A finite presentation of a module is given by a finite set of generators and a finite set of relations among these generators. In homalg a set of relations of a left/right module is given by a matrix rel, the rows/columns of which are interpreted as relations among n generators, n being the number of columns/rows of the matrix rel.
The data structure of a module in homalg is designed to contain not only one but several sets of relations (together with corresponding sets of generators (--> Chapter 8)). The different sets of relations are linked with so-called transition matrices (--> Chapter 9).
The relations of a homalg module are evaluated in a lazy way. This avoids unnecessary computations.
> IsHomalgRelations ( rel ) | ( category ) |
Returns: true
or false
The GAP category of homalg relations.
> IsHomalgRelationsOfLeftModule ( rel ) | ( category ) |
Returns: true
or false
The GAP category of homalg relations of a left module.
(It is a subcategory of the GAP category IsHomalgRelations
.)
> IsHomalgRelationsOfRightModule ( rel ) | ( category ) |
Returns: true
or false
The GAP category of homalg relations of a right module.
(It is a subcategory of the GAP category IsHomalgRelations
.)
> IsRelationsOfFinitelyPresentedModuleRep ( rel ) | ( representation ) |
Returns: true
or false
The GAP representation of a finite set of relations of a finitely presented homalg module.
(It is a representation of the GAP category IsHomalgRelations
(7.1-1))
> CanBeUsedToDecideZeroEffectively ( rel ) | ( property ) |
Returns: true
or false
Check if the homalg set of relations rel can be used for normal form reductions.
(no method installed)
> IsInjectivePresentation ( rel ) | ( property ) |
Returns: true
or false
Check if the homalg set of relations rel has zero syzygies.
> FreeResolution ( rel ) | ( attribute ) |
Returns: a homalg complex
The computed (part of a) free resolution of the module presented by homalg set of relations rel.
generated by GAPDoc2HTML