Implement characteristic() for ring of coordinate functions

[jdemeyer]

CC: @egourgoulhon @tscrim @sagetrac-mbejger

Component: commutative algebra

Author: Frédéric Chapoton

Branch/Commit: 86d0ef3

Reviewer: David Roe

Issue created by migration from https://trac.sagemath.org/ticket/23329

[jdemeyer]

comment:1

The characteristic should be the characteristic of the K from this documentation:

r"""
Symbolic Coordinate Functions

In the context of a topological manifold `M` over a topological field `K`,
a *coordinate function*  is a function from a chart codomain
to `K`. In other words, a coordinate function is a `K`-valued function of
the coordinates associated to some chart.

Now please tell me: how does one retrieve the K from the coordinate ring?

On the other hand, the focus on symbolics might imply that the characteristic is always zero, but it would be good if somebody could confirm this.

[jdemeyer]

comment:2

Thinking more about it, this could be handled in the category of Algebras.

[jdemeyer]

comment:3

Replying to @jdemeyer:

Thinking more about it, this could be handled in the category of Algebras.

Not really, since you cannot in general know the base ring of an element of Algebras.

[fchapoton]

Commit: 86d0ef3

[fchapoton]

New commits:

86d0ef3

trac 23329 characteristic of coordinate chart function ring

[fchapoton]

Branch: u/chapoton/23329

[fchapoton]

comment:5

green bot, please review

[roed314]

comment:6

Looks good to me.

[roed314]

Reviewer: David Roe