RespectsAddition( mapp ) P
Let mapp be a general mapping with underlying relation
F Í S ×R,
where S and R are the source and the range of mapp, respectively.
Then RespectsAddition returns true if
S and R are additive magmas such that
(s1,r1), (s2,r2) Î F implies (s1 + s2,r1 + r2) Î F,
and false otherwise.
If mapp is single-valued then RespectsAddition returns true
if and only if the equation
s1^mapp + s2^mapp = (s1+s2)^mapp
holds for all s1, s2 in S.
RespectsAdditiveInverses( mapp ) P
Let mapp be a general mapping with underlying relation
F Í S ×R,
where S and R are the source and the range of mapp, respectively.
Then RespectsAdditiveInverses returns true if
S and R are additive-magmas-with-inverses such that
(s,r) Î F implies (-s,-r) Î F,
and false otherwise.
If mapp is single-valued then RespectsAdditiveInverses returns true
if and only if the equation
AdditiveInverse( s )^mapp = AdditiveInverse( s^mapp )
holds for all s in S.
RespectsZero( mapp ) P
Let mapp be a general mapping with underlying relation
F Í S ×R,
where S and R are the source and the range of mapp, respectively.
Then RespectsZero returns true if
S and R are additive-magmas-with-zero such that
( Zero(¢S¢), Zero(¢R¢) ) Î F,
and false otherwise.
If mapp is single-valued then RespectsZero returns true
if and only if the equation
Zero( S )^mapp = Zero( R )
holds.
IsAdditiveGroupGeneralMapping( mapp ) P
IsAdditiveGroupHomomorphism( mapp ) P
KernelOfAdditiveGeneralMapping( mapp ) A
Let mapp be a general mapping.
Then KernelOfAdditiveGeneralMapping returns the set of all
elements in the source of mapp that have the zero of the range in
their set of images.
CoKernelOfAdditiveGeneralMapping( mapp ) A
Let mapp be a general mapping.
Then CoKernelOfAdditiveGeneralMapping returns the set of all
elements in the rqange of mapp that have the zero of the source in
their set of preimages.
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GAP 4 manual