NearAdditiveMagma( gens ) F
NearAdditiveMagma( Fam, gens ) F
returns the (near-)additive magma A that is generated by the elements
in the list gens, that is,
the closure of gens under addition +.
The family Fam of A can be entered as first argument;
this is obligatory if gens is empty (and hence also A is empty).
NearAdditiveMagmaWithZero( gens ) F
NearAdditiveMagmaWithZero( Fam, gens ) F
returns the (near-)additive magma-with-zero A that is generated by
the elements in the list gens, that is,
the closure of gens under addition + and Zero.
The family Fam of A can be entered as first argument;
this is obligatory if gens is empty (and hence A is trivial).
NearAdditiveGroup( gens ) F
NearAdditiveGroup( Fam, gens ) F
returns the (near-)additive group A that is generated by the elements
in the list gens, that is,
the closure of gens under addition +, Zero, and AdditiveInverse.
The family Fam of A can be entered as first argument;
this is obligatory if gens is empty (and hence A is trivial).
The underlying operations for which methods can be installed are the following.
NearAdditiveMagmaByGenerators( gens ) O
NearAdditiveMagmaByGenerators( Fam, gens ) O
NearAdditiveMagmaWithZeroByGenerators( gens ) O
NearAdditiveMagmaWithZeroByGenerators( Fam, gens ) O
NearAdditiveGroupByGenerators( gens ) O
NearAdditiveGroupByGenerators( Fam, gens ) O
Substructures of an additive magma can be formed as follows.
SubnearAdditiveMagma( D, gens ) F
SubnearAdditiveMagmaNC( D, gens ) F
SubadditiveMagma returns the near-additive magma generated by
the elements in the list gens, with parent the domain D.
SubadditiveMagmaNC does the same, except that it is not checked
whether the elements of gens lie in D.
SubnearAdditiveMagmaWithZero( D, gens ) F
SubnearAdditiveMagmaWithZeroNC( D, gens ) F
SubadditiveMagmaWithZero returns the near-additive magma-with-zero
generated by the elements in the list gens, with parent the domain D.
SubadditiveMagmaWithZeroNC does the same, except that it is not checked
whether the elements of gens lie in D.
SubnearAdditiveGroup( D, gens ) F
SubnearAdditiveGroupNC( D, gens ) F
SubadditiveGroup returns the near-additive group generated by
the elements in the list gens, with parent the domain D.
SubadditiveGroupNC does the same, except that it is not checked
whether the elements of gens lie in D.
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GAP 4 manual