abel's problem (2000) (minpoly of exp(int(a,x)) where a is an algebraic function).
- diffop package which includes
- DFactor. Cited by Mathematica. Special code for order 4.
- eigenring and DFactorLCLM
- formal solutions and generalized exponents
- integrate_sols
- expsols. Improvements (not implemented) in CH'2004.
- Hom (there is no paper for this in the differential case, only for the difference case)
- other tools (adjoint, mult, GCRD, LCLM, rightdivision, symmetric product, symmetric/exterior power).

- Liouvillian solutions for order 2 (paper) and imprimitive case for order 3.
- Detecting a symmetric product or symmetric power of second order operators and other patterns.
- FindODE, Maple 2019 help page (last example is solved due to symmetric product program in the previous item), source code.
- ReduceOrder, detects if a 3rd order equation is gauge-equivalent to a symmetric square of a 2nd order equation.
- Desingularization
- Compute invariants of the differential Galois group.
- Solving 2nd order equations in closed form, see "Algorithms with former students" above.
- Hypergeometric solutions. Cited by Mathematica. Improvements (not implemented) in CH'2006.
- Desingularization
- Rational definite summation
- Hom, Liouvillian and other closed-form solutions, see "Algorithms with former students" above.
- Modular curve X1(N): Gonality (with Derickx), and Low Degree Places.
- Belyi and near Belyi maps with four resp. five exceptional points, with Vidunas resp. Kunwar.
- Optimized equations for X1(N) (with Sutherland) and for X_H(l) (to compute Galois representations, with Derickx and Zeng).

Notes:

Algorithms with former students: