Hello,
The bug is caused by FreeModule_generic._mul_():
def _mul_(self, other, switch_sides=False):
if switch_sides:
return self.span([v * other for v in self.basis()])
return self.span([other * v for v in self.basis()])
It looks like the effect of the switch_sides flag is exactly the wrong
way around.
Peter
> Indeed
>
> sage: V.subspace([x*v]) == V.subspace([v])*x
> True
>
> Sage matrices are allow indifferently on vectors from left to right.
> But of course, the action is not the same but there is no row vectors
> vs column vectors.
>
> sage: v*x
> (1, 1)
> sage: x*v
> (1, 0)
>
> Your example shows that when acting on subspaces it is actually the
> left action which is used... which is silly, I definitely agree, since
> the action on subspaces is on right.
>
> Vincent
>
> 2015-01-30 15:51 UTC+01:00, Peter Mueller <ypf...@googlemail.com>:
>> After hours of debugging some program code, I found out that right
>> multiplication of a row subspace of K^n by an element x from GL(n,K) does
>> *not* do what I expected!
>>
>> sage: V = GF(2)^2
>> sage: v = V((1,0))
>> sage: x = GL(2,2)(matrix([[1,1],[0,1]]))
>> sage: V.subspace([v*x]) == V.subspace([v])*x
>> False
>>
>> It seems that right multiplication by x actually multiplies by the
>> *transpose* of x? Is there any reason for that? That is even worse than the
>>
>> completely silly and error prone notation for permutation groups, where a
>> *right action* is written from the left, so g(h(x)) isn't (g*h)(x).
>>
>> -- Peter Mueller
>>
>>
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