[GAP Forum] (no subject)

Fri Jul 12 05:27:11 BST 2019

Dear Forum
Sometimes Filter command work, sometimes it gives "break".
Please read it and suggest the solution:

*gap> LI:=List([1..5], i->SmallLoop(5,i));[ <small loop 5/1>, <small loop
5/2>, <small loop 5/3>, <small loop 5/4>, <small loop 5/5> ]gap>
Inv:=x->Inverse(x)=true;function( x ) ... endgap> LIn:=List(LI,
y->List(y,x->Inv(x)));[ [ false, false, false, false, false ], [ false,
false, false, false, false ], [ false, false, false, false, false ],  [
false, false, false, false, false ], [ false, false, false, false, false ]
]gap> Inv:=x->Inverse(x);function( x ) ... endgap> LIn:=List(LI,
y->List(y,x->Inv(x)));[ [ l1, l2, fail, fail, fail ], [ l1, l2, fail, fail,
fail ], [ l1, l2, l3, l4, l5 ], [ l1, l2, fail, fail, fail ],   [ l1, fail,
fail, fail, fail ] ]gap> L:=LI[4];<small loop 5/4>gap>
G:=SymmetricGroup(Size(L));; H:=Stabilizer(G,1);Sym( [ 2 .. 5 ] )gap>
A:=AutomorphismGroup(L);;gap> Size(A);3gap> A;Group([ (3,4,5), (3,5,4)
])gap> rc:=RightCosets(H,A);[ RightCoset(Group([ (3,4,5), (3,5,4) ]),()),
RightCoset(Group([ (3,4,5), (3,5,4) ]),(4,5)), RightCoset(Group([ (3,4,
5), (3,5,4) ]),(2,5)), RightCoset(Group([ (3,4,5), (3,5,4) ]),(2,5,4)),
RightCoset(Group([ (3,4,5), (3,5,  4) ]),(2,3,5)), RightCoset(Group([
(3,4,5), (3,5,4) ]),(2,3,5,4)), RightCoset(Group([ (3,4,5), (3,5,4)
]),(2,4,5)),   RightCoset(Group([ (3,4,5), (3,5,4) ]),(2,4)) ]gap>
k:=Size(rc);8gap> taut:=i->Filtered(rc[i], h->ForAll(L,
x->ForAll(L,y->(x*y)^h=Inverse(Inverse(x)^h)*y^h)));function( i ) ...
endgap> TA:=List([1..k], l->taut(l));Error, no method found! For debugging
hints type ?Recovery from NoMethodFoundError, no 1st choice method found
for `^' on 2 argumentsThe 1st argument is 'fail' which might point to an
earlier problem at /proc/cygdrive/C/gap-4.10.2/lib/methsel2.g:250 called
fromInverse( x ) ^ h at *stdin*:15 called fromfunc( elm ) at
/proc/cygdrive/C/gap-4.10.2/lib/coll.gi:1551 <http://coll.gi:1551> called
fromForAllOp( C, func ) at /proc/cygdrive/C/gap-4.10.2/lib/coll.gi:1536
<http://coll.gi:1536> called fromForAll( L, function ( y )      return (x *
y) ^ h = Inverse( Inverse( x ) ^ h ) * y ^ h;  end ) at *stdin*:15 called
fromfunc( elm ) at /proc/cygdrive/C/gap-4.10.2/lib/coll.gi:1551
<http://coll.gi:1551> called from...  at *stdin*:16type 'quit;' to quit to
outer loopbrk> quti;Syntax warning: Unbound global variable in
*errin*:1quti;    ^Error, Variable: 'quti' must have a value in  <corrupted
statement>  called from Inverse( x ) ^ h at *stdin*:15 called fromfunc( elm
) at /proc/cygdrive/C/gap-4.10.2/lib/coll.gi:1551 <http://coll.gi:1551>
