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symmetrica 2.0+ds-6
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COMMENT:
	GROUP ALGEBRA
	-------------

	This is a variant of the POLYNOM type, the name of this class
	of objects is GRAL (for group algebra). The type of the self part
	is a permutation instead of a vector as in the case of POLYNOM.
	So a general object of type GRAL is a list of permutations with
	arbitrary coefficients.
	For the selection of parts you have to use the macros for polynom
	objects (up to now)
	There are two routines for the construction

NAME:		
		m_skn_gral
SYNOPSIS:
	INT m_skn_gral(OP self, OP koeff, OP next, OP res)
DESCRIPTION: 	
	same as  m_skn_po in the file poly.doc

NAME:		
		b_skn_gral
SYNOPSIS:
	INT b_skn_gral(OP self, OP koeff, OP next, OP res)
DESCRIPTION: 	
	same as  b_skn_po in the file poly.doc


NAME:		
	hplus_hecke
SYNOPSIS:	
	INT hplus_hecke(OP a,b)
DESCRIPTION:
	none

NAME:		
	hplus
SYNOPSIS:	
	INT hplus(OP a,b)
DESCRIPTION:	
	computes the sum over all horizonatl permutation of a 
	TABLEAUX object a. cf. Mueller: Darstellungstheorie
	The result is a GRAL object.
BUG:		
	only for TABLEAUX of PARTITION shape

NAME:		
	vminus_hecke
SYNOPSIS:	
	INT vminus_hecke(OP a,b)
DESCRIPTION:
	none

NAME:		
	vminus_tabloid
SYNOPSIS:	
	INT vminus_tabloid(OP a,b)
DESCRIPTION:
	none

NAME:		
	vminus
SYNOPSIS:	
	INT vminus(OP a,b)
DESCRIPTION:	
	computes the signed sum over all vertical permutations of a 
	TABLEAUX object a. cf. Mueller: Darstellungstheorie
	The result is a GRAL object.
BUG:		
	only for TABLEAUX of PARTITION shape

NAME:		
	random_gral
SYNOPSIS:	
	INT random_gral(OP a,b)
DESCRIPTION:	
	computes a random element of the group algebra. The degree
	of the involved permutations is given by the INTEGER object a. The
	coefficients are INTEGER object given by random_integer, so they lay
	between -10 and 10. There are maximal ten terms.

NAME:		
	operate_gral_polynom
SYNOPSIS:	
	INT operate_gral_polynom(OP a,b,c)
DESCRIPTION:	
	applies the element of the group algebra a to a 
	POLYNOM b, and the result is a new POLYNOM c

NAME:		
	vertikal_sum
SYNOPSIS:	
	INT vertikal_sum(OP a,b)
DESCRIPTION:	
	computes the sum over all permutations of degree a, 
	the result is the object b, a element of type GROUPALGEBRA

NAME:		
	garnir
SYNOPSIS:	
	INT garnir(OP tab,v,x,res)
DESCRIPTION:	
	cf. James/Kerber p.301, tab is a TABLEAUX object
	v and x a VECTOR objects of INTEGERS containing entries of
	different coulmns, the result is a GROUPALGEBRA object.

COMMENT:
	GENERAL ROUTINES
	----------------

	add
	add_apply
	addinvers
	comp
	copy
	fprint
	fprintln
	freeall
	freeself
	mult
	objectread
	objectwrite
	print
	println
	scan
	tex