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COMMENT:
ZYK
___
We are describing the routines of the file zyk.c. These are routines
for the computation of cycle index polynomials, and for the computation
with general permutation groups.
NAME:
zykelind_Sn
SYNOPSIS:
INT zykelind_Sn(OP n,pol)
DESCRIPTION:
computes the cycleindex polynomial of the symmetric
group of the degree n. n is a INTEGER object, pol becomes a
POLYNOM object.
BUG:
n and pol must be different
NAME:
zykelind_Dn
SYNOPSIS:
INT zykelind_Dn(OP n,pol)
DESCRIPTION:
computes the cycleindex polynomial of the dihedral
group of the degree n. n is a INTEGER object, pol becomes a
POLYNOM object.
BUG:
n and pol must be different
NAME:
zykelind_Cn
SYNOPSIS:
INT zykelind_Cn(OP n,pol)
DESCRIPTION:
computes the cycleindex polynomial of the cyclic
group of the degree n. n is a INTEGER object, pol becomes a
POLYNOM object.
BUG:
n and pol must be different
NAME:
zykelind_An
SYNOPSIS:
INT zykelind_An(OP n,pol)
DESCRIPTION:
computes the cycleindex polynomial of the alternating
group of the degree n. n is a INTEGER object, pol becomes a
POLYNOM object.
BUG:
n and pol must be different
NAME:
zykelind_arb
SYNOPSIS:
INT zykelind_arb(OP vec,pol)
DESCRIPTION:
computes the cycle index polynomial of a arbitrary permutation
group . vec is a VECTOR object, whose entries are PERMUTATION
objects whose degrees are equal. These permutations are the generators
of the group. pol becomes a POLYNOM object.
BUG:
vec and pol must be different
NAME:
dimino
SYNOPSIS:
INT dimino(OP vec)
DESCRIPTION:
computes the elements of a arbitrary permutation group.
vec is a VECTOR object, whose elements are PERMUTATION objects,
which generates the group. At the end of dimino, this vector
contains all elements of the group.
BUG:
the permutations in the vector must be of the same
degree, and they must be of VECTOR type.
NAME:
polya_n_sub
SYNOPSIS:
INT polya_n_sub(OP p,n,e)
DESCRIPTION:
you enter a POLYNOM object p, and a INTEGER object n, and
the output is the POLYNOM object which you get using the substitution
x_i --> a_1^i + ... + a_n^i
NAME:
grf_Sn
SYNOPSIS:
INT grf_Sn(OP degree, OP n, OP result)
DESCRIPTION:
you enter the degree of the symmetric group, and the number of
variables for the polya substitution. The routine computes the group reduction
function. The first step is the computation of cycle index and the second step is
the polya substitution with n variables.
EXAMPLE:
#include "def.h"
#include "macro.h"
ANFANG
sscan("9",INTEGER,a); sscan("4",INTEGER,b);
grf_Sn(a,b,c); println(c);
ENDE
NAME:
grf_Cn
SYNOPSIS:
INT grf_Cn(OP degree, OP n, OP result)
DESCRIPTION:
you enter the degree of the cyclic group, and the number of
variables for the polya substitution. The routine computes the group reduction
function. The first step is the computation of cycle index and the second step is
the polya substitution with n variables.
EXAMPLE:
#include "def.h"
#include "macro.h"
ANFANG
sscan("9",INTEGER,a); sscan("4",INTEGER,b);
grf_Cn(a,b,c); println(c);
ENDE
NAME:
grf_An
SYNOPSIS:
INT grf_An(OP degree, OP n, OP result)
DESCRIPTION:
you enter the degree of the alternating group, and the number of
variables for the polya substitution. The routine computes the group reduction
function. The first step is the computation of cycle index and the second step is
the polya substitution with n variables.
EXAMPLE:
#include "def.h"
#include "macro.h"
ANFANG
sscan("9",INTEGER,a); sscan("4",INTEGER,b);
grf_An(a,b,c); println(c);
ENDE
NAME:
grf_Dn
SYNOPSIS:
INT grf_Dn(OP degree, OP n, OP result)
DESCRIPTION:
you enter the degree of the dihedral group, and the number of
variables for the polya substitution. The routine computes the group reduction
function. The first step is the computation of cycle index and the second step is
the polya substitution with n variables.
EXAMPLE:
#include "def.h"
#include "macro.h"
ANFANG
sscan("9",INTEGER,a); sscan("4",INTEGER,b);
grf_Dn(a,b,c); println(c);
ENDE
NAME:
grf_arb
SYNOPSIS:
INT grf_arb(OP generators, OP n, OP result)
DESCRIPTION:
you enter the generators (VECTOR of PERMUTATION objects)
of a permutaion group, and the number of
variables for the polya substitution. The routine computes the group reduction
function. The first step is the computation of cycle index and the second step is
the polya substitution with n variables.
EXAMPLE:
#include "def.h"
#include "macro.h"
ANFANG
sscan("[[6,5,4,3,2,1,8,7],[2,1,8,7,6,5,4,3],[5,6,7,8,1,2,3,4]]",
PERMUTATIONVECTOR,a); sscan("4",INTEGER,b);
grf_arb(a,b,c); println(c);
ENDE
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