chap6.txt

  
  6 Ring Relations
  
  
  6.1 Ring Relations: Categories and Representations
  
  6.1-1 IsHomalgRingRelations
  
  IsHomalgRingRelations( rel )  Category
  Returns:  true or false
  
  The GAP category of homalg ring relations.
  
  6.1-2 IsHomalgRingRelationsAsGeneratorsOfLeftIdeal
  
  IsHomalgRingRelationsAsGeneratorsOfLeftIdeal( rel )  Category
  Returns:  true or false
  
  The GAP category of homalg ring relations as generators of a left ideal.
  
  (It is a subcategory of the GAP category IsHomalgRingRelations.)
  
  6.1-3 IsHomalgRingRelationsAsGeneratorsOfRightIdeal
  
  IsHomalgRingRelationsAsGeneratorsOfRightIdeal( rel )  Category
  Returns:  true or false
  
  The GAP category of homalg ring relations as generators of a right ideal.
  
  (It is a subcategory of the GAP category IsHomalgRingRelations.)
  
  6.1-4 IsRingRelationsRep
  
  IsRingRelationsRep( rel )  Representation
  Returns:  true or false
  
  The GAP representation of a finite set of relations of a homalg ring.
  
  (It is a representation of the GAP category IsHomalgRingRelations (6.1-1))
  
  
  6.2 Ring Relations: Constructors
  
  
  6.3 Ring Relations: Properties
  
  6.3-1 CanBeUsedToDecideZero
  
  CanBeUsedToDecideZero( rel )  property
  Returns:  true or false
  
  Check  if  the  homalg  set  of  relations  rel  can be used for normal form
  reductions.
  (no method installed)
  
  6.3-2 IsInjectivePresentation
  
  IsInjectivePresentation( rel )  property
  Returns:  true or false
  
  Check if the homalg set of relations rel has zero syzygies.
  
  
  6.4 Ring Relations: Attributes
  
  
  6.5 Ring Relations: Operations and Functions