FreeModule

• Examples
• User documentation for the class FreeModule
• Maintainer documentation for the classes FreeModule and FreeModuleImpl
• Bugs, Shortcomings and other ideas

Examples

• ex-module1.C

User documentation for the class FreeModule

For normal use there are only a few functions of interest:

NewFreeModule(R, NumCompts)

creates an object of type FGModule representing the free module of dimension NumCompts over the ring R.

FreeModule(M)

where M is a module; if M is genuinely a FreeModule then that FreeModule is returned otherwise an error is generated.

IsFreeModule(M)

true iff the module M is genuinely a FreeModule.

CanonicalBasis(M)

returns a read-only vector whose entry with index k contains the k-th unit vector (all coords 0 except k-th; recall that indexes start from 0).

NewFreeModule(R, NumCompts, shifts)

creates an object of type FGModule representing the free module of dimension NumCompts over the ring R. R must be a PolyRing, and shifts is a vector<degree> containing NumCompts elements, the i-th element being the shift applied to degrees of values in the i-th component. For example: ?????

Maintainer documentation for the classes FreeModule and FreeModuleImpl

I shall suppose that the maintainer documentation for modules and FGModules 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.

As one would expect, FreeModule is simple a reference counting smart pointer class to a FreeModuleImpl object.

FreeModuleImpl turns out to be a little more complex than one might naively guess. The extra complexity arises from two causes: one is compatibility with the general structure of modules, and the other is that a FreeModule manages the memory used to represent the values of ModuleElems belonging to itself.

GradedFreeModuleImpl is derived from FreeModuleImpl and allows storing and using ordering and shifts: it requires a SparsePolyRing as BaseRing. It provides these functions for FreeModule:

    FreeModule NewFreeModule(const ring& P, const ModuleTermOrdering& O);
    bool IsGradedFreeModule(const module& M);

The following functions are defined only if FreeModule is implemented as GradedFreeModuleImpl

    const std::vector<degree>& shifts(const FreeModule& M);
    const ModuleTermOrdering& ordering(const FreeModule& M);
    long LPos(const ModuleElem& v);
    degree wdeg(const ModuleElem& v);
    int CmpWDeg(const ModuleElem& v1, const ModuleElem& v2);
    ConstRefPPMonoidElem LPP(const ModuleElem& v);
    bool IsHomog(const ModuleElem& v);

Bugs, Shortcomings and other ideas

Documentation rather incomplete.