Chart-wise assumptions

[mkoeppe]

(from #31901 comment:19)

The assumptions should not be global but chart-wise.

There is already a context manager assuming. We could create it at initialization and invoke it using with whenever computations are done with this chart.

We go through a new method assuming of CalculusMethod that dispatches in the same way as the simplify method does.

CC: @egourgoulhon @mjungmath

Component: manifolds

Issue created by migration from https://trac.sagemath.org/ticket/32120

[mjungmath]

comment:4

Another way could be to write a own class for the variables of a chart instead of seeing them as pure symbolic expressions. That could also solve the problem described in #30232.

[mkoeppe]

comment:5

I don't think that would help - assumptions are really per chart, not per variable; and in the end, they do need to be communicated to the symbolic engine.

[mjungmath]

comment:6

Replying to @mkoeppe:

not per variable; and in the end, they do need to be communicated to the symbolic engine.

That is indeed true.

[mkoeppe]

comment:7

Related to the discussion in #30232, perhaps it makes sense to introduce rings of expressions under symbolic assumptions. Simplifying an expression using an additional assumption would then be a coercion!

[mkoeppe]

comment:8

(This is now #32276.)