called fromForAllOp( C, func ) at
/proc/cygdrive/C/gap-4.10.2/lib/coll.gi:1536 <http://coll.gi:1536> called
fromForAll( L, function ( y )      return (x * y) ^ h = Inverse( Inverse( x
) ^ h ) * y ^ h;  end ) at *stdin*:15 called fromfunc( elm ) at
/proc/cygdrive/C/gap-4.10.2/lib/coll.gi:1551 <http://coll.gi:1551> called
from...  at *errin*:1brk> taut(1);Error, no method found! For debugging
hints type ?Recovery from NoMethodFoundError, no 1st choice method found
for `^' on 2 argumentsThe 1st argument is 'fail' which might point to an
earlier problem at /proc/cygdrive/C/gap-4.10.2/lib/methsel2.g:250 called
fromInverse( x ) ^ h at *stdin*:15 called fromfunc( elm ) at
/proc/cygdrive/C/gap-4.10.2/lib/coll.gi:1551 <http://coll.gi:1551> called
fromForAllOp( C, func ) at /proc/cygdrive/C/gap-4.10.2/lib/coll.gi:1536
<http://coll.gi:1536> called fromForAll( L, function ( y )      return (x *
y) ^ h = Inverse( Inverse( x ) ^ h ) * y ^ h;  end ) at *stdin*:15 called
fromfunc( elm ) at /proc/cygdrive/C/gap-4.10.2/lib/coll.gi:1551
<http://coll.gi:1551> called from...  at *errin*:2type 'quit;' to quit to
outer loopbrk_2> quit;brk> quit;gap>
ta1:=Filtered(H,h->(L.3*L.5)^h=Inverse(Inverse(L.3)^h)*L.5^h);Error, no
method found! For debugging hints type ?Recovery from NoMethodFoundError,
no 1st choice method found for `^' on 2 argumentsThe 1st argument is 'fail'
which might point to an earlier problem at
/proc/cygdrive/C/gap-4.10.2/lib/methsel2.g:250 called fromInverse( L.3 ) ^
h at *stdin*:16 called fromfunc( elm ) at
/proc/cygdrive/C/gap-4.10.2/lib/coll.gi:1363 <http://coll.gi:1363> called
fromFilteredOp( C, func ) at /proc/cygdrive/C/gap-4.10.2/lib/coll.gi:1347
<http://coll.gi:1347> called from<function "Filtered">( <arguments>
) called from read-eval loop at *stdin*:16type 'quit;' to quit to outer
loopbrk> quit;gap> L.3;L.5;l3l5gap> L;<small loop 5/4>gap>
List(L,x_Inverse(x));Error, Variable: 'x_Inverse' must have a valuenot in
any function at *stdin*:18gap> List(L,x->Inverse(x));[ l1, l2, fail, fail,
fail ]gap> sl15:=SmallLoop(5,1);<small loop 5/1>gap> CayleyTable(sl15);[ [
1, 2, 3, 4, 5 ], [ 2, 1, 4, 5, 3 ], [ 3, 4, 5, 1, 2 ], [ 4, 5, 2, 3, 1 ], [
5, 3, 1, 2, 4 ] ]gap> mt15:=List(sl15, x->List(sl15,y->x*y));[ [ l1, l2,
l3, l4, l5 ], [ l2, l1, l4, l5, l3 ], [ l3, l4, l5, l1, l2 ], [ l4, l5, l2,
l3, l1 ],   [ l5, l3, l1, l2, l4 ] ]gap> Inv:=List(sl15,x->Inverse(x));[
l1, l2, fail, fail, fail ]gap> s25:=SmallLoop(5,2);<small loop 5/2>gap>
mt25:=List(sl15, x->List(sl15,y->x*y));[ [ l1, l2, l3, l4, l5 ], [ l2, l1,
l4, l5, l3 ], [ l3, l4, l5, l1, l2 ], [ l4, l5, l2, l3, l1 ],   [ l5, l3,
