GAP (MatricesForHomalg) - Chapter 6: Ring Relations

Goto Chapter: Top 1 2 3 4 5 6 A B C D E F Bib Ind
[Top of Book] [Contents] [Previous Chapter] [Next Chapter]

[MathJax on]

6 Ring Relations
6.1 Ring Relations: Categories and Representations
6.1-1 IsHomalgRingRelations
6.1-2 IsHomalgRingRelationsAsGeneratorsOfLeftIdeal
6.1-3 IsHomalgRingRelationsAsGeneratorsOfRightIdeal
6.1-4 IsRingRelationsRep
6.2 Ring Relations: Constructors
6.3 Ring Relations: Properties
6.3-1 CanBeUsedToDecideZero
6.3-2 IsInjectivePresentation
6.4 Ring Relations: Attributes
6.5 Ring Relations: Operations and Functions

### 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

[Top of Book] [Contents] [Previous Chapter] [Next Chapter]
Goto Chapter: Top 1 2 3 4 5 6 A B C D E F Bib Ind

generated by GAPDoc2HTML