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- Gregory J. Reid
- 1991

We present several algorithms, executable in a finite number of steps, which have been implemented in the symbolic language maple . The standard form algorithm reduces a system of PDEs to a… (More)

New classes of symmetries for partial differential equations are introduced. By writing a given partial differential equation S in a conserved form, a related system T with potentials as additional… (More)

We introduce the CDiffElim environment, written in C, and an algorithm developed in this environment for simplifying systems of overdetermined partial differential equations by using differentiation… (More)

- Gregory J. Reid
- 1991

There are symbolic programs based on heuristics that sometimes, but not always, explicitly integrate the determining equations for the infinitesimal Lie symmetries admitted by systems of differential… (More)

- Ian G. Lisle, Gregory J. Reid
- J. Symb. Comput.
- 1998

An algorithm is described which uses a finite number of differentiations and linear operations to determine the Cartan structure of a transitive Lie pseudogroup from its infinitesimal defining… (More)

- Wenyuan Wu, Gregory J. Reid
- ISSAC
- 2013

In this paper we extend complex homotopy methods to finding witness points on the irreducible components of real varieties. In particular we construct such witness points as the isolated real… (More)

Existence and Uniqueness Theorems for Formal Power Series Solutions of Analytic Differential Systems

- C. J. Rust, Gregory J. Reid, Allan D. Wittkopf
- ISSAC
- 1999

We present Existence ant1 Uniqueness Theorems for formal pO\Wr series solutions Of ilnd~t.i(’ s\lSteIlls Of PDF. in il cmtain form. ‘This form can be obtained by it finil.c number of differediations… (More)

- Gregory J. Reid, Lihong Zhi
- J. Symb. Comput.
- 2009

We briefly survey several existing methods for solving polynomial systems with inexact coefficients, then introduce our new symbolic-numeric method which is based on the geometric (Jet) theory of… (More)

- Wenyuan Wu, Gregory J. Reid, Yong Feng
- Theor. Comput. Sci.
- 2017

Abstract We consider a critical point method for finding certain solution (witness) points on real solution components of real polynomial systems of equations. The method finds points that are… (More)