MixedFormAlgebra - More Flexible Coercions

[gh-DeRhamSource]

This makes the coercion model of mixed forms more robust against modifications regarding differential forms. For instance: As soon as all differential forms of another mixed form have a coerce map, the mixed form has one too. The same now holds for any algebraic element which is coercible into a single differential form.

At this stage, the method degree is used and special cases are handled separately. But notice that not all coercible objects provide this method (symbolic ring). Or conversely, having this method doesn't mean being coercible into a differential form. Hence this invocation is now entirely avoided.

In particular we have:

sage: M = Manifold(2, 'M')
sage: Omega = M.mixed_form_algebra()
sage: Omega1 = M.diff_form_module(1)
sage: T01 = M.tensor_field_module((0,1))
sage: Omega1.has_coerce_map_from(T01)
True

But at this stage:

sage: Omega.has_coerce_map_from(T01)
False

With this ticket:

sage: Omega.has_coerce_map_from(T01)
True

[gh-DeRhamSource]

This makes the coercion model of mixed forms more robust against modifications regarding differential forms. For instance: As soon as differential forms of every degree have coerce maps, the mixed form has one too.

---

New commits:

​4ba780e

Trac 28916: Flexible coercion of mixed forms

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​3132acc

Trac 28916: Bugs fixed and code cleaned

[gh-DeRhamSource]

I spared the try...except block now completely. I think this is a negligible loss of computation time. Also this is more robust and works everytime.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​6775b86

Trac 28916: try...except removed

[tscrim]

Do you have some examples that demonstrates that this change now covers something that it didn't (correctly) do before? If so, please add them to the documentation, but if not, can you give a more detailed explanation as to why you think this is better?

[gh-DeRhamSource]

Fair enough. I'm not sure this change covers even more at this stage.

The only improvement so far: There might be objects with a method degree which are not coercible into differential forms. Or conversely there are coercible objects without having a degree method (like elements of the symbolic ring). So I avoid invoking degree completely.

Assume in a future version there come more objects not having a degree method but are coercible into differential forms (I admit, I have no idea what else it could be). Nevertheless, these cases have to be handled separately now. But with this changes, all potential coercions are covered.

Was that clearer? What do you think about it? And how could I improve my description?

By the way: Merry christmas retrospectively. :)

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​ee4ad93

Merge branch 'develop' into t/28916/mixedformalgebra___more_flexible_coercions

[tscrim]

Yes, that is more clear, thank you. So can you please add such an example that now coerces that previously did not?