Opened 10 years ago
Closed 5 years ago
#12073 closed defect (wontfix)
MatrixGroup() or order() incorrect for G_2(F_3)
Reported by: | robharron | Owned by: | joyner |
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Priority: | major | Milestone: | sage-duplicate/invalid/wontfix |
Component: | group theory | Keywords: | MatrixGroup, GAP, order |
Cc: | Merged in: | ||
Authors: | Reviewers: | Travis Scrimshaw | |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
If I use the generators for the exceptional group G_2(F_3) in its natural 7-dimensional representation over F_3 in the MatrixGroup? constructor, the order of the group returned is 8491392 (twice what it should be). However, if I use the same generators through the gap console within sage, I get the correct size.
K=GF(3) sage: gens=[matrix(K,7,[ ....: [0,2,0,0,0,0,0], ....: [2,0,0,0,0,0,0], ....: [0,0,0,2,0,0,0], ....: [0,0,2,0,0,0,0], ....: [0,0,0,0,0,2,0], ....: [0,0,0,0,2,0,0], ....: [2,2,2,2,1,1,1]]), ....: matrix(K,7,[ ....: [2,0,0,0,0,0,0], ....: [0,0,2,0,0,0,0], ....: [1,1,1,0,0,0,0], ....: [0,0,0,0,2,0,0], ....: [1,0,0,1,1,0,0], ....: [0,0,0,0,0,0,2], ....: [1,0,0,0,0,1,1]])] sage: M = MatrixGroup(gens); M.order() 8491392 sage: M.gap().Size() 8491392 sage: M.gap().Order() 8491392 sage: gap.Group([gap(gens[0]),gap(gens[1])]).Order() 8491392
gap> m1:= [ > [0,2,0,0,0,0,0], > [2,0,0,0,0,0,0], > [0,0,0,2,0,0,0], > [0,0,2,0,0,0,0], > [0,0,0,0,0,2,0], > [0,0,0,0,2,0,0], > [2,2,2,2,1,1,1] > ]*Z(3); gap> m2:= [ > [2,0,0,0,0,0,0], > [0,0,2,0,0,0,0], > [1,1,1,0,0,0,0], > [0,0,0,0,2,0,0], > [1,0,0,1,1,0,0], > [0,0,0,0,0,0,2], > [1,0,0,0,0,1,1] > ]*Z(3); gap> Order(Group( m1, m2 )); 4245696
Change History (14)
comment:1 Changed 8 years ago by
- Milestone changed from sage-5.11 to sage-5.12
comment:2 Changed 8 years ago by
- Milestone changed from sage-6.1 to sage-6.2
comment:3 Changed 8 years ago by
- Milestone changed from sage-6.2 to sage-6.3
comment:4 Changed 7 years ago by
- Milestone changed from sage-6.3 to sage-6.4
comment:5 Changed 6 years ago by
- Stopgaps set to todo
comment:6 Changed 5 years ago by
- Description modified (diff)
comment:7 Changed 5 years ago by
- Description modified (diff)
comment:8 Changed 5 years ago by
- Description modified (diff)
comment:9 Changed 5 years ago by
comment:10 Changed 5 years ago by
same problems for other finite fields of prime order
sage: p=5; L = [gap(GF(p)(i)) for i in range(p)]; L [0*Z(5), Z(5)^0, Z(5), Z(5)^3, Z(5)^2]
versus
gap> p:=5; [0..p-1]*Z(p); 5 [ 0*Z(5), Z(5), Z(5)^2, Z(5)^0, Z(5)^3 ]
EDIT Note also that
gap> One(ZmodnZ(5)); Z(5)^0 gap> One(Z(5)); Z(5)^0 gap> One(GF(5)); Z(5)^0
So our conversion seems to be consistent with gap..
comment:11 Changed 5 years ago by
This boils down to
gap> 1*Z(5); Z(5) gap> One(Z(5)); Z(5)^0
which is indeed not very-good looking.
comment:12 Changed 5 years ago by
- Milestone changed from sage-6.4 to sage-duplicate/invalid/wontfix
- Status changed from new to needs_review
- Stopgaps todo deleted
ok, so this must come from a confusion: in Gap, Z(5) is not the one of the finite field, but a generator of the group of invertible elements. This means that your matrices are not the correct ones, I think.
I propose to close this as invalid.
comment:13 Changed 5 years ago by
- Reviewers set to Travis Scrimshaw
- Status changed from needs_review to positive_review
Confirmed:
gap> One(GF(5)); Z(5)^0
and replacing by the above yields:
gap> Order(Group( m1, m2 )); 8491392
From the GAP manual:
The root returned by
Z
is a generator of the multiplicative group of the finite field with p^{d} elements, which is cyclic.
comment:14 Changed 5 years ago by
- Resolution set to wontfix
- Status changed from positive_review to closed
Closing tickets in the sage-duplicate/invalid/wontfix module with positive_review (i.e. someone has confirmed they should be closed).
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