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symmetrica 2.0+ds-6
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NAME:		
	specht_poly
SYNOPSIS:	
	INT specht_poly(OP a,b)
DESCRIPTION:	
	you enter  a TABLEAUX object a, and the output is
	the corresponding Specht polynomial b, a object of the type
	POLYNOM. The mathematical background is described in
	Specht: Math. Zeitschr. ??
	You may enter also a skewtableaux.
EXAMPLE:
	#include "def.h"
	#include "macro.h"
	BEGIN
	scan(TABLEAUX,a);
	specht_poly(a,b);
	println(b);
	END

NAME:		
	specht_dg
SYNOPSIS:	
	INT specht_dg(OP a,b,c)
DESCRIPTION:	
	you enter a PARTITION or SKEWPARTITION object a, and a
	PERMUTATION object  b, and the output is the corresponding
	representation of the symmetric group. This representation is
	integral and in the case of a PARTITION object a, it is  irreducible.
EXAMPLE:
	#include "def.h"
	#include "macro.h"

	BEGIN
	scan(scanobjectkind(),a);
	scan(PERMUTATION,b);
	specht_dg(a,b,c);
	println(c);
	END

NAME:       
	an_odg
SYNOPSIS:    
	INT an_odg(OP part,perm,D)
DESCRIPTION: 
	computes the unitary matrix D representing a PERMUTATION perm
   in the irreducible resresentation [part] of a partition part restricted
   to An (part has to be a VECTOR of length 2, the compnents of which are
   a partition and an integer 0L or 1L). 0L means, that [part]+ is
   concerned in case of a selfconjugate partition, and 1L indicates
   [part]-.

NAME:       
	an_rz_perm
SYNOPSIS:    
	INT an_rz_perm(OP per,res)
DESCRIPTION: 
	computes the decomposition of the PERMUTATION per into the
   generating elements (1,2)(2,3), .... ,(1,2)(n-1,n) of An. The result is a VECTOR
   of INTEGER, which is to read from right to left.

NAME:       
	an_sdg
SYNOPSIS:    
	INT an_sdg(OP part,perm,D)
DESCRIPTION: 
	computes the seminormal matrix D representing a PERMUTATION perm
   in the irreducible resresentation [part] of a partition part restricted
   to An (part has to be a VECTOR of length 2, the compnents of which are
   a partition and an integer 0L or 1L). 0L means, that [part]+ is
   concerned in case of a selfconjugate partition, and 1L indicates
   [part]-.

NAME:       
	an_trafo_odg
SYNOPSIS:    
	INT an_trafo_odg(OP part,perm,D)
DESCRIPTION: 
	computes the unitary matrix D representing a PERMUTATION perm
   in the irreducible resresentation [part] of a partition part restricted
   to An (part has to be a VECTOR of length 2, the components of which are
   a partition and an integer 0L or 1L). 0L means, that [part]+ is
   concerned in case of a selfconjugate partition, and 1L indicates
   [part]-. The result arises from the transformation of the according
   matrix of [part] over Sn.

NAME:       
	an_trafo_sdg
SYNOPSIS:    
	INT an_trafo_sdg(OP part,perm,D)
DESCRIPTION: 
	computes the seminormal matrix D representing a PERMUTATION perm
   in the irreducible resresentation [part] of a partition part restricted
   to An (part has to be a VECTOR of length 2, the components of which are
   a partition and an integer 0L or 1L). 0L means, that [part]+ is
   concerned in case of a selfconjugate partition, and 1L indicates
   [part]-. The result arises from the transformation of the according
   matrix of [part] over Sn.

NAME:
       alt_sdg_trafo
SYNOPSIS:
    INT alt_sdg_trafo(OP part,D)
DESCRIPTION:
 transforms the seminormal MATRIX D, belonging to the irreducible
   representation [part] of a selfconjugate PARTITION part of Sn into a
   matrix containing only two blocks in the main diagonal, the blocks of
   the seminormal matrices belonging to [part]+ and [part]-.

