homalg-2019.09.01/gap/Complexes.gi

23     local degrees, mor, def;
32         Error( "the second argument ", i, " is outside the degree range of the complex\n" );
34         mor := CertainMorphism( C, i + 1 );
35         def := Cokernel( mor );
37         mor := CertainMorphism( C, i );
38         def := Kernel( mor );
40         mor := CertainTwoMorphismsAsSubcomplex( C, i );
41         mor := AsATwoSequence( mor );
42         def := DefectOfExactness( mor );
55     local degrees, mor, def;
64         Error( "the second argument ", i, " is outside the degree range of the complex\n" );
66         mor := CertainMorphism( C, i );
67         def := Kernel( mor );
69         mor := CertainMorphism( C, i - 1 );
70         def := Cokernel( mor );
72         mor := CertainTwoMorphismsAsSubcomplex( C, i );
73         mor := AsATwoSequence( mor );
74         def := DefectOfExactness( mor );
89         Error( "this is a cocomplex: use \033[1mCohomology\033[0m instead\n" );
104         Error( "this is a complex: use \033[1mHomology\033[0m instead\n" );
170         Error( "the input is not a complex" );
294         Error( "the input is not a cocomplex" );
371         Error( "this is a cocomplex: use \033[1mCohomology\033[0m instead\n" );
386         Error( "this is a complex: use \033[1mHomology\033[0m instead\n" );
445         # if certain objects are known to be zero, the remaining morphism is an isomorphism
527     # the resolution is build the way such that "epsilonM/psi" works.
616     # (if there is anything to fill)
661     local zero, cpx, seq, mor, emb, ker, P, epi, i;
682     mor := HighestDegreeMorphism( C );
684     emb := KernelEmb( mor );
724     local zero, cpx, seq, mor, emb, ker, P, epi, i;
745     mor := LowestDegreeMorphism( C );
747     emb := KernelEmb( mor );
834 …snake := PreCompose( snake, bn );	## the connecting homomorphism is what b[n] induces between cert…
1119     local q, degrees, l, def, d, mor, index_pairs, QFB, FB, CE, natural_epis,
1123         Error( "the second argument is not a complex\n" );
1150     mor := MorphismsOfComplex( C );
1152     index_pairs := List( mor, PairOfPositionsOfTheDefaultPresentations );
1155     QFB := Resolution( q, CokernelSequence( mor[1] ) );
1173             HZB := DefectOfExactnessSequence( mor[2], mor[1] );
1193             BFZ := Resolution( q, KernelSequence( mor[1] ) );
1208             HZB := DefectOfExactnessSequence( mor[1], mor[2] );
1228             BFZ := Resolution( q, KernelSequence( mor[1] ) );
1247             HZB := DefectOfExactnessSequence( mor[i], mor[i-1] );
1261             BFZ := Resolution( q, KernelSequence( mor[i-1] ) );
1281             HZB := DefectOfExactnessSequence( mor[i-1], mor[i] );
1295             BFZ := Resolution( q, KernelSequence( mor[i-1] ) );
1315     BFZ := Resolution( q, KernelSequence( mor[l] ) );
1359     local q, degrees, l, def, d, mor, index_pairs, ZFB, FB, CE, natural_epis,
1363         Error( "the second argument is not a cocomplex\n" );
1390     mor := MorphismsOfComplex( C );
1392     index_pairs := List( mor, PairOfPositionsOfTheDefaultPresentations );
1395     ZFB := Resolution( q, KernelCosequence( mor[1] ) );
1414             BZH := DefectOfExactnessCosequence( mor[i-1], mor[i] );
1417             BZH := DefectOfExactnessCosequence( mor[i], mor[i-1] );
1438         ZFB := Resolution( q, KernelCosequence( mor[i] ) );
1454     BFQ := Resolution( q, CokernelCosequence( mor[l] ) );