Opened 3 years ago

Closed 3 years ago

# Issue in calculus on manifolds with incomplete set of transition maps

Reported by: Owned by: egourgoulhon major sage-8.9 geometry manifolds, scalar field tscrim Eric Gourgoulhon Travis Scrimshaw N/A 7d13b13 7d13b136fc258009992a042953ffdf3085edecf0

In Sage 8.8, we have

```sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: Y.<u,v> = M.chart()
sage: X_to_Y = X.transition_map(Y, [x+y, x-y])
sage: f = M.scalar_field({X: x*y})
sage: g = M.scalar_field({Y: u*v})
sage: f + g
...
KeyError: (Chart (M, (u, v)), Chart (M, (x, y)))
```

If one initializes the inverse transition map, things are OK:

```sage: X_to_Y.inverse()
Change of coordinates from Chart (M, (u, v)) to Chart (M, (x, y))
sage: f + g
Scalar field on the 2-dimensional differentiable manifold M
sage: _.display()
M --> R
(x, y) |--> x^2 + x*y - y^2
(u, v) |--> 1/4*u^2 + u*v - 1/4*v^2
```

But even without knowing the inverse transition map, Sage should be capable to compute the value of `f + g`, with the result expressed in the chart `X` only.

### comment:1 Changed 3 years ago by egourgoulhon

• Authors set to Eric Gourgoulhon
• Branch set to public/manifolds/incomplete_transition_map-28072
• Commit set to 7d13b136fc258009992a042953ffdf3085edecf0
• Description modified (diff)
• Status changed from new to needs_review

New commits:

 ​7d13b13 `Fix issue with incomplete set of transition maps (Trac #28072)`

### comment:2 Changed 3 years ago by tscrim

• Reviewers set to Travis Scrimshaw
• Status changed from needs_review to positive_review

LGTM.

### comment:3 Changed 3 years ago by egourgoulhon

Thanks for the review!

### comment:4 Changed 3 years ago by vbraun

• Branch changed from public/manifolds/incomplete_transition_map-28072 to 7d13b136fc258009992a042953ffdf3085edecf0
• Resolution set to fixed
• Status changed from positive_review to closed
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