Dimension system refactoring

[Upabjojr]

Dimensional dependencies are not absolute, they depend on the dimension system (class DimensionSystem).

Even relations like velocity == length / time actually depend on the dimension system you're currently using. If you are in special relativity, maybe you want to use length == time so that the velocity is dimensionless.

In the gaussian units, the unit of charge is the statcoulomb, which does not depend on the Ampere (the current is not a fundamental dimension and the charge can be expressed as a combination of length, time, and mass without current).

This PR makes the relation between base dimensions and derived dimensions part of DimensionSystem, so that they are no longer absolute.

For compatibility reasons, the SI dimension standard is kept as a reference point.

TODO:

• release deprecation warnings

[Upabjojr]

@schymans

[schymans]

This looks very nice. Would you be able to give some usage examples, especially of the new class DimensionalDependency(Basic)? I have been struggling a lot with figuring out the motivations for some past code changes in sympy and realised that simple usage examples of the intended behaviour would have helped. Thanks!

[Upabjojr]

especially of the new class DimensionalDependency(Basic)?

I have merged that class into DimensionSystem in my last commit.

I have been struggling a lot with figuring out the motivations for some past code changes

The DimensionSystem class should contain information about the relations between dimensions, for example that velocity == length / time.

[Upabjojr]

@schymans I know you are using a lot the code in units, I was wondering whether you can check if you find any trouble by using this branch (to make sure it won't break too much).

[schymans]

OK, I'll try and report, but it won't be until next week.

[Upabjojr]

#13336