| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/crime/gap/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 17.2.2022 mit Größe 741 B |
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Quelle comments Sprache: JAVA |
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General comments on multiplying chain maps.
Let L be a chain map of degree d. Then L is represented as a list having in position 1 a map P_d -> P_0, in position 2 a map P_{d+1} -> P_1, etc. such that the standard diagram commutes. Let M be a chain map of degree e. Observe that in position e+1, L has a map P_{e+d} -> P_e. Therefore, the product of M*L has L[e+1] * M[1] in position 1 L[e+2] * M[2] in position 2, etc. However, since L and M are represented as lists of non-lifted matricies, we have to lift the matrix on the right using LiftHom. So M*L actually has L[e+1] * LiftHom(...,M[1],...) in position 1, L[e+2] * LiftHom(...,M[2],...) in position 2, etc. The result is non-lifted because the matrix on the left is non-lifted. ¤ Dauer der Verarbeitung: 0.5 Sekunden ¤*© Formatika GbR, Deutschland |
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2026-03-28