Goto Chapter: Top 1 2 3 4 5 6 7 8 9 10 11 12 13 A B C Bib Ind
 [Top of Book]  [Contents]   [Previous Chapter]   [Next Chapter] 

9 Module Elements
 9.1 Module Elements: Category and Representations
 9.2 Module Elements: Constructors
 9.3 Module Elements: Properties
 9.4 Module Elements: Attributes
 9.5 Module Elements: Operations and Functions

9 Module Elements

An element of a module M is internally represented by a module map from the (distinguished) rank 1 free module to the module M. In particular, the data structure for module elements automatically profits from the intrinsic realization of morphisms in the homalg project.

9.1 Module Elements: Category and Representations

9.1-1 IsHomalgElement
‣ IsHomalgElement( M )( category )

Returns: true or false

The GAP category of module elements.

9.1-2 IsElementOfAModuleGivenByAMorphismRep
‣ IsElementOfAModuleGivenByAMorphismRep( M )( representation )

Returns: true or false

The GAP representation of elements of modules.

(It is a subrepresentation of IsElementOfAnObjectGivenByAMorphismRep (homalg: IsElementOfAnObjectGivenByAMorphismRep).)

9.2 Module Elements: Constructors

9.3 Module Elements: Properties

9.3-1 IsElementOfIntegers
‣ IsElementOfIntegers( m )( property )

Returns: true or false

Check if the m is an element of the integers viewed as a module over itself.

gap> zz := HomalgRingOfIntegers( );
Z
gap> a := HomalgElement( HomalgMap( "[[2]]", 1 * zz, 1 * zz ) );
2
gap> IsElementOfIntegers( a );
true
gap> Z4 := zz / 4;
Z/( 4 )
gap> b := HomalgElement( HomalgMap( "[[-1]]", 1 * Z4, 1 * Z4 ) );
|[ 3 ]|
gap> IsElementOfIntegers( b );
false

9.4 Module Elements: Attributes

9.5 Module Elements: Operations and Functions

9.5-1 HomalgRing
‣ HomalgRing( m )( operation )

Returns: a homalg ring

The homalg ring of the homalg module element m.

gap> zz := HomalgRingOfIntegers( );
Z
gap> a := HomalgElement( HomalgMap( "[[2]]", 1 * zz, 1 * zz ) );
2
gap> IsIdenticalObj( zz, HomalgRing( a ) );
true
 [Top of Book]  [Contents]   [Previous Chapter]   [Next Chapter] 
Goto Chapter: Top 1 2 3 4 5 6 7 8 9 10 11 12 13 A B C Bib Ind

generated by GAPDoc2HTML