Opened 15 months ago
Last modified 2 months ago
#30232 new defect
symbolic ring, coercion, restriction: compatible?
Reported by: | gh-mjungmath | Owned by: | |
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Priority: | major | Milestone: | sage-9.5 |
Component: | manifolds | Keywords: | |
Cc: | egourgoulhon, mkoeppe, tscrim | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
At the current stage, we get the following output:
sage: M = Manifold(2, 'M', structure='topological') # the 2-dimensional sphere S^2 sage: U = M.open_subset('U') # complement of the North pole sage: c_xy.<x,y> = U.chart() # stereographic coordinates from the North pole sage: V = M.open_subset('V') # complement of the South pole sage: c_uv.<u,v> = V.chart() # stereographic coordinates from the South pole sage: M.declare_union(U,V) # S^2 is the union of U and V sage: xy_to_uv = c_xy.transition_map(c_uv, (x/(x^2+y^2), y/(x^2+y^2)), ....: intersection_name='W', ....: restrictions1= x^2+y^2!=0, ....: restrictions2= u^2+v^2!=0) sage: uv_to_xy = xy_to_uv.inverse() sage: f = M.scalar_field_algebra()(x+u) sage: f.display() M --> R sage: f._express {}
This output is not consistent with the coercion model, in particular not with the coercion SR -> ScalarFieldAlgebra
. First of all, each element in SR
should give rise to a well-defined element in ScalarFieldAlgebra
. This is not fulfilled in the first example. More precisely:
sage: g = A(x) sage: g.display() M --> R on U: (x, y) |--> x on W: (u, v) |--> u/(u^2 + v^2) sage: h = V.scalar_field_algebra()(x) sage: h.display() V --> R on W: (u, v) |--> u/(u^2 + v^2) on W: (x, y) |--> x
The scalar fields resulting from the coercion SR -> ScalarFieldAlgebra
are not defined on the whole manifold, as they should be for a coercion. In fact, the results are not even well-defined since they are not uniquely determined by the input.
Things get more out of control if no transition map is stated (for example, the transitivity axiom for coercions is violated). However, we probably can assume that this would not reflect the intended usage.
Change History (17)
comment:1 Changed 15 months ago by
- Description modified (diff)
comment:2 Changed 15 months ago by
- Description modified (diff)
comment:3 Changed 15 months ago by
comment:4 Changed 15 months ago by
I can't comment on the details, but if it's not canonical, it should not be a coercion but only a conversion.
comment:5 Changed 15 months ago by
I agree. However, the symbolic ring is stated as the base ring of the commutative algebra of scalar fields, which means that there must be a coercion by definition.
Alternatively, the base ring must be changed. But to what?
comment:6 Changed 15 months ago by
The implementation of the scalar field algebra is currently a bit of an abuse since SR
is not the true base topological field of the manifold, just an approximation for it. However, there is a good case for the convenience of having it. If you decide to not keep the abuse, then I would change the base field of the scalar field algebra to be the base field of the manifold.
comment:7 follow-up: ↓ 8 Changed 14 months ago by
What about this stating as our base ring? It seems that this is exactly what we need.
comment:8 in reply to: ↑ 7 ; follow-up: ↓ 9 Changed 14 months ago by
Replying to gh-mjungmath:
What about this stating as our base ring? It seems that this is exactly what we need.
Well, I am not sure, because in addition to the coordinate symbols, we need other variables, which may represent some parameters in the scalar field. For instance, we may have
sage: M = Manifold(2, 'M') sage: X.<x,y> = M.chart() sage: a = var('a') sage: f = M.scalar_field(a*x)
comment:9 in reply to: ↑ 8 ; follow-up: ↓ 11 Changed 14 months ago by
Replying to egourgoulhon:
Replying to gh-mjungmath:
What about this stating as our base ring? It seems that this is exactly what we need.
Well, I am not sure, because in addition to the coordinate symbols, we need other variables, which may represent some parameters in the scalar field.
To clarify, we have currently:
sage: M = Manifold(2, 'M') sage: X.<x,y> = M.chart() sage: a = var('a', domain='real') sage: f = M.scalar_field(a*x) sage: g = a*f sage: g Scalar field on the 2-dimensional differentiable manifold M sage: g.display() M --> R (x, y) |--> a^2*x
Having SR
be the base field of the scalar field algebra allows the operation a*f
to work directly, but maybe there is a better way...
comment:10 Changed 14 months ago by
- Milestone changed from sage-9.2 to sage-9.3
comment:11 in reply to: ↑ 9 ; follow-up: ↓ 12 Changed 14 months ago by
Replying to egourgoulhon:
Replying to egourgoulhon:
Replying to gh-mjungmath:
What about this stating as our base ring? It seems that this is exactly what we need.
Well, I am not sure, because in addition to the coordinate symbols, we need other variables, which may represent some parameters in the scalar field.
To clarify, we have currently:
sage: M = Manifold(2, 'M') sage: X.<x,y> = M.chart() sage: a = var('a', domain='real') sage: f = M.scalar_field(a*x) sage: g = a*f sage: g Scalar field on the 2-dimensional differentiable manifold M sage: g.display() M --> R (x, y) |--> a^2*xHaving
SR
be the base field of the scalar field algebra allows the operationa*f
to work directly, but maybe there is a better way...
I see your point. What about using the option accepting_variables
and then successively add parameters to the base ring?
comment:12 in reply to: ↑ 11 Changed 13 months ago by
Replying to gh-mjungmath:
Having
SR
be the base field of the scalar field algebra allows the operationa*f
to work directly, but maybe there is a better way...I see your point. What about using the option
accepting_variables
and then successively add parameters to the base ring?
Do you mean calling accepting_variables
internally, i.e. in a way transparent to the user? I don't think we can ask the end user to do something more fancy than `var('a')...
comment:13 Changed 9 months ago by
comment:14 Changed 7 months ago by
- Milestone changed from sage-9.3 to sage-9.4
Sage development has entered the release candidate phase for 9.3. Setting a new milestone for this ticket based on a cursory review of ticket status, priority, and last modification date.
comment:15 Changed 3 months ago by
+1 on encoding dependence on parameters via subrings. #32008 (CallableSymbolicExpressionRing
over subrings of SR
) may be relevant.
comment:16 Changed 3 months ago by
We probably have to subclass that subring, so that it dynamically keeps track of charts defined on the manifold and thus rejects all variables coming from charts.
comment:17 Changed 2 months ago by
- Milestone changed from sage-9.4 to sage-9.5
What about applying
add_expr_by_continuation
to obtain a scalar field on the whole manifold? This would also result in an error message if no transition map has been stated and solve two problems at once.