submodule

© 2005 John Abbott
GNU Free Documentation License, Version 1.2



index page

User documentation for the class SubmoduleImpl

For normal use there is only one function of interest:

NewSubmodule(M, gens)
creates an object of type EFGModule representing the submodule of the EFGModule M generated by the elements in gens; note that M must be specified even though it is usually implicit in the values contained in gens (unless gens is empty).

Maintainer documentation for the classes module, and ModuleElem

I shall suppose that the maintainer documentation for modules and EFGModules has already been read and digested. It could also be helpful to have read ring.txt since the "design philosophy" here imitates that used for rings.

SubmoduleImpl is a concrete class derived from EFGModuleBase, i.e. objects of this class represent submodules of explicitly finitely generated modules. The data members comprise the two obvious values:

    FreeModule myM;                 // the ambient module in which the generators live
    vector<ModuleElem> myGensArray; // the generators as specified by the user

Additionally there are two other data members:

    bool myTidyGensIsValid;             // true iff myTidyGensArray contains a correct value
    vector<ModuleElem> myTidyGensArray; // a "nice" set of generators

It is difficult to be precise about the value which myTidyGensArray should contain (when valid) since it depends upon the module. If the module is over a polynomial ring then it will be a Groebner basis. If the module is over Z then it will presumably be either a "Hermite Basis" or an "LLL Basis".

Bugs, Shortcomings and other ideas

Implementation and documentation are rather incomplete.

Why is myM a FreeModule and not an EFGModule???

What is myTidyGensArray for a module over Z???