Eamonn's List

[joshmaglione]

Eamonn sent us an email with bugs. Some of them were fixed, and some are still issues. Here are the groups/tensors that still pose issues.

1. (FIXED) G is p-class 3. Here's the code that will produce the bug.

G:=PCGroup(\[ 8, -7, 7, 7, 7, 7, -7, -7, 7, 269025, 77075, 6453893, 5762413 ]);
SetVerbose ("Autotopism", 2);
A:=AutomorphismGroupByInvariants (G);

Here is the output.

Group is small genus, using small genus package.

AutomorphismGroupByInvariants(
    G: GrpPC
)
PseudoIsometryGroupSG(
    B: Tensor of valence 3, U2 x U1 >-> U0 U2 : Full Vector space o...
)
In file "/home/josh/Magma/GitPackages/SmallGenus/src/PIsomGroup.m", line 199, 
column 31:
>>     T, H := TensorOverCentroid(B);
                                 ^
Runtime error in 'TensorOverCentroid': Centroid is not a commutative ring.

2. Here is a bug that might be caused by the LMG package. Instead, maybe we are passing it something problematic?

G := PCGroup(\[ 11, -11, 11, 11, 11, 11, -11, 11, 11, 11, 11, 11, 389743663, 47836142, 649542, 644713, 1072599664, 1071867625, 1071801086, 1071795047 ]);
A := AutomorphismGroupByInvariants (G);

The output is very long. Here is the start of the error report.

Error of type ErrUser during composition tree creation
Full error info:
AutomorphismGroupByInvariants(
G: GrpPC
)
PseudoIsometryGroup(
T: Tensor of valence 3, U2 x U1 >-> U0 U2 : Full Vector space o...
)
__report(
U: MatrixGroup(11, GF(11)),
L: MatrixGroup(11, GF(11)) of order 1,
piV: Mapping from: GL(11, GF(11)) to GL(5, GF(11)) given by a rul...,
piW: Mapping from: GL(11, GF(11)) to GL(6, GF(11)) given by a rul...
)
......

Eamonn: I don't think this has anything to do with LMG. See 5 below.

3. Here is one that isn't really a bug but is an issue. This should mostly be resolved when filters get fixed.

G := PCGroup(\[ 7, -7, 7, 7, 7, -7, 7, 7, 33713, 240108, 353978, 108061, 68610, 67441, 18056 ]);

From Eamonn:

Default AutomorphismGroup find lots of char structure, gives up after deducing that stab of order at most 6 survives, shows that stab has order 1.

AutomorphismGroupByInvariants also find lots of char structure, then reports "Could not place into filter" many times, does some more work, and goes home with surviving subgroup of GL(4, 7) of order 2^9 3^3 7^2.

4. (FIXED) The following issue comes from the verbose printing. It should be an easy fix.

G := PCGroup(\[ 8, -3, 3, 3, -3, 3, 3, -3, 3, 17496, 481, 19449, 2162, 2026, 11682, 24195, 23627, 10483, 32404, 10812, 3620, 221621 ]);
SetVerbose ("Autotopism", 2);
AutomorphismGroupByInvariants(G);

Here is the output.

Lie algebra methods not fully supported for this tensor 
AutomorphismGroupByInvariants(
    G: GrpPC
)
PseudoIsometryGroup(
    T: Tensor of valence 3, U2 x U1 >-> U0 U2 : Full Vector space o...
)
ExponentiateDerivations(
    T: Tensor of valence 3, U2 x U1 >-> U0 U2 : Full Vector space o...
)
In file "/home/eobr007/auto/Automorphism/src/DerAuto.m", line 151, column 59:
>> vprint Autotopism, 2 : "[INFO]   Dim(Levi) =", Dimension (Levi); 
                                                             ^
Runtime error: Variable 'Levi' has not been initialized

Entering graph cut down....
|point_part| = 1
|line_part| = 1
|ref_line_part| = 1
Relabeling graph with full signatures.
|point_part| = 1
|line_part| = 1

Probably just needs to execute line 151 only when the Lie stuff is successful.

Eamonn: we checked in fix for this. But see 6. below.

[joshmaglione]

I fixed issue 1. I think AutomorphismGroupByInvariants assumes p-class 2 (and exponent p), but there is no error when you run the sample code for 1.

[eamonnaobrien]

5. Here's another example leading to Segmentation fault for me after considerable time.

G := PCGroup([ 11, -11, 11, 11, 11, 11, -11, 11, 11, 11, 11, 11, 389743663, 478 36142, 649542, 644713, 1072599664, 1071867625, 1071801086, 1071795047 ]) ; A := AutomorphismGroupByInvariants (G);

Eamonn

[eamonnaobrien]

5 cont/ As a follow-up to the last entry, here's the output before the crash.

[INFO] here is the structure of Isom(T): G | GO ( 1 , 11 ^ 1 ) * | 11 ^ 0 (unipotent radical) 1

[INFO] Dim(DerT) = 13 [INFO] Dim(DerTW) = 13 [INFO] DerTW acting irreducibly on W? false RModule of dimension 2 over GF(11) RModule of dimension 4 over GF(11)

[INFO] Dim(Levi) = 6 [INFO] Dim(LeviW) = 6 [INFO] LeviW acting irreducibly on W? false RModule of dimension 1 over GF(11) RModule of dimension 5 over GF(11) attempting to decompose Levi into simple ideals ... ... done!

