Bug in __InverseNormSimple

[joshmaglione]

G:=PCGroup(\[ 8, -3, 3, 3, 3, 3, -3, 3, 3, 3937, 17714, 17578, 164163, 62507, 9619,
236524, 1460, 7708 ]);
A:=AutomorphismGroupByInvariants(G);

This produces the following.

> G:=PCGroup(\[ 8, -3, 3, 3, 3, 3, -3, 3, 3, 3937, 17714, 17578, 164163, 62507\
, 9619,
> 236524, 1460, 7708 ]);
> A:=AutomorphismGroupByInvariants(G);
(orthogonal degree 1: entry has no square root in ground field)

AutomorphismGroupByInvariants(
    G: GrpPC
)
PseudoIsometryGroup(
    T: Tensor of valence 3, U2 x U1 >-> U0 U2 : Full Vector space o...
)
__SearchCosetsW(
    T: Tensor of valence 3, U2 x U1 >-> U0 U2 : Full Vector space o...,
    Supergroup: MatrixGroup(8, GF(3)) of order 2^14 * 3^11 * 5 * 11^2 * 13,
    Subgroup: MatrixGroup(8, GF(3)) of order 2^3 * 3,
    piV: Mapping from: GL(8, GF(3)) to GL(5, GF(3)) given by a rule [...,
    piW: Mapping from: GL(8, GF(3)) to GL(3, GF(3)) given by a rule [...,
    __THE_W_INDEX: 4,
    MAX: 1073741824
)
__test_pseudo_extension(
    T: Tensor of valence 3, U2 x U1 >-> U0 U2 : Full Vector space o...,
    Supergroup: MatrixGroup(8, GF(3)) of order 2^14 * 3^11 * 5 * 11^2 * 13,
    Subgroup: MatrixGroup(8, GF(3)) of order 2^3 * 3,
    h: [1 0 0] [0 1 0] [2 2 2]
)
IsIsometric(
    T1: Tensor of valence 3, U2 x U1 >-> U0 U2 : Full Vector space o...,
    T2: Tensor of valence 3, U2 x U1 >-> U0 U2 : Full Vector space o...
)
__IsIsometric_ND(
    S: Tensor of valence 3, U2 x U1 >-> U0 U2 : Full Vector space o...,
    T: Tensor of valence 3, U2 x U1 >-> U0 U2 : Full Vector space o...
)
InverseNorm(
    A: Matrix Algebra of degree 5 and dimension 1 with 1 generator ...,
    s: [2 0 0 0 0] [0 2 0 0 0] [0 0 2 0 0] [0 0 0 2 0] [0 0 0 0 2]
)
__InverseNormSemisimple(
    T: Matrix Algebra of degree 5 and dimension 1 with 1 generator ...,
    s: [2 0 0 0 0] [0 2 0 0 0] [0 0 2 0 0] [0 0 0 2 0] [0 0 0 0 2]
)
__InverseNormSimple(
    STAN: Full Matrix Algebra of degree 1 with 1 generator over GF(3),
    s: [2]
)
In file "/home/josh/Magma/GitPackages/Automorphism/src/inv-norm.m", line 45, 
column 29:
>>          return true, STAN![aa];
                               ^
Runtime error: Variable 'aa' has not been initialized

[algeboy]

This is because Magma doesn't treat small orthogonal groups as classical groups, so they don't have a form. This was fixed in an version before by Pete....perhaps we are no the wrong branch....TBD

[galois60]

Ah, just saw James' reply.

But in any case, I cannot replicate the error. I get another one (below). I believe I have pulled all of the necessary repos, but the error suggests that I am missing something?

G:=PCGroup([ 8, -3, 3, 3, 3, 3, -3, 3, 3, 3937, 17714, 17578, 164163, 62507, 9619, 236524, 1460, 7708 ]); A:=AutomorphismGroupByInvariants(G);

AutomorphismGroupByInvariants( G: GrpPC ) PseudoIsometryGroup( T: Tensor of valence 3, U2 x U1 >-> U0 U2 : Full Vector space o... ) __report( U: MatrixGroup(8, GF(3)) of order 2^15 3^13 5 11^2 13^2, L: MatrixGroup(5, GF(3)) of order 2, piV: Mapping from: GL(8, GF(3)) to GL(5, GF(3)) given by a rule [..., piW: Mapping from: GL(8, GF(3)) to GL(3, GF(3)) given by a rule [... ) In file "/Users/peterbrooksbank/MagmaGit/Auto-Sandbox/src/isom-test.m", line 271, column 11:

LV := L @ piV; ^ Runtime error in map application: Element is not in the domain of the map

[joshmaglione]

Sorry Pete, this "issue" is from more than two years ago. I don't know if any of it is relevant anymore. Feel free to close or leave open.

[galois60]

Ah, I see that now. Ok, I'm closing it then. I think James is right––I fixed this a while ago.