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COMMENT:
BARRED PERMUTATION
------------------
These are elements of group S_2 wreath S_n, the elements are
objects of the type PERMUTATION, but where the kind of the
permutation is BAR or BARCYCLE.
The permutation is of length n, and the
entries are between 1 and n , but may be positiv or negativ.
NAME:
class_bar
SYNOPSIS:
INT class_bar(OP a,b)
DESCRIPTION:
computes the label of the conjugacy class of the
element a.
NAME:
class_rep_bar
SYNOPSIS:
INT class_rep_bar(OP a,b)
DESCRIPTION:
you enter the label of a class, and the routine computes
a element 'b' of that class
NAME:
first_bar
SYNOPSIS:
INT first_bar(OP a,b)
DESCRIPTION:
computes the first barred permutation = [1,2,3..]
of degree a. a must be a INTEGER object.
NAME:
lehmercode_bar
SYNOPSIS:
INT lehmercode_bar(OP a,b)
DESCRIPTION:
computes the lehmercode of a barred permutation a.
The result is a two-element VECTOR object, whose two entries
are INTEGER - VECTOR objects, whose length are the length of the
PERMUTATION object a.
The first VECTOR is a 0-1 vector, the i-th entry is one if the
element i+1 is negativ in the PERMUTATION object a.
The second VECTOR is the ordinary Lehmercode of a permutation,
but taken into account that we have negative entries.
EXAMPLE:
given the barred permutation
3 -5 2 -1 4
the result of lehmercode_bar is
[[1,0,0,0,1][3,0,1,0,0]]
NAME:
lehmercode_vector_bar
SYNOPSIS:
INT lehmercode_vector_bar(OP a,b)
DESCRIPTION:
is the inverse routine to the above routine
lehmercode_bar
NAME:
length_bar
SYNOPSIS:
INT length_bar(OP a,b)
DESCRIPTION:
computes the reduced length of the barred permutation a.
NAME:
makevectorof_class_bar
SYNOPSIS:
INT makevectorof_class_bar(OP a,b)
DESCRIPTION:
computes a vector with all labelings of the classes of
the group S_2 wreath S_a
NAME:
makevectorof_class_rep_bar
SYNOPSIS:
INT makevectorof_class_rep_bar(OP a,b)
DESCRIPTION:
computes a vector with reps of all the classes of
the group S_2 wreath S_a, the ordering of classes is as in the
function makevectorof_class_bar.
NAME:
mult_bar_bar
SYNOPSIS:
INT mult_bar_bar(OP a,b,c)
DESCRIPTION:
multiplies first b than a , the result becomes c.
Better to use the general routine mult(OP,OP,OP)
NAME:
next_bar
SYNOPSIS:
INT next_bar(OP a,b)
DESCRIPTION
: computes the next barred permutation b. The algorithm
uses the lehmercode. The last barred permutation will be
[-1,-2,-3,...]
NAME:
ordcen_bar
SYNOPSIS:
INT ordcen_bar(OP a,b)
DESCRIPTION:
computes the order of the centralicer of the class
labeled by 'a'.
NAME:
ordcon_bar
SYNOPSIS:
INT ordcon_bar(OP a,b)
DESCRIPTION:
computes the order of the class labeled by 'a'.
NAME:
random_bar
SYNOPSIS:
INT random_bar(OP a,b)
DESCRIPTION:
computes a random element of given length, so b becomes
an elements of S_2 wreath S_a, a is an INTEGER object.
NAME:
scan_bar
SYNOPSIS:
INT scan_bar(OP a)
DESCRIPTION:
reads a barred permutation from input, and checks
wether the input was correct. You may better use the routine
scan(BARPERM,a).
NAME:
t_BAR_BARCYCLE
SYNOPSIS:
INT t_BAR_BARCYCLE(OP a,b);
DESCRIPTION:
transforms a barred permutation 'a' in list-notation into
cycle notation
BUG:
a and b must be different
NAME:
t_BARCYCLE_BAR
SYNOPSIS:
INT t_BARCYCLE_BAR(OP a,b);
DESCRIPTION:
transforms a barred permutation 'a' in cycle-notation into
list notation
BUG:
a and b must be different
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