[INFO] processing summand 1 (out of 1 simple summands) [INFO] Type = A1 A1 [INFO] Dim(L) = 6 [INFO] LW acting on a module of dimension 6 [WARNING] LW acts reducibly on W Segmentation fault

Best wishes. Eamonn

[eamonnaobrien]

6. Here's a problem with NormStar. The order stored in result of NormStar does NOT equal the order of the group generated. More worryingly is that repeated calls to NormStar often produces different answers. See below where I store N and M as values returned by NormStar. Often each generates a group whose orders are different and neither agrees with the order set in N and M.

[ MatrixAlgebra(GF(3), 6) | [ GF(3) | 0, 1, 0, 1, 0, 2, 2, 0, 2, 2, 0, 1, 0, 1, 0, 1, 0, 2, 2, 1, 2, 0, 2, 0, 0, 0, 0, 1, 0, 2, 1, 2, 1, 0, 1, 0 ], [ GF(3) | 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 2, 1, 0, 1, 0, 1, 0 ] ] ; S := $1; N:=NormStar (S); "reported order for N is ", FactoredOrder (N);

H := sub<Generic (N) | [N.i: i in [1..Ngens (N)]]>; "actual order for N", FactoredOrder (H);

M := NormStar (S); "reported order for N is ", FactoredOrder (N);

H := sub<Generic (N) | [M.i: i in [1..Ngens (M)]]>; "actual order for M", FactoredOrder (H);

// James suggests it may be because T is degenerate

T:=Tensor(S, 2,1); IsNondegenerate (T);

Best wishes. Eamonn

[eamonnaobrien]

6. This is really an update to 4. James and I resolved 4 earlier today and checked in a fix. Now the code gives up with no output at all on the first call, and on the second call reports an error. See below. Eamonn

G := PCGroup([ 8, -3, 3, 3, -3, 3, 3, -3, 3, 17496, 481, 19449, 2162, 2026, 1168\ 2, 24195, 23627, 10483, 32404, 10812, 3620, 221621 ]) ; SetVerbose ("Autotopism", 2); A := AutomorphismGroupByInvariants(G); BITS OF WORK:............................................ 14 Reducing action on W.... Searching for characteristic subgroups by Maglione-Wilson filters. Searching for characteristic subgroups by Eick--Leedham-Green--O'Brien. BITS OF WORK:............................................ 2 Entering pseudo-isometry group.... INDEX ON V: 14 / 15 bits INDEX ON W: 14 / 15 bits. Adding isometries by Brooksbank-Wilson algorithm. G | GO ( 1 , 3 ^ 1 ) * | 3 ^ 0 (unipotent radical) 1 INDEX ON V: 13 / 15 bits INDEX ON W: 14 / 15 bits. Adding exponential of derivations by Brooksbank-Maglione-Wilson. ======ExponentiateDerivations=============== [INFO] Dim(V) = 3 [INFO] Dim(W) = 3 [INFO] Dim(Rad) = 0 [INFO] Dim(CoRad) = 0

[INFO] here is the structure of Isom(T): G | GO ( 1 , 3 ^ 1 ) * | 3 ^ 0 (unipotent radical) 1

[INFO] Dim(DerT) = 9 [INFO] Dim(DerTW) = 9 [INFO] DerTW acting irreducibly on W? true

[WARNING] Der(G) is solvable INDEX ON V: 13 / 15 bits INDEX ON W: 14 / 15 bits. Entering graph cut down.... |point_part| = 1 |line_part| = 1 |ref_line_part| = 1 Relabeling graph with full signatures. |point_part| = 1 |line_part| = 1 A := AutomorphismGroupByInvariants(G); BITS OF WORK:............................................ 14 Reducing action on W.... Searching for characteristic subgroups by Maglione-Wilson filters. THIS IS THE FCT Searching for characteristic subgroups by Eick--Leedham-Green--O'Brien. BITS OF WORK:............................................ 2 Entering pseudo-isometry group.... INDEX ON V: 14 / 15 bits INDEX ON W: 14 / 15 bits. Adding isometries by Brooksbank-Wilson algorithm. G | GO ( 1 , 3 ^ 1 ) * | 3 ^ 0 (unipotent radical) 1 INDEX ON V: 13 / 15 bits INDEX ON W: 14 / 15 bits. Adding exponential of derivations by Brooksbank-Maglione-Wilson. ======ExponentiateDerivations=============== [INFO] Dim(V) = 3 [INFO] Dim(W) = 3 [INFO] Dim(Rad) = 0 [INFO] Dim(CoRad) = 0

[INFO] here is the structure of Isom(T): G | GO ( 1 , 3 ^ 1 ) * | 3 ^ 0 (unipotent radical) 1

[INFO] Dim(DerT) = 9 [INFO] Dim(DerTW) = 9 [INFO] DerTW acting irreducibly on W? true

[WARNING] Der(G) is solvable INDEX ON V: 13 / 15 bits INDEX ON W: 14 / 15 bits. Entering graph cut down.... |point_part| = 1 |line_part| = 1 |ref_line_part| = 1 Relabeling graph with full signatures. |point_part| = 1 |line_part| = 1

In file "/home/eobr007/auto/eMAGma/src/Tensor/../TensorCategory/Hom.m", line 11, column 44:

return forall{ x : x in Bas | (< x[i] @ H.(v-i) : i in [1..#x] > @ C) eq ^ Runtime error in '.': Integer should be in range [0..1].

[galois60]

Pertaining to 5, I wouldn't try to use the old NormStar function at the moment. I am rewriting this from the ground at present. I will let you all know when this is ready to be tested / incorporated.