## File: misc.doc

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symmetrica 2.0+ds-6
 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596` ``````COMMENT: MISCellaneous-Functions ----------------------- NAME: complete_complete_plet SYNOPSIS: INT complete_complete_plet(OP a, OP b, OP c) DESCRIPTION: Computes the plethysm of two complete symmetric functions labeled by INTEGER objects. The first parameter is the outer one, so we compute h_a(h_b). The result is a SCHUR object. EXAMPLE: #include "def.h" #include "macro.h" ANFANG scan(INTEGER,a); scan(INTEGER,b); complete_complete_plet(a,b,c); println(c); ENDE NAME: complete_schur_plet SYNOPSIS: INT complete_schur_plet(OP a, OP b, OP c) DESCRIPTION: Computes the plethysm of a complete symmetric function labeled by the INTEGER object a and the Schurfunction labeled by the INTEGER or PARTITION object b. The result will be a SCHUR function c. The complete function is the outer one, so we compute h_a(s_b) EXAMPLE #include "def.h" #include "macro.h" ANFANG scan(INTEGER,a); scan(PARTITION,b); complete_schur_plet(a,b,c); println(c); ENDE NAME: elementary_schur_plet SYNOPSIS: INT elementary_schur_plet(OP a, OP b, OP c) DESCRIPTION: Computes the plethysm of a elementary symmetric function labeled by the INTEGER object a and the Schurfunction labeled by the INTEGER or PARTITION object b. The result will be a SCHUR function c. The elementary function is the outer one, so we compute e_a(s_b). EXAMPLE: #include "def.h" #include "macro.h" ANFANG scan(INTEGER,a); scan(PARTITION,b); elementary_schur_plet(a,b,c); println(c); ENDE NAME: power_schur_plet SYNOPSIS: INT power_schur_plet(OP a, OP b, OP c) DESCRIPTION: Computes the plethysm of a power symmetric function labeled by the INTEGER object a and the Schurfunction labeled by the INTEGER or PARTITION object b. The result will be a SCHUR function c. The complete function is the outer one, so we compute p_a(s_b). EXAMPLE: #include "def.h" #include "macro.h" ANFANG scan(INTEGER,a); scan(PARTITION,b); power_schur_plet(a,b,c); println(c); ENDE NAME: schur_schur_plet SYNOPSIS: INT schur_schur_plet(OP a, OP b, OP c) DESCRIPTION: Computes the plethysm of two Schurfunctions labeled by a PARTITION object or by an INTEGER object. The first parameter is the outer one, so we compute s_a(s_b). The result is a SCHUR object. EXAMPLE: #include "def.h" #include "macro.h" ANFANG scan(PARTITION,a); scan(PARTITION,b); schur_schur_plet(a,b,c); println(c); ENDE ``````