FreeModule — finite-rank free module R^n, the type-level anchor for every Matrix. More...

#include "ring.hpp"
#include "schorder.hpp"

Classes
class	FreeModule
	Engine-side free module R^n over a Ring. More...

Detailed Description

FreeModule — finite-rank free module R^n, the type-level anchor for every Matrix.

Note: AI-generated documentation. Verify against the source before relying on it.

Declares FreeModule, an EngineObject that holds its base Ring *R, the per-generator degree vectors in gc_vector<monomial> components (the rank is just components.size()), and an optional SchreyerOrder *schreyer (NULL when no Schreyer structure is installed). Every Matrix stores pointers to a source and target FreeModule, so this class is what gives matrix shapes their static guarantees — degree compatibility and base-ring agreement are checked through these pointers. Once a FreeModule is interned its EngineObject hash freezes it, but during construction it is built up imperatively: the fresh-return transformations sub_space, direct_sum, tensor, exterior and the static make_schreyer allocate a new FreeModule, while append, append_schreyer, change_degree, and the in-place direct_sum_to mutate the receiver and are used to fill it in before it escapes.

When a Schreyer order is installed, the comparison compare(e_i * m, e_j * m') first compares m_{i} * m against m_{j} * m' using the stored leading monomials of the inducing generators and then tiebreaks by index, which is what lets a syzygy module remember the order structure of the resolution step it came from. The standalone #undef FreeModule near the top of the header defuses a stray MinGW system-header macro of the same name.

See also: ring.hpp; schorder.hpp; matrix.hpp

Definition in file freemod.hpp.

Classes

Detailed Description