Use new MultiplyColumnwiseBandMatrixField alias

[charleskawczynski]

The \cdot alias for MultiplyColumnwiseBandMatrixField is a pain-- it collides with LinearAlgebra's \cdot, and it's exported by ClimaCore.MatrixFields.

This PR doesn't fix this issue per-say, but I would like to at least isolate where we are doing this and fix collisions for the ClimaCore examples.

I think we unfortunately can't remove the export from ClimaCore.MatrixFields, as this will technically be a breaking change. Perhaps we can deprecate this change and phase it out.

I spoke with @dennisYatunin, and he believes that we can replace all of these \cdots with *. This PR applies these changes to all of the appropriate places, but instead replacing it with \star. This will allow us to do a replace-all once we are ready to apply this fix.

[Sbozzolo]

This also caused me a lot of troubles and hard-to-debug problems (see #1771).

However, I think that the difference between ⋆ and * is way too small for ⋆ to be an acceptable symbol to use: it's extremely hard to distinguish and will cause a lot of confusion

EDIT: I misread the PR. Using ⋆ is not the intended interface, so the problem won't be as big. That said, if this is internal, I would still lean towards a different symbol.

[charleskawczynski]

This also caused me a lot of troubles and hard-to-debug problems (see #1771).

💯

However, I think that the difference between ⋆ and * is way too small for ⋆ to be an acceptable symbol to use: it's extremely hard to distinguish and will cause a lot of confusion

EDIT: I misread the PR. Using ⋆ is not the intended interface, so the problem won't be as big. That said, if this is internal, I would still lean towards a different symbol.

That's fair. I really don't have a preference on what we use, especially since this is temporary. I went through the effort of replacing all of the places where we need to use a new symbol, while skipping places where we need to use LinearAlgebra's \cdot. I only care that it's uniquely different from \cdot and *, so that we can easily do a replace-all when we're ready to settle on something more final.

How about ◌?

help?> ◌
"◌" can be typed by \dottedcircle<tab>

[Sbozzolo]

This also caused me a lot of troubles and hard-to-debug problems (see #1771).

💯

However, I think that the difference between ⋆ and * is way too small for ⋆ to be an acceptable symbol to use: it's extremely hard to distinguish and will cause a lot of confusion

EDIT: I misread the PR. Using ⋆ is not the intended interface, so the problem won't be as big. That said, if this is internal, I would still lean towards a different symbol.

That's fair. I really don't have a preference on what we use, especially since this is temporary. I went through the effort of replacing all of the places where we need to use a new symbol, while skipping places where we need to use LinearAlgebra's \cdot. I only care that it's uniquely different from \cdot and *, so that we can easily do a replace-all when we're ready to settle on something more final.

How about ◌?

help?> ◌
"◌" can be typed by \dottedcircle<tab>

Sounds good with me!

[dennisYatunin]

◌ is similar to Base's function composition operator, and it isn't generally an appropriate symbol for multiplication. I think it would be much simpler and clearer to use the standard multiplication symbol * instead, so I'll open a PR for that.

[charleskawczynski]

◌ is similar to Base's function composition operator

Which operator is that?

[dennisYatunin]

I was referring to the following operator:

julia> ∘
∘ (generic function with 3 methods)

I really don't see a need to export any new symbol (either ⋆ or ◌), when we could just use the standard *. Adding more symbols that are hard to distinguish is not the direction we want to go in, even if they are temporary. I have updated #2232 to retain the value of ⋅ exported in this PR, while also allowing us to switch ClimaAtmos/ClimaLand/ClimaCoupler to *, so let's use that PR instead.