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# This is a module for the GAP package MAPCLASS
# computing the orbit of the mapping class group.
# This module contains various utility functions.
#
# A. James, K. Magaard, S. Shpectorov 2011
#
# NumberOfCommutatorProducts
# function for computing the number of ways to write a given
# group element as a product of n commutators.
# Reference: R. Guralnick's thesis
# t=table, c= index of some conjugacy class wrt t, n= number of commutators
InstallGlobalFunction(NumberOfCommutatorProducts,function(t,c,n)
return SizesCentralizers(t)[1]^(2*n-1)*
Sum(List(Irr(t),x->x[c]/(x[1]^(2*n-1))));
end);
#
# PrintlnIf
# function takes a string as its first argument which is printed
# if a sequence of bools are all true
#
#InstallGlobalFunction(PrintlnIF, function(arg)
# local pstring, args, istrue;
# pstring:=arg[1];
# args:=arg{[2..Length(arg)]};
# istrue:=true;
# for i in [1..Length(args)] do
# istrue:= istrue and arg[1];
# if not istrue then
# break;
# fi;
# od;
# Print(pstring, "\n");
#end);
#
# TotalNumberOfTuples
# function computing the structure constant
# t = character table
# g = genus
# cc = the principal tuple in terms of it character table cc
#
InstallGlobalFunction(TotalNumberOfTuples,function(t,g,cc)
local i,s;
if Length(cc)=0 then
return NumberOfCommutatorProducts(t,1,g);
fi;
s:=0;
for i in [1..Length(SizesCentralizers(t))] do
s:=s+NumberOfCommutatorProducts(t,i,g)*
ClassStructureCharTable(t,Concatenation([InverseClasses(t)[i]],cc));
od;
return s;
end);
#
# TotalNumberTuples
# Computes the structure constant using group data
InstallGlobalFunction(TotalNumberTuples, function(group, tuple, genus)
local tups, tbl, cc;
tbl:=CharacterTable(group);
cc:=ConjugacyClasses(tbl);
tups:=List(tuple, i -> Filtered([1..Length(cc)], x -> i in cc[x])[1]);
return TotalNumberOfTuples(tbl, genus, tups);
end);
#
# MaybePrint
# Wraps print by takes three lists as arguments and passing them to print based
# on output.
InstallGlobalFunction(MaybePrint, function(listn, listsl, listf)
local output;
output:= ValueOption("OutputStyle");
# check that the value exists and is valid.
if not output in ["silent", "single-line", "full"] then
output := "full";
fi;
if output = "silent" then
CallFuncList(Print, listn);
elif output = "single-line" then
CallFuncList(Print, listsl);
elif output = "full" then
CallFuncList(Print, listf);
fi;
end);
InstallGlobalFunction(ClearLine, function()
local width, height, i, blank;
blank := " ";
for i in [1..SizeScreen()[1]-10] do
blank := Concatenation(blank, " ");
od;
Print("\c\r",blank,"\r");
end);
# End
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