Opened 10 months ago
Last modified 5 months ago
#31276 new enhancement
Tensor Product Method for FiniteRankFreeModule
Reported by: | gh-mjungmath | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-9.5 |
Component: | algebra | Keywords: | |
Cc: | tscrim, egourgoulhon, jhpalmieri, mkoeppe | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
We introduce the methods tensor_product
and tensor_power
as per #30373.
Furthermore, we introduce a method tensor_product
for elements.
Things that are probably nice to get to work:
sage: M = FiniteRankFreeModule(QQ, 2) sage: N = FiniteRankFreeModule(QQ, 3) sage: M.tensor(N) sage: M.tensor(M) sage: M.tensor(M.tensor_module(1,2)) sage: N.tensor(M.tensor_module(1,2)) sage: M.tensor_module(1,2).tensor(M) sage: N.tensor_module(1,2).tensor(M) sage: M.tensor_module(1,1).tensor(M.tensor_module(1,2)) sage: N.tensor_module(1,1).tensor(M.tensor_module(1,2)) sage: M.tensor_power(3) sage: M.tensor_module(1,2).tensor_power(3)
and for elements respectively.
Change History (12)
comment:1 follow-up: ↓ 2 Changed 10 months ago by
- Cc jhpalmieri mkoeppe added
comment:2 in reply to: ↑ 1 ; follow-up: ↓ 3 Changed 10 months ago by
Replying to gh-mjungmath:
- Trying to wrap the patch over, it turns out that
TensorFreeModule
inherits fromFiniteRankFreeModule
and therefore inherits all methods and attributes. So far so good, but as I understand the code, instances ofTensorFreeModule
are not intended to use most of these methods.
Indeed, so maybe a better inheritance structure should be devised.
FiniteRankFreeModule
is intended to be the "control center" that takes care of things.
Yes. This avoids information redundancy, in particular regarding the bases.
This leads to somewhat strange (and probably unwanted) behavior:
sage: M = FiniteRankFreeModule(QQ, 3) sage: T11 = M.tensor_module(1, 1) sage: T11 is M.tensor_module(1, 1) True sage: T11 is T11.tensor_module(1, 1) False
Why do you call this strange behavior? Both answers, True
and False
, are mathematically correct.
and
sage: M = FiniteRankFreeModule(ZZ, 2) sage: e = M.basis('e') sage: f = M.basis('f', from_family=(e[0]-e[1], -2*e[0]+3*e[1])) sage: M.change_of_basis(e, f) Automorphism of the Rank-2 free module over the Integer Ring sage: T11 = M.tensor_module(1, 1) sage: T11.change_of_basis(e, f) Traceback (most recent call last): ... TypeError: Basis (e_0,e_1) on the Rank-2 free module over the Integer Ring is not a basis of the Free module of type-(1,1) tensors on the Rank-2 free module over the Integer Ring
The latter might be acceptable because
e
andf
are, strictly speaking, no bases ofT11
.
Yes, the TypeError
sounds correct here.
However, this methods has then no use in
TensorFreeModule
. Nevertheless, these are just two examples and there is a lot more. Furthermore,TensorFreeModule
initializes a bunch of dictionaries, sets and further attributes that are not used anywhere else.
You mean those attributes inherited from FiniteRankFreeModule
?
comment:3 in reply to: ↑ 2 ; follow-up: ↓ 4 Changed 10 months ago by
Replying to egourgoulhon:
Why do you call this strange behavior? Both answers,
True
andFalse
, are mathematically correct.
Of course, right, it's the tensor module of the tensor module. But we also have:
sage: T22 = T11.tensor_module(1, 1) sage: T22 is M.tensor_module(1, 1) False
But one could argue here that these objects are different mathematical entities which are just isomorphic. On the other hand, they behave exactly the same as instances of TensorFreeModule
.
You mean those attributes inherited from
FiniteRankFreeModule
?
Indeed. At least those that are not needed in TensorFreeModule
.
comment:4 in reply to: ↑ 3 ; follow-up: ↓ 5 Changed 10 months ago by
Replying to gh-mjungmath:
Replying to egourgoulhon:
Why do you call this strange behavior? Both answers,
True
andFalse
, are mathematically correct.Of course, right, it's the tensor module of the tensor module. But we also have:
sage: T22 = T11.tensor_module(1, 1) sage: T22 is M.tensor_module(1, 1) False
I guess you mean
sage: T22 = T11.tensor_module(1, 1) sage: T22 is M.tensor_module(2, 2) False
What would be the purpose to implement such an identification? Do you have a use case in mind?
comment:5 in reply to: ↑ 4 ; follow-up: ↓ 6 Changed 10 months ago by
Replying to egourgoulhon:
I guess you mean
sage: T22 = T11.tensor_module(1, 1) sage: T22 is M.tensor_module(2, 2) False
Yes, indeed...it was late yesterday..
What would be the purpose to implement such an identification? Do you have a use case in mind?
Alright, it should be fine. I totally missed the tensor module inception going on here. Then, it would be nice to have at least the canonical isomorphism from T11.tensor_module(1, 1)
to M.tensor_module(2, 2)
implemented, in particular make the following work:
sage: t = T11.tensor((1,1)) sage: M.tensor_module(2,2)(t) Traceback (most recent call last): ... StopIteration:
and the other way around.
Nevertheless, what do we do about my first point in comment:1? An instanceof
check for each object coming in?
comment:6 in reply to: ↑ 5 Changed 10 months ago by
Replying to gh-mjungmath:
Replying to egourgoulhon:
Nevertheless, what do we do about my first point in comment:1? An
instanceof
check for each object coming in?
I see no reason why FiniteRankFreeModule
should not have a tensor_type()
method (returning (1, 0)
), as TensorFreeModule
.
comment:7 Changed 10 months ago by
Alright, then let's do this. This method would also be beneficial to introduce the above coercion.
comment:8 Changed 10 months ago by
- Description modified (diff)
comment:9 follow-up: ↓ 10 Changed 10 months ago by
Relevant previous discussions: #30241, https://trac.sagemath.org/ticket/30229#comment:6
comment:10 in reply to: ↑ 9 Changed 10 months ago by
Replying to mkoeppe:
Relevant previous discussions: #30241, https://trac.sagemath.org/ticket/30229#comment:6
Thanks for pointing out this! Especially the comment:2 in the second ticket provides details for the "Yes. This avoids information redundancy, in particular regarding the bases" in comment:2 of the current ticket.
comment:11 Changed 10 months ago by
- Milestone changed from sage-9.3 to sage-9.4
Setting new milestone based on a cursory review of ticket status, priority, and last modification date.
comment:12 Changed 5 months ago by
- Milestone changed from sage-9.4 to sage-9.5
Turns out that this is not as easy as expected.
FiniteRankFreeModule
has no attribute (or method)tensor_type
in contrast toTensorFreeModule
. If it had, one could just add the tensor types and return the corresponding module. However, I see no point whyFiniteRankFreeModule
should have such a method/attribute apart from this single purpose.TensorFreeModule
inherits fromFiniteRankFreeModule
and therefore inherits all methods and attributes. So far so good, but as I understand the code, instances ofTensorFreeModule
are not intended to use most of these methods.FiniteRankFreeModule
is intended to be the "control center" that takes care of things. This leads to somewhat strange (and probably unwanted) behavior: