| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/nq/examples/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 12.0.2024 mit Größe 89 kB |
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Spracherkennung für: .out vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen] #
# Calculating a nilpotent quotient # Nilpotency class: 12 # Size of exponents: 8 bytes # # Calculating the abelian quotient ... # The abelian quotient has 4 generators # with the following exponents: 0 0 0 0 # # Calculating the class 2 quotient ... ## Sizes: 4 10 # Maximal entry: 0 # Layer 2 of the lower central series has 3 generators # with the following exponents: 0 0 0 # # Calculating the class 3 quotient ... ## Sizes: 4 7 22 # Maximal entry: 0 # Layer 3 of the lower central series has 3 generators # with the following exponents: 0 0 0 # # Calculating the class 4 quotient ... ## Sizes: 4 7 10 34 # Maximal entry: 0 # Layer 4 of the lower central series has 3 generators # with the following exponents: 0 0 0 # # Calculating the class 5 quotient ... ## Sizes: 4 7 10 13 46 # Maximal entry: 2 # Layer 5 of the lower central series has 4 generators # with the following exponents: 0 2 3 0 # # Calculating the class 6 quotient ... ## Sizes: 4 7 10 13 17 64 # Maximal entry: 6 # Layer 6 of the lower central series has 6 generators # with the following exponents: 2 2 3 3 0 6 # # Calculating the class 7 quotient ... ## Sizes: 4 7 10 13 17 23 93 # Maximal entry: 14 # Layer 7 of the lower central series has 9 generators # with the following exponents: 2 2 2 3 3 6 2 3 6 # # Calculating the class 8 quotient ... ## Sizes: 4 7 10 13 17 23 32 138 # Maximal entry: 36 # Layer 8 of the lower central series has 13 generators # with the following exponents: 2 2 2 2 3 3 3 2 2 3 3 6 2 # # Calculating the class 9 quotient ... ## Sizes: 4 7 10 13 17 23 32 45 203 # Maximal entry: 2019 # Layer 9 of the lower central series has 16 generators # with the following exponents: 2 2 2 2 2 3 3 3 2 2 2 3 3 3 2 2 # # Calculating the class 10 quotient ... ## Sizes: 4 7 10 13 17 23 32 45 61 283 # Maximal entry: 22320 # Layer 10 of the lower central series has 21 generators # with the following exponents: 2 2 2 2 2 2 2 3 3 3 2 2 2 2 3 3 3 3 3 2 2 # # Calculating the class 11 quotient ... ## Sizes: 4 7 10 13 17 23 32 45 61 82 388 # Maximal entry: 9921 # Layer 11 of the lower central series has 28 generators # with the following exponents: 2 2 2 2 2 2 2 2 2 3 3 3 3 2 2 2 2 2 3 3 3 3 3 3 3 2 2 2 # # Calculating the class 12 quotient ... ## Sizes: 4 7 10 13 17 23 32 45 61 82 110 528 # Maximal entry: 9093 # Layer 12 of the lower central series has 36 generators # with the following exponents: 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 2 2 2 # # The epimorphism : # e1 |---> A # e2 |---> B # e3 |---> C # e4 |---> D # The nilpotent quotient : <A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J |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lass : 12 # Nr of generators of each class : 4 3 3 3 4 6 9 13 16 21 28 36 # The definitions: # E := [ B, A ] # F := [ C, B ] # G := [ D, C ] # H := [ C, B, A ] # I := [ C, B, C ] # J := [ D, C, B ] # K := [ C, B, C, A ] # L := [ D, C, B, A ] # M := [ D, C, B, C ] # N := [ D, C, B, C, A ] # O := [ D, C, B, C, B ] # P := [ D, C, B, C, C ] # Q := [ D, C, B, C, D ] # R := [ D, C, B, C, A, B ] # S := [ D, C, B, C, B, C ] # T := [ D, C, B, C, C, A ] # U := [ D, C, B, C, C, B ] # V := [ D, C, B, C, D, A ] # W := [ D, C, B, C, D, C ] # X := [ D, C, B, C, A, B, A ] # Y := [ D, C, B, C, A, B, C ] # Z := [ D, C, B, C, B, C, B ] # A1 := [ D, C, B, C, C, B, A ] # B1 := [ D, C, B, C, C, B, C ] # C1 := [ D, C, B, C, D, C, A ] # D1 := [ D, C, B, C, D, C, B ] # E1 := [ D, C, B, C, D, C, C ] # F1 := [ D, C, B, C, D, C, D ] # G1 := [ D, C, B, C, A, B, C, A ] # H1 := [ D, C, B, C, A, B, C, D ] # I1 := [ D, C, B, C, B, C, B, A ] # J1 := [ D, C, B, C, B, C, B, C ] # K1 := [ D, C, B, C, C, B, A, A ] # L1 := [ D, C, B, C, C, B, C, A ] # M1 := [ D, C, B, C, C, B, C, C ] # N1 := [ D, C, B, C, D, C, A, B ] # O1 := [ D, C, B, C, D, C, B, C ] # P1 := [ D, C, B, C, D, C, C, A ] # Q1 := [ D, C, B, C, D, C, C, B ] # R1 := [ D, C, B, C, D, C, D, A ] # S1 := [ D, C, B, C, D, C, D, C ] # T1 := [ D, C, B, C, A, B, C, A, B ] # U1 := [ D, C, B, C, A, B, C, D, C ] # V1 := [ D, C, B, C, B, C, B, C, A ] # W1 := [ D, C, B, C, B, C, B, C, B ] # X1 := [ D, C, B, C, B, C, B, C, D ] # Y1 := [ D, C, B, C, C, B, C, A, A ] # Z1 := [ D, C, B, C, C, B, C, C, A ] # A2 := [ D, C, B, C, C, B, C, C, B ] # B2 := [ D, C, B, C, D, C, A, B, A ] # C2 := [ D, C, B, C, D, C, A, B, C ] # D2 := [ D, C, B, C, D, C, B, C, B ] # E2 := [ D, C, B, C, D, C, C, A, B ] # F2 := [ D, C, B, C, D, C, C, B, A ] # G2 := [ D, C, B, C, D, C, C, B, C ] # H2 := [ D, C, B, C, D, C, D, C, A ] # I2 := [ D, C, B, C, D, C, D, C, D ] # J2 := [ D, C, B, C, A, B, C, A, B, A ] # K2 := [ D, C, B, C, A, B, C, A, B, C ] # L2 := [ D, C, B, C, A, B, C, D, C, B ] # M2 := [ D, C, B, C, B, C, B, C, A, B ] # N2 := [ D, C, B, C, B, C, B, C, B, C ] # O2 := [ D, C, B, C, B, C, B, C, D, A ] # P2 := [ D, C, B, C, B, C, B, C, D, C ] # Q2 := [ D, C, B, C, C, B, C, C, A, A ] # R2 := [ D, C, B, C, C, B, C, C, A, B ] # S2 := [ D, C, B, C, C, B, C, C, B, C ] # T2 := [ D, C, B, C, D, C, A, B, C, A ] # U2 := [ D, C, B, C, D, C, A, B, C, D ] # V2 := [ D, C, B, C, D, C, B, C, B, A ] # W2 := [ D, C, B, C, D, C, B, C, B, C ] # X2 := [ D, C, B, C, D, C, C, A, B, C ] # Y2 := [ D, C, B, C, D, C, C, B, A, A ] # Z2 := [ D, C, B, C, D, C, C, B, C, A ] # A3 := [ D, C, B, C, D, C, C, B, C, C ] # B3 := [ D, C, B, C, D, C, C, B, C, D ] # C3 := [ D, C, B, C, D, C, D, C, A, B ] # D3 := [ D, C, B, C, D, C, D, C, D, C ] # E3 := [ D, C, B, C, A, B, C, A, B, C, A ] # F3 := [ D, C, B, C, A, B, C, A, B, C, D ] # G3 := [ D, C, B, C, A, B, C, D, C, B, A ] # H3 := [ D, C, B, C, A, B, C, D, C, B, C ] # I3 := [ D, C, B, C, B, C, B, C, A, B, A ] # J3 := [ D, C, B, C, B, C, B, C, A, B, C ] # K3 := [ D, C, B, C, B, C, B, C, B, C, B ] # L3 := [ D, C, B, C, B, C, B, C, D, C, A ] # M3 := [ D, C, B, C, B, C, B, C, D, C, B ] # N3 := [ D, C, B, C, C, B, C, C, A, B, A ] # O3 := [ D, C, B, C, C, B, C, C, A, B, C ] # P3 := [ D, C, B, C, C, B, C, C, B, C, C ] # Q3 := [ D, C, B, C, C, B, C, C, B, C, D ] # R3 := [ D, C, B, C, D, C, A, B, C, A, B ] # S3 := [ D, C, B, C, D, C, A, B, C, D, C ] # T3 := [ D, C, B, C, D, C, B, C, B, C, A ] # U3 := [ D, C, B, C, D, C, B, C, B, C, B ] # V3 := [ D, C, B, C, D, C, B, C, B, C, D ] # W3 := [ D, C, B, C, D, C, C, A, B, C, C ] # X3 := [ D, C, B, C, D, C, C, A, B, C, D ] # Y3 := [ D, C, B, C, D, C, C, B, C, A, A ] # Z3 := [ D, C, B, C, D, C, C, B, C, C, A ] # A4 := [ D, C, B, C, D, C, C, B, C, C, B ] # B4 := [ D, C, B, C, D, C, C, B, C, D, A ] # C4 := [ D, C, B, C, D, C, C, B, C, D, C ] # D4 := [ D, C, B, C, D, C, D, C, A, B, A ] # E4 := [ D, C, B, C, D, C, D, C, A, B, C ] # F4 := [ D, C, B, C, D, C, D, C, D, C, D ] # G4 := [ D, C, B, C, A, B, C, A, B, C, A, B ] # H4 := [ D, C, B, C, A, B, C, A, B, C, D, A ] # I4 := [ D, C, B, C, A, B, C, A, B, C, D, C ] # J4 := [ D, C, B, C, A, B, C, D, C, B, C, A ] # K4 := [ D, C, B, C, A, B, C, D, C, B, C, D ] # L4 := [ D, C, B, C, B, C, B, C, A, B, C, A ] # M4 := [ D, C, B, C, B, C, B, C, A, B, C, D ] # N4 := [ D, C, B, C, B, C, B, C, B, C, B, A ] # O4 := [ D, C, B, C, B, C, B, C, B, C, B, C ] # P4 := [ D, C, B, C, B, C, B, C, D, C, A, B ] # Q4 := [ D, C, B, C, B, C, B, C, D, C, B, A ] # R4 := [ D, C, B, C, B, C, B, C, D, C, B, C ] # S4 := [ D, C, B, C, C, B, C, C, A, B, A, A ] # T4 := [ D, C, B, C, C, B, C, C, A, B, C, A ] # U4 := [ D, C, B, C, C, B, C, C, A, B, C, C ] # V4 := [ D, C, B, C, C, B, C, C, A, B, C, D ] # W4 := [ D, C, B, C, C, B, C, C, B, C, C, B ] # X4 := [ D, C, B, C, C, B, C, C, B, C, D, C ] # Y4 := [ D, C, B, C, D, C, A, B, C, A, B, A ] # Z4 := [ D, C, B, C, D, C, A, B, C, A, B, C ] # A5 := [ D, C, B, C, D, C, A, B, C, D, C, B ] # B5 := [ D, C, B, C, D, C, B, C, B, C, A, B ] # C5 := [ D, C, B, C, D, C, B, C, B, C, B, C ] # D5 := [ D, C, B, C, D, C, B, C, B, C, D, A ] # E5 := [ D, C, B, C, D, C, B, C, B, C, D, C ] # F5 := [ D, C, B, C, D, C, C, A, B, C, D, C ] # G5 := [ D, C, B, C, D, C, C, B, C, C, A, A ] # H5 := [ D, C, B, C, D, C, C, B, C, C, A, B ] # I5 := [ D, C, B, C, D, C, C, B, C, C, B, A ] # J5 := [ D, C, B, C, D, C, C, B, C, C, B, C ] # K5 := [ D, C, B, C, D, C, C, B, C, D, A, A ] # L5 := [ D, C, B, C, D, C, C, B, C, D, C, A ] # M5 := [ D, C, B, C, D, C, C, B, C, D, C, C ] # N5 := [ D, C, B, C, D, C, D, C, A, B, C, A ] # O5 := [ D, C, B, C, D, C, D, C, A, B, C, D ] # P5 := [ D, C, B, C, D, C, D, C, D, C, D, C ] [Dauer der Verarbeitung: 0.34 Sekunden, vorverarbeitet 2026-04-27] |
2026-05-26