Just fixing the == method is probably not good enough:
On Thursday, September 21, 2017 at 4:10:10 PM UTC+2, Maarten Derickx wrote:
>
>
> Note that there is no distinction between the FreeModule with
> inner_product_matrix=matrix.identity(1)*2 and FreeQuadraticModusince the
> sage object created in both ways is the same object. Not just equal, but
> literally the same object in memory, so any change will automatically
> affect both.
>
> FreeQuadraticModule(ZZ,1,matrix.identity(1)*2) is
> FreeModule(ZZ,1,inner_product_matrix=matrix.identity(1)*2)
>
> I think it is good to open a ticket to make == also take the inner product
> matrix into account, and I think no deprecation is needed since it fixes
> something which is mathematically incorrect.
>
> One more subtle question is wether we want:
>
> sage:
> FreeModule(ZZ,1)==FreeModule(ZZ,1,inner_product_matrix=matrix.identity(1))
>
> I think so. It is mathematically the same thing. But just changing the ==
operator is not good enough. Then we also need to reconsider < ,<= etc.
Currently:
"
Modules are ordered by their ambient spaces, then by dimension,
then in order by their echelon matrices. However, if
other is a sub-module or is a quotient module then its
comparison method is used instead of generic comparison.
"
Ambient spaces are ordered by rank and base ring.
So I think that ambient spaces should be ordered by
rank, inner_product_matrix, and then base ring.
This change should take place in
sage.modules.free_module.FreeModule_ambient
One might need to adapt the hash function there?
Objections?
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