@hackage oalg-base1.0.0.1

Algebraic structures on oriented entities and limits as a tool kit to solve algebraic problems.

Basic definition of algebraic structures, viewing through the lens of categories.

  • Most algebraic operations, e.g. multiplication, addition etc, are partially defined operators, but have precise definition for there applicability.

  • Limits serve as a backbone for solving algebraic problems, e. g. finding all solutions of the equation a * x == 0 is given by the kernel of a.

The actual release contains a minimum of functionality to define finitely generated abelian groups and the kernels and cokernels respectively. As such, a lot of more work has to be done to get a complete base for solving algebraic problems.

To Do:

  • Property for Generator more precise.

  • Exact sequences.

  • Kernel and cokernels for matrices over a field.

  • As Double is not implemented as an algebraic structure here (it dose not comply to the stated properties),it is not so obvious how to handle reals.

  • More statements for validation.