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Speed up IrrBaumClausen (used for computing character tables of supersolvable groups, including $p$-groups) #4905

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Jun 24, 2022
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Speed up IrrBaumClausen (used for computing character tables of supersolvable groups, including $p$-groups) #4905

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70 changes: 38 additions & 32 deletions lib/ctblsolv.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -2038,30 +2038,33 @@ InstallMethod( IrrBaumClausen,
info, # result of `BaumClausenInfo'
pcgs, # value of `info.pcgs'
lg, # composition length
evl, # list encoding exponents of class representatives
i, j, k, # loop variables
exps, # exponent vector of a group element
exps, # exponents of class representatives
cr, # exps sorted
dobylevel, # generate matrices and traces of class reps
i, j, jj, k, # loop variables
t, # intermediate representation value
irreducibles, # list of irreducible characters
rep, # loop over the representations
l, # list of monomial matrices
gcd, # g.c.d. of the exponents in `rep'
q, #
o, # order of root of unity
e, # exponent
Ee, # complex root of unity needed for `rep'
chi, # one character values list
deg, # character degree
idmat, # identity matrix
perm, # entries of monomial matrix
diag,
trace; # trace of a matrix

mulmoma:= function( a, b )
local prod, i;
local prod;
prod:= rec( perm := b.perm{ a.perm },
diag := [] );
for i in [ 1 .. deg ] do
prod.diag[ b.perm[i] ]:= b.diag[ b.perm[i] ] + a.diag[i];
od;
prod.diag{b.perm} := b.diag{b.perm} + a.diag;
return prod;
end;

tbl:= CharacterTable( G );
ccl:= ConjugacyClasses( tbl );
SetExponent( G, Exponent( tbl ) );
Expand Down Expand Up @@ -2092,40 +2095,43 @@ InstallMethod( IrrBaumClausen,

# Compute the nonlinear irreducibles.
if not IsEmpty( info.nonlin ) then
evl:= [];
for i in [ 2 .. Length( ccl ) ] do
t:= [];
for j in [ 1 .. lg ] do
for k in [ 1 .. exps[i][j] ] do
Add( t, j );
od;
od;
evl[ i-1 ]:= t;
od;
cr := SortedList(exps);
for rep in info.nonlin do
gcd:= GcdInt( Gcd( List( rep, x -> Gcd( x.diag ) ) ), info.exponent );
Ee:= E( info.exponent / gcd );
o := info.exponent / gcd;
deg:= Length( rep[1].perm );
chi:= [ deg ];
idmat:= rec( perm := [ 1 .. deg ], diag := [ 1 .. deg ] * 0 );
for j in evl do

# Compute the value of the representation at the representative.
t:= idmat;
for k in j do
t:= mulmoma( t, rep[k] );
Add(cr[1], deg);
l := List([1..lg], i-> idmat);
# We go through sorted list of exponents and reuse
# partial product from previous representative.
for i in [2..Length(cr)] do
j := 1;
while cr[i-1][j] = cr[i][j] do
j := j+1;
od;
for k in [cr[i-1][j]+1..cr[i][j]] do
l[j] := mulmoma(l[j], rep[j]);
od;
for jj in [j+1..lg] do
l[jj] := l[jj-1];
for k in [1..cr[i][jj]] do
l[jj] := mulmoma(l[jj], rep[jj]);
od;
od;

# Compute the character value.
trace:= 0;
trace:= 0*[1..o];
perm := l[lg].perm;
diag := l[lg].diag;
for k in [ 1 .. deg ] do
if t.perm[k] = k then
trace:= trace + Ee^( t.diag[k] / gcd );
if perm[k] = k then
e := (diag[k] / gcd) mod o;
trace[e+1]:= trace[e+1] + 1;
fi;
od;
Add( chi, trace );

Add(cr[i], CycList(trace));
od;
chi := List(exps, Remove);
Add( irreducibles, Character( tbl, chi ) );
od;
fi;
Expand Down