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- NAMES:
*b_skn_s, m_skn_s* - SYNOPSES:
*INT b_skn_s(OP self,koeff,next,result)**INT m_skn_s(OP self,koeff,next,result)* - DESCRIPTION: first the result is freed to an empty object,
if it is not yet an empty object. Then the SCHUR
object is build out of the components, given as arguments.
in
*m_skn_s*the components are copied, so you may use them in the further program, in*b_skn_s*they become part of*result,*so using them may destroy the SCHUR object. - RETURN: OK or ERROR

- NAMES:
*b_pa_s, m_pa_s* - SYNOPSES:
*INT b_pa_s(OP part,result)**INT m_pa_s(OP part,result)* - DESCRIPTION: you call
*b_skn_s*(or*m_skn_s*) with*self==part**koeff*is one and*next==NULL.* - RETURN: OK or ERROR

- NAMES:
*b_v_s, m_v_s* - SYNOPSES:
*INT b_v_s(OP vec, result)**INT m_v_s(OP vec, result)* - DESCRIPTION: the difference is again in copying or not copying
the
*vec,*which must be a VECTOR of INTEGER. The INTEGERs are not allowed to be negative. Look at*m_v_pa().* - RETURN: OK or ERROR

- NAME:
*schnitt_schur* - SYNOPSIS:
*INT schnitt_schur(OP a,b,c)* - DESCRIPTION: you enter two SCHURobjects, and the result is the common part.

- NAME:
*outerproduct_schur* - SYNOPSIS:
*INT outerproduct_schur(OP parta,partb,result)* - DESCRIPTION: you enter two PARTITIONobjects, and the result is
a SCHURobject, which is the expansion of the product
of the two schurfunctions, labeled by
the two PARTITIONobjects
*parta*and*partb.*

- NAME:
*newtrans* - SYNOPSIS:
*INT newtrans(OP perm, schur)* - DESCRIPTION: computes the decomposition of a
schubertpolynomial labeled by
the permutation
*perm,*as a sum of Schur polynomials.

- NAME:
*compute_schur_with_alphabet* - SYNOPSIS:
*INT compute_schur_with_alphabet(OP part,laenge,erg)* - DESCRIPTION: computes the expansion of a schurfunction labeled by a
partition PART as a POLYNOM
*erg.*The INTEGER*laenge*specifies the length of the alphabet.

Expansion of a complete symmetric function:Example:... scan(PARTITION,a); scan(INTEGER,b); compute_schur_with_alphabet(a,b,c);println(c); ...

- NAME:
*compute_complete_with_alphabet* - SYNOPSIS:
*INT compute_complete_with_alphabet(OP num,length,res)* - DESCRIPTION: computes the expansion of a complete symmetric
function labeled by an INTEGER
*num*as a POLYNOM*res.*The INTEGER*length*specifies the length of the alphabet.

- NAME:
*compute_monomial_with_alphabet* - SYNOPSIS:
*INT compute_monomial_with_alphabet(OP num,length,res)* - DESCRIPTION: computes the expansion of a monomial symmetric
function labeled by a PARTITION
*num*as a POLYNOM*res.*The INTEGER*length*specifies the length of the alphabet.

Expansion of power sum symmetric functions:Example:... scan(PARTITION,a); scan(INTEGER,b); compute_monomial_with_alphabet(a,b,c); println(c); ...

- NAME:
*compute_power_with_alphabet* - SYNOPSIS:
*INT compute_power_with_alphabet(OP label,laenge,erg)* - DESCRIPTION: computes the expansion of a power symmetric
function labeled by a INTEGER
*label*or by a PARTITION*label*as a POLYNOM*erg.*The INTEGER*laenge*specifies the length of the alphabet.

- NAME:
*compute_schur_with_alphabet_det* - SYNOPSIS:
*INT compute_schur_with_alphabet_det(OP part,length,erg)* - DESCRIPTION: computes the expansion of a schurfunction labeled by the
PARTITION
*part,*using the Jacobi Trudi Identity, the result is the POLYNOM*erg,*the length of the alphabet is given by the INTEGER*length.*

- NAME:
*compute_skewschur_with_alphabet_det* - SYNOPSIS:
*INT compute_skewschur_with_alphabet _det(OP sp,l,res)* - DESCRIPTION: computes the expansion of a skewschurfunction labeled by the
SKEWPARTITION
*sp,*using the Jacobi Trudi Identity, the result is the POLYNOM*res,*the length of the alphabet is given by the INTEGER*l.*

The evaluation of the Hall-Littlewood polynomials:Example:... scan(SKEWPARTITION,a); scan(INTEGER,b); compute_skewschur_with_alphabet_det(a,b,d);println(d); ...

- NAME:
*hall_littlewood* - SYNOPSIS:
*INT hall_littlewood(OP part, OP res)* - DESCRIPTION: computes the-so called Hall-Littlewood polynomials, i.e. a SCHURobject, whose coefficient are polynomials in one variable. The method, which is used for the computation is described in the paper: A.O. Morris The Characters of the group GL(n,q) Math Zeitschr 81, 112-123 (1963)

harald.fripertinger@kfunigraz.ac.at,

last changed: November 19, 2001

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