l1, l2, l4 ] ]gap> Inv:=List(sl25,x->Inverse(x));Error, Variable: 'sl25'
must have a valuenot in any function at *stdin*:26gap>
sl25:=SmallLoop(5,2);<small loop 5/2>gap> Inv:=List(sl25,x->Inverse(x));[
l1, l2, fail, fail, fail ]gap> sl35:=SmallLoop(5,3);<small loop 5/3>gap>
Inv:=List(sl35,x->Inverse(x));[ l1, l2, l3, l4, l5 ]gap>
G:=SymmetricGroup(Size(L));; H:=Stabilizer(G,1);Sym( [ 2 .. 5 ] )gap>
A:=AutomorphismGroup(L);;gap> rc:=RightCosets(H,A);[ RightCoset(Group([
(3,4,5), (3,5,4) ]),()), RightCoset(Group([ (3,4,5), (3,5,4) ]),(4,5)),
RightCoset(Group([ (3,4,  5), (3,5,4) ]),(2,5)), RightCoset(Group([
(3,4,5), (3,5,4) ]),(2,5,4)), RightCoset(Group([ (3,4,5), (3,5,  4)
]),(2,3,5)), RightCoset(Group([ (3,4,5), (3,5,4) ]),(2,3,5,4)),
RightCoset(Group([ (3,4,5), (3,5,4) ]),(2,4,5)),   RightCoset(Group([
(3,4,5), (3,5,4) ]),(2,4)) ]gap> k:=Size(rc);8gap> taut:=i->Filtered(rc[i],
h->ForAll(L, x->ForAll(L,y->(x*y)^h=Inverse(Inverse(x)^h)*y^h)));function(
i ) ... endgap> taut(1);Error, no method found! For debugging hints type
?Recovery from NoMethodFoundError, no 1st choice method found for `^' on 2
argumentsThe 1st argument is 'fail' which might point to an earlier
problem at /proc/cygdrive/C/gap-4.10.2/lib/methsel2.g:250 called
fromInverse( x ) ^ h at *stdin*:35 called fromfunc( elm ) at
/proc/cygdrive/C/gap-4.10.2/lib/coll.gi:1551 <http://coll.gi:1551> called
fromForAllOp( C, func ) at /proc/cygdrive/C/gap-4.10.2/lib/coll.gi:1536
<http://coll.gi:1536> called fromForAll( L, function ( y )      return (x *
y) ^ h = Inverse( Inverse( x ) ^ h ) * y ^ h;  end ) at *stdin*:35 called
fromfunc( elm ) at /proc/cygdrive/C/gap-4.10.2/lib/coll.gi:1551
<http://coll.gi:1551> called from...  at *stdin*:36type 'quit;' to quit to
outer loopbrk> quit;gap>
ta1:=Filtered(H,h->(L.3*L.5)^h=Inverse(Inverse(L.3)^h)*L.5^h);Error, no
method found! For debugging hints type ?Recovery from NoMethodFoundError,
no 1st choice method found for `^' on 2 argumentsThe 1st argument is 'fail'
which might point to an earlier problem at
/proc/cygdrive/C/gap-4.10.2/lib/methsel2.g:250 called fromInverse( L.3 ) ^
h at *stdin*:36 called fromfunc( elm ) at
/proc/cygdrive/C/gap-4.10.2/lib/coll.gi:1363 <http://coll.gi:1363> called
fromFilteredOp( C, func ) at /proc/cygdrive/C/gap-4.10.2/lib/coll.gi:1347
<http://coll.gi:1347> called from<function "Filtered">( <arguments>
) called from read-eval loop at *stdin*:36type 'quit;' to quit to outer
loopbrk> quit;*

*Regards*
*Akhilesh Chandra Yadav*
*Head and Associate Professor*
*Department of Mathematics*
*M G Kashi Vidyapith Varanasi*