CommutativeDiagram( paramap1, paramap2, paramap3, paramap4 )
CommutativeDiagram( paramap1, paramap2, paramap3, paramap4,
improvements )
If [ CompositionMaps(paramap2,paramap1 ) =
CompositionMaps(paramap4,paramap3 )
]
shall hold, the consistency is checked and the four maps
will be improved according to this condition.
If a record improvements with fields imp1
, imp2
, imp3
, imp4
(all lists) is entered as parameter, only diagrams containing elements of
impi
as positions in the i-th paramap are considered.
CommutativeDiagram
returns false
if an inconsistency was found,
otherwise a record is returned that contains four lists imp1
, ldots,
imp4
, where impi
is the list of classes where the i-th paramap was
improved.
gap> map1:= [ [ 1, 2, 3 ], [ 1, 3 ] ];; gap> map2:= [ [ 1, 2 ], 1, [ 1, 3 ] ];; gap> map3:= [ [ 2, 3 ], 3 ];; map4:= [ , 1, 2, [ 1, 2 ] ];; gap> CommutativeDiagram( map1, map2, map3, map4 ); rec( imp1 := [ 2 ], imp2 := [ 1 ], imp3 := [ ], imp4 := [ ] ) gap> imp:= last;; map1; map2; map3; map4; [ [ 1, 2, 3 ], 1 ] [ 2, 1, [ 1, 3 ] ] [ [ 2, 3 ], 3 ] [ , 1, 2, [ 1, 2 ] ] gap> CommutativeDiagram( map1, map2, map3, map4, imp ); rec( imp1 := [ ], imp2 := [ ], imp3 := [ ], imp4 := [ ] )
GAP 3.4.4