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 6)). The different sets of relations are linked with so-called transition matrices (--> Chapter 7).
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 (5.1-1))
‣ 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.
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