- Start + Stop
- Permutationen, {1,2, ..., n } ---> {1,2, ..., n }
Zyklen Notation, cycle notation
1 2 3 4 5 6 7 8 9
im 2 3 4 1 6 7 8 9 5
cycl (1,2,3,4)(5,6,7,8,9)
gap> im:=[2,3,4,1,6,7,8,9,5];
[ 2, 3, 4, 1, 6, 7, 8, 9, 5 ]
gap> e:=PermList(im);
(1,2,3,4)(5,6,7,8,9)
- Bild, Produkt, Konjugation
gap> SignPerm(e);
-1
gap> 4^e;
1
gap> f:=e*e;
(1,3)(2,4)(5,7,9,6,8)
gap> i:=1;
1
gap> repeat f:=e^i; Print("e^",i," = ",f,"\n");
i:=i+1; until f = ();
e^1 = (1,2,3,4)(5,6,7,8,9)
e^2 = (1,3)(2,4)(5,7,9,6,8)
e^3 = (1,4,3,2)(5,8,6,9,7)
e^4 = (5,9,8,7,6)
e^5 = (1,2,3,4)
e^6 = (1,3)(2,4)(5,6,7,8,9)
e^7 = (1,4,3,2)(5,7,9,6,8)
e^8 = (5,8,6,9,7)
e^9 = (1,2,3,4)(5,9,8,7,6)
e^10 = (1,3)(2,4)
e^11 = (1,4,3,2)(5,6,7,8,9)
e^12 = (5,7,9,6,8)
e^13 = (1,2,3,4)(5,8,6,9,7)
e^14 = (1,3)(2,4)(5,9,8,7,6)
e^15 = (1,4,3,2)
e^16 = (5,6,7,8,9)
e^17 = (1,2,3,4)(5,7,9,6,8)
e^18 = (1,3)(2,4)(5,8,6,9,7)
e^19 = (1,4,3,2)(5,9,8,7,6)
e^20 = ()
gap> while f <> () do f:=e^i; Print("e^",i," = ",f,"\n");
i:=i+1; od;
gap> for i in [1..20] do Print("e^",i," = ",e^i,"\n"); od;
gap> repeat Print("e^",i," = ",e^i,"\n");
i:=i+1; until e^i = ();
gap> Ordnung:=function(g)
> local i, f;
> f:=g; i:=1;
> while f <> () do i:=i+1; f:=f*g; od;
> return i;
> end;
function ( g ) ... end
gap> Ordnung(e);
20
gap> e^-1;
(1,4,3,2)(5,9,8,7,6)
gap> e^-1*f*e;
(1,3)(2,4)(5,7,9,6,8)
gap> f^e;
(1,3)(2,4)(5,7,9,6,8)
3 Bedeutungen von ^: n^g, g^n, g^f
- Hilfe
gap> ?Read
Read ________________________________________________________ Environment
'Read( )'
'Read' reads the input from the file with the filename , which
must be a string.
'Read' first opens the file . If the file does not exist, or
if GAP can not open it, e.g., because of access restrictions, an error
is signalled.
...
gap> ?PrintTo
PrintTo _____________________________________________________ Environment
'PrintTo( , , ... )'
'PrintTo' works like 'Print', except that the output is printed to the
file with the name instead of the standard output. This file
must of course be writable by GAP, otherwise an error is signalled.
Note that 'PrintTo' will overwrite the previous contents of this file if
it already existed. 'AppendTo' can be used to append to a file (see
"AppendTo").
...
- Read, Print, PrintTo, AppendTo
repeat AppendTo("xxx", "e.",i," := ",e^i,";\n");
i:=i+1; until e^i = ();
gap> f:=rec();
rec(
)
gap> Read("xxx");
gap> f;
rec(
1 := (1,2,3,4)(5,6,7,8,9),
2 := (1,3)(2,4)(5,7,9,6,8),
3 := (1,4,3,2)(5,8,6,9,7),
4 := (5,9,8,7,6),
5 := (1,2,3,4),
6 := (1,3)(2,4)(5,6,7,8,9),
7 := (1,4,3,2)(5,7,9,6,8),
8 := (5,8,6,9,7),
9 := (1,2,3,4)(5,9,8,7,6),
10 := (1,3)(2,4),
11 := (1,4,3,2)(5,6,7,8,9),
12 := (5,7,9,6,8),
13 := (1,2,3,4)(5,8,6,9,7),
14 := (1,3)(2,4)(5,9,8,7,6),
15 := (1,4,3,2),
16 := (5,6,7,8,9),
17 := (1,2,3,4)(5,7,9,6,8),
18 := (1,3)(2,4)(5,8,6,9,7),
19 := (1,4,3,2)(5,9,8,7,6),
20 := () )
gap> f.3;
(1,4,3,2)(5,8,6,9,7)
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