This page is a repository of results related to the following paper:

- M. England
*Deriving bases for Abelian functions.*Comput. Methods Funct. Theory**11:2**(2011).

Preprint: arXiv:1103.0468.

This paper makes reference to large sets of relations, which for reasons of brevity have not been included in the paper. As such links to these relations are provided here. We also provide text files of some of the results in the paper for use by anyone who is interested.

- Bfunction.txt. Poles or order 3 and 5 indices.
- Tfunction.txt. Poles or order 3 and 6 indices.
- Sfunction.txt. Poles or order 3 and 6 indices.
- Pfunction.txt. Poles or order 3 and 7 indices.
- I5P4a.txt. Poles or order 4 and 5 indices.
- I6P4.txt. Poles or order 4 and 6 indices.
- Ffunction.txt. Poles or order 4 and 6 indices. (May be constructed from functions above).
- I7P4.txt. Poles or order 4 and 7 indices.
- I8P4.txt. Poles or order 4 and 8 indices.
- Gfunction.txt. Poles or order 4 and 8 indices. (One of the function above which was has been used elsewhere).

Throughout the paper we refer to a power series expansion for the sigma function associated to the curve. This was constructed by partitioning it into polynomials whose terms have the same weight ratio. The expansion was given as

- SW.txt.
- C11.txt
- C14.txt
- C17.txt
- C20.txt
- C23.txt
- C26.txt
- C29.txt
- C32.txt
- C35.txt
- C38.txt
- C41.txt
- C44.txt
- C47.txt
- C50.txt

In Section 4 of the paper we derived three complete sets of differential equations for the functions associated with the (3,5)-curve.

- Theorem 4.1 presented a set of relations that express all the 4-index P-functions as a degree 2 polynomial in the fundamental basis entries. They were printed in Appendix B and are available in a text file here.

- Theorem 4.2 presented an expression for each of the 210 products of pairs of 3-index functions as a degree 3 polynomial in the fundamental basis entries. They are available in a text file here. The first few were printed in the paper while a full print out may be viewed in this Maple File.

- Theorem 4.3 derived a set of 65 relations bilinear in the 2 and 3-index functions, from which all others can be constructed. They are available in a text file here. This text file also contains the relations in the notation of B-functions, which is how they were derived. The first few relations were printed in the paper while a full print out may be viewed in this Maple File.

- Text file defining Maple procedure to multiply out product of sigma derivatives.
- Classic Maple Worksheet giving toy example to demonstrate code.
- Text file with definitions of P functions.

This page is maintained by Matthew England.