| | | Special routines for wreath products |
INT init_kranz(a) OP a;initializes a KRANZ object
a.
Given a PERMUTATION of n elements and a VECTOR of length n you can compute the corresponding KRANZ object with
INT m_perm_vector_kranz(p,v,a) OP p,v,a;
p stands for the PERMUTATION, v for the VECTOR
and a for the KRANZ object.
INT scan_kranz(a) OP a;can be used to scan the KRANZ object
a.
INT mult_kranz_kranz(a,b,c) OP a,b,c;you can multiply two KRANZ objects
a and b
according to the definition given above
to get c.
There are various routines for selecting the different parts of a KRANZ object.
OP s_kr_g(a) OP a; OP s_kr_v(a) OP a; OP s_kr_i(a,i) OP a; INT i; INT s_kr_gli(a) OP a; OP s_kr_gl(a) OP a; OP s_kr_gi(a,i) OP a; INT i; S_KR_GI(a,i) OP a; INT i; INT s_kr_gii(a,i) OP a; INT i; S_KR_GII(a,i) OP a; INT i; OP s_kr_ij(a,i,j) OP a; INT i,j; S_KR_IJ(a,i,j) OP a; INT i,j; INT s_kr_iji(a,i,j) OP a; INT i,j; S_KR_IJI(a,i,j) OP a; INT i,j;In all these cases
a is a KRANZ object.
s_kr_g stands for select_kranz_grobpermutation, which
selects the first part (the PERMUTATION part) of a.
s_kr_v selects the VECTOR part (the second part) of a.
s_kr_i selects the i-th entry of the VECTOR part of
a. s_kr_gli returns the integervalue of the length
of the PERMUTATION part of a.
s_kr_gl is the length (as an INTEGER object) of the
PERMUTATION part of a.
s_kr_gi selects the i-th entry of the PERMUTATION
part of a.
s_kr_gii returns the integervalue of the
i-th entry of the PERMUTATION part of a.
In order to use the next two routines you must take care
that the entries of the VECTOR part of a are also
PERMUTATION objects.
s_kr_ij selects the j-th entry of the
i-th entry of the VECTOR part of a.
s_kr_iji returns the integervalue of the
j-th entry of the
i-th entry of the VECTOR part of a.
Given two permutation groups G and H by their sets of generators, we can compute the generators of H wr G with the following routine:
INT gen_full_mon_group(a,b,c) OP a,b,c;
a and b are the VECTORs of generators
of H and G. c is a VECTOR object, where
each entry is a KRANZ object. These entries are the
generators of H wr G.
The generators of the plethysm H pleth G can be computed with
INT gen_plethysm(a,b,c) OP a,b,c;where
a and b are the VECTORS of
generators of H and G. c is a VECTOR of
generators of H pleth G.
The permutation representation of a KRANZ object where the entries of the VECTOR part are PERMUTATIONs is computed by
INT t_kranz_plethysm(a,b) OP a,b;
a is a KRANZ object where all the entries of
the VECTOR part are PERMUTATIONs of the same degree.
b is a PERMUTATION object, the induced
permutation in form of the plethysm.
| | | Special routines for wreath products |