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^ Subject:

Dear GAP Forum,

on Tue, 23 Feb 99 14:51:25 +0100 Thomas Breuer wrote as reply to the mail of Dima Pasechnik:

So if one really wants to compute this character table,

it is perhaps worth a try to use the Dixon-Schneider method,

since computers are getting faster and larger.

More precisely, one could follow use the functions described

in the manual section ``Advanced Methods for Dixon-Schneider

Calculations'' (and the example in the following section).

I tested two years ago the program to compute character table

described in the GAP-manual section Dixon-Schneider "An Example of Advanced

Calculations" and I had some problems for some finite groups, for example, for

G:=MathieuGroup(22) of Order 443520 and for G:=PrimitiveGroup(8,4) of Order 336

(=PGL(2,7)).

After comments

"...#Finally we calculate the characters induced from all cyclic subgroups

# and obtain the missing irreducibles by applying the LLL-algorithm to them."

and after GAP-commands:

ic:= InducedCyclic( c, "all" );;

ro:= ReducedOrdinary( c, c.irreducibles, ic );;

and before GAP-command:

l:= LLL( c, ro.remainders );;

I received the message:

Error, List Element: <list>[1] must have a value at

B := [ scpr( L, b[1], b[1] ) ] ... in

LLLReducedBasis( arg[1], arg[2], y ) called from

LLL( c, ro.remainders ) called from

main loop

brk>

Now I work with the package GAP3r4p4. The problems have remained.

The reason of the message about an error is in following:

for some groups after GAP-commands:

ro:= ReducedOrdinary( c, c.irreducibles, ic );;

we have record 'ro' with empty record components:

ro = rec( remainders := [ ], irreducibles := [ ] ) Length(ro.irreducibles) = 0

In such situation the command LLL(...) does not work.

For correction of the program it is enough add the trivial character

[1, 1, ... ,1 ] to record components ro.irreducibles,

if Length(ro.irreducibles) = 0,

and add the zero string [0, 0, ... ,0 ] to record components ro.remainders,

if Length(ro.remainders) = 0.

It will be good if you replace the last GAP-command of "An Example

of Advanced ... "

Sum( last, i -> i^2 );

by:

Print(" c.irreducibles = \n",c.irreducibles,"\n");

I have a GAP-code with this corrections and can send it

if it will be necessary for somebody.

Sincerely yours,

Anatolii^ V. Rukolaine (St.Petersburg, Russia).

PS:

My home e-mail: rukolaha@tower.hop.stu.neva.ru

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