File: bar.doc

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COMMENT:
	BARRED PERMUTATION
	------------------

	These are elements of group S_2 wreath S_n, the elements are
	objects of the type PERMUTATION, but where the kind of the
	permutation is BAR or BARCYCLE. 
	The permutation is of length n, and the
	entries are between 1 and n , but may be positiv or negativ.


NAME:	
	class_bar
SYNOPSIS:
	INT class_bar(OP a,b)
DESCRIPTION:
	computes the label of the conjugacy class of the
	element a.

NAME:	
	class_rep_bar
SYNOPSIS:
	INT class_rep_bar(OP a,b)
DESCRIPTION:
	you enter the label of a class, and the routine computes
	a element 'b' of that class

NAME:
		first_bar
SYNOPSIS:
	INT first_bar(OP a,b)
DESCRIPTION:
	computes the first barred permutation = [1,2,3..]
	of degree a. a must be a INTEGER object.

NAME:
		lehmercode_bar
SYNOPSIS:
	INT lehmercode_bar(OP a,b)
DESCRIPTION:
    computes the lehmercode of a barred permutation a.
	The result is a two-element VECTOR object, whose two entries
	are INTEGER - VECTOR objects, whose length are the length of the
	PERMUTATION object a.
	The first VECTOR is a 0-1 vector, the i-th entry is one if the
	element i+1 is negativ in the PERMUTATION object a.
	The second VECTOR is the ordinary Lehmercode of a permutation, 
	but taken into account that we have negative entries.
EXAMPLE:
	given the barred permutation
	3 -5  2 -1 4
		the result of lehmercode_bar is
	[[1,0,0,0,1][3,0,1,0,0]]

NAME:
		lehmercode_vector_bar
SYNOPSIS:
	INT lehmercode_vector_bar(OP a,b)
DESCRIPTION:
	is the inverse routine to the above routine
	lehmercode_bar

NAME:	
	length_bar
SYNOPSIS:
	INT length_bar(OP a,b)
DESCRIPTION:
	computes the reduced length of the barred permutation a.

NAME:
		makevectorof_class_bar
SYNOPSIS:
	INT makevectorof_class_bar(OP a,b)
DESCRIPTION:
	computes a vector with all labelings of the classes of
	the group S_2 wreath S_a

NAME:
		makevectorof_class_rep_bar
SYNOPSIS:
	INT makevectorof_class_rep_bar(OP a,b)
DESCRIPTION:
	computes a vector with reps  of all the classes of
	the group S_2 wreath S_a, the ordering of classes is as in the
	function makevectorof_class_bar.

NAME:	
	mult_bar_bar
SYNOPSIS:
	INT mult_bar_bar(OP a,b,c)
DESCRIPTION:
	multiplies first b than a , the result becomes c. 
	Better to use the general routine mult(OP,OP,OP)

NAME:	
		next_bar
SYNOPSIS:
		INT next_bar(OP a,b)
DESCRIPTION:
	:	computes the next barred permutation b. The algorithm
	uses the lehmercode. The last barred permutation will be
	[-1,-2,-3,...]

NAME:
			ordcen_bar
SYNOPSIS:
		INT ordcen_bar(OP a,b)
DESCRIPTION:
		computes the order of the centralicer of the class 
	labeled by 'a'.

NAME:
			ordcon_bar
SYNOPSIS:
		INT ordcon_bar(OP a,b)
DESCRIPTION:
		computes the order of the  class labeled by 'a'.

NAME:
			random_bar
SYNOPSIS:
		INT random_bar(OP a,b)
DESCRIPTION:
		computes a random element of given length, so b becomes
	an elements of S_2 wreath S_a, a is an INTEGER object.

NAME:
			scan_bar
SYNOPSIS:
		INT scan_bar(OP a)
DESCRIPTION:
		reads a barred permutation from input, and checks
	wether the input was correct. You may better use the routine
	scan(BARPERM,a).

NAME:
			t_BAR_BARCYCLE
SYNOPSIS:
		INT t_BAR_BARCYCLE(OP a,b)
DESCRIPTION:
		transforms a barred permutation 'a' in list-notation into
	cycle notation
BUG:
			a and b must be different

NAME:
			t_BARCYCLE_BAR
SYNOPSIS:
		INT t_BARCYCLE_BAR(OP a,b)
DESCRIPTION:
		transforms a barred permutation 'a' in cycle-notation into
	list notation
BUG:
			a and b must be different