NAME:
       alt_odg_trafo
SYNOPSIS:
    INT alt_odg_trafo(OP part,D)
DESCRIPTION:
 transforms the orthogonal MATRIX D, belonging to the irreducible
   representation [part] of a selfconjugate PARTITION part of Sn into a
   matrix containing only two blocks in the main diagonal, the blocks of
   the orthogonal matrices belonging to [part]+ and [part]-.

NAME:
       gen_mat
SYNOPSIS:
    INT gen_mat(OP part;INT index,ref;OP res)
DESCRIPTION:
 computes the unitary matrix representing the permutation 
   (12)(index+1,index+2) within the irreducible representation [part]+
   oder [part]- of the selfconjugated PARTITION part, where the number ref
   handles, which part of the representing martix, transformed by
   alt_odg_trafo(), has to be given back as result. ref=0L indicates the
   first block, and ref=1L the second.

NAME:
       gen_smat
SYNOPSIS:
    INT gen_smat(OP part;INT index,ref;OP res)
DESCRIPTION:
 computes the seminormal matrix representing the permutation 
   (12)(index+1,index+2) within the irreducible representation [part]+
   oder [part]- of the selfconjugated PARTITION part, where the number ref
   handles, which part of the representing martix, transformed by
   alt_odg_trafo(), has to be given back as result. ref=0L indicates the
   first block, and ref=1L the second.

NAME:
       get_ax_dist
SYNOPSIS:
    INT get_ax_dist(OP tab;INT r,s;OP res)
DESCRIPTION:
 computes the axial distance between the INTEGERs r and s in a 
   standard-young-TABLEAU tab.

NAME:
       get_position
SYNOPSIS:
    INT get_position(OP tab;INT r;OP res)
DESCRIPTION:
 computes the position of the INTEGER r in a TABLEAU tab. The first
      appearence of r is taken. The result is a VECTOR of length 2 of
      INTEGER.

NAME:
       make_all_st_tabs
SYNOPSIS:
    INT make_all_st_tabs(OP par,res)
DESCRIPTION:
 computes all standard-young-tableaux belonging to a PARTITION 
      par ordered in last letter sequence. The result is a VECTOR.
BUG:
       The matrices in which the tableaux are stated can be bigger than
          necessary!

NAME:
       make_tab_signs
SYNOPSIS:
    INT make_tab_signs(OP par,res)
DESCRIPTION:
 computes a vector of integers, that contain the signs of the 
      permutations transforming the first standard-young-tableau of a
      PARTITION par into the ith, where the tableaux are ordered according
      the last letter sequence.

NAME:
       mat_comp
SYNOPSIS:
    INT mat_comp(OP a,b)
DESCRIPTION:
 compares two MATRICES a and b allowing the entries to be of type
      SQ_RADICAL.
RETURN:
       0L in case a equal b, else 1L.

NAME:
       op_transpo_tab
SYNOPSIS:
    INT op_transpo_tab(INT transpo;OP tab,res)
DESCRIPTION:
 computes the TABLEAU (transpo,transpo+1)*tab, where tab is a 
      TABLEAU, too.

NAME:
       tab_funk
SYNOPSIS:
    INT tab_funk(OP n,part,tab,res)
DESCRIPTION:
 computes the value of the tableau function of a TABLEAU tab
      belonging to a PARTITION part of a INTEGER n. tab has to be a
      standard-young-tableau.

NAME:
       tab_index
SYNOPSIS:
    INT tab_index(OP tab,vector)
DESCRIPTION:
 computes the index of a TABLEAU tab in a VECTOR of tableaux
      vector.
RETURN:
       index, in case that tab is in vector, else -1.

NAME:
       trafo_check
SYNOPSIS:
    INT trafo_check(OP part)
DESCRIPTION:
 checks in case of a selfconjugate PARTITION part, where the 
      representing matrices of the representation [part]+ and [part]-
      will occur, if the representing martix of [part] is reduced with the
      transforming matrices given by B.M. Puttaswamaiah (1963), as
      implemented in alt_odg_trafo.
RETURN:
     0L in case that [part]+ is in the first block, else 1L.