Wrong order of finite matrix groups #37934
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This seems to have been introduced by #36881, since the formula given there only works if the finite base ring is a field; previously (for your example) the method called GAP to compute the order instead. |
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There is also some other funny stuff introduced by this change, such as |
vbraun
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May 18, 2024
sagemathgh-37980: Fix order computation for linear groups GL(n, R) and SL(n, R) sagemath#36881 introduced some wrong results for orders of linear groups since it did not check whether the base ring is a field. We add the necessary checks as well as formulas for some further cases, namely $\mathbb{Z}$ and $\mathbb{Z}/q\mathbb{Z}.$ Finally, we add a `NotImplementedError` for the cases that are not supported. The formula for the general linear group over $\mathbb{Z}/q\mathbb{Z}$ is taken from https://math.stackexchange.com/a/2044571, and for the order of the special linear group we use the group isomorphism induced by the determinant. Fixes sagemath#37934. URL: sagemath#37980 Reported by: Sebastian A. Spindler Reviewer(s): Travis Scrimshaw
vbraun
pushed a commit
to vbraun/sage
that referenced
this issue
May 18, 2024
sagemathgh-37980: Fix order computation for linear groups GL(n, R) and SL(n, R) sagemath#36881 introduced some wrong results for orders of linear groups since it did not check whether the base ring is a field. We add the necessary checks as well as formulas for some further cases, namely $\mathbb{Z}$ and $\mathbb{Z}/q\mathbb{Z}.$ Finally, we add a `NotImplementedError` for the cases that are not supported. The formula for the general linear group over $\mathbb{Z}/q\mathbb{Z}$ is taken from https://math.stackexchange.com/a/2044571, and for the order of the special linear group we use the group isomorphism induced by the determinant. Fixes sagemath#37934. URL: sagemath#37980 Reported by: Sebastian A. Spindler Reviewer(s): Travis Scrimshaw
vbraun
pushed a commit
to vbraun/sage
that referenced
this issue
May 24, 2024
sagemathgh-37980: Fix order computation for linear groups GL(n, R) and SL(n, R) sagemath#36881 introduced some wrong results for orders of linear groups since it did not check whether the base ring is a field. We add the necessary checks as well as formulas for some further cases, namely $\mathbb{Z}$ and $\mathbb{Z}/q\mathbb{Z}.$ Finally, we add a `NotImplementedError` for the cases that are not supported. The formula for the general linear group over $\mathbb{Z}/q\mathbb{Z}$ is taken from https://math.stackexchange.com/a/2044571, and for the order of the special linear group we use the group isomorphism induced by the determinant. Fixes sagemath#37934. URL: sagemath#37980 Reported by: Sebastian A. Spindler Reviewer(s): Travis Scrimshaw
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Steps To Reproduce
On Sage 10.3 running in CoCalc, run
Expected Behavior
First one works in sage version 10.2, second one returns recursion error.
Actual Behavior
See above. Seems to be computing GL(2,Integers(q)).order() as (q-1)^2q(q+1).
Additional Information
Explanation of correct computation: here.
Environment
Checklist
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