#
#	Permutation class
#
#				Gaston H. Gonnet (Sep 26, 2005)
#
Permutation := proc( p:{list(posint),posint} )
if nargs <> 1 then error('invalid number of arguments')
elif type(p,posint) then noeval( procname( [seq(i,i=1..p)] ))
elif {op(p)} <> {seq(i,i=1..length(p))} then
    error('permutation is not over consecutive integers')
else noeval( procname(args) ) fi
end:

Permutation_times := proc( a, b )
if type(a,Permutation) and type(b,Permutation) then
     a1 := a[1];
     b1 := b[1];
     n := length(a1);
     if length(b1) <> n then error(args,
	'product of Permutations must be of the same length') fi;
     noeval( Permutation( [ seq( b1[a1[i]], i=1..n ) ] ))
else error( args,
    'Permutations can only be mutiplied (composed) by Permutations') fi
end:

Permutation_power := proc( a, b )
if type(a,Permutation) and type(b,integer) then
     n := length(a[1]);
     if b < 0 then
	  a1 := procname(a,-b)[1];
	  r := CreateArray(1..n);
	  for i to n do r[a1[i]] := i od;
	  noeval( Permutation(r) )
     elif b=0 then Permutation(n)
     elif b=1 then a
     elif mod(b,2)=0 then r := procname(a,b/2);  r*r
     else a * procname(a,b-1)
     fi
else error( args,
    'Permutations can only be powered to integer powers') fi
end:

Permutation_Rand := proc( p )
noeval( Permutation( Shuffle(op(p)) ))
end:

CompleteClass( Permutation );