Update differences.md

[HansOlsson]

Describe change for unbalanced if-equations, and reason for change.
I noticed that the original text had "rank" as short-hand for "number of scalarized equations". I didn't think that was clear, but we might find a better name than "number of scalarized equations"

[henrikt-ma]

Might be easier to read if split in two sentences, with a comma after else.

[HansOlsson]

I see the point but on the other hand they are part of the same concept: a missing else has zero equations, and thus the other branches must have the same number of equations (i.e. zero).

[henrikt-ma]

It would still be true that all branches must have the same number. One could also just add a sentence like:

Absence of an else branch is equivalent to having an empty else branch with "equation rank" 0.

[olivleno]

Not controversial.
Decision:

• poll
  "scalar equation count" 1
  "equation dimension" 1 1 1
  "equation rank" 1
  "equation size" 1 1 1 1 1 1 = 6 votes

Decision:

• Use term "equation size" until we have better proposal.
• Use formulation: "Absence of an else branch is equivalent to having an empty else branch with equation size 0."
• Define "equation size" in Modelica Specification so that "local equation size" is using that definition. --> Hans
• Merge --> Hans

[henrikt-ma]

I noticed that the original text had "rank" as short-hand for "number of scalarized equations". I didn't think that was clear, but we might find a better name than "number of scalarized equations"

Perhaps we could say structural rank, make a definition of this term at a suitable location, and add a link to the definition?

[HansOlsson]

Perhaps we could say structural rank, make a definition of this term at a suitable location, and add a link to the definition?

Maybe.

I agree that having a defined term would be good, but searching for "structural rank" found a different definition that could cause confusion (the maximum rank of a matrix having a certain sparsity pattern).

[henrikt-ma]

Yes, you are right, it was a very bad proposal to call it structural rank. I think equation rank would be a much better term.

One particular reason why I'd like to avoid number of scalarized equations is that it I don't see that it would generalize nicely if we were to get records with algebraic constraints in the future. For example, imagine an Orientation record with 4 scalar members and 1 algebraic constraint, resulting in a space of dimension 3.
This is the number we should get when counting an equation with Orientation on both sides. To me, saying number of scalarized equations strongly suggests that the number would be 4, since this is what results from breaking the equation down into the scalar members of the record. However, on the SO(3) manifold, the 4 equations are not independent (how could they, when there are just 3 coordinates?), and I think some variant of rank sounds like the right term to capture this way